id	sid	tid	token	lemma	pos
iajs-1009	1	1	ibn	ibn	PROPN
iajs-1009	1	2	alhaitham	alhaitham	NOUN
iajs-1009	1	3	j.	j.	PROPN
iajs-1009	2	1	fo	fo	ADP
iajs-1009	2	2	r	r	NOUN
iajs-1009	2	3	pure	pure	ADJ
iajs-1009	2	4	&	&	CCONJ
iajs-1009	2	5	appl	appl	PROPN
iajs-1009	2	6	.	.	PUNCT
iajs-1009	3	1	sc	sc	PROPN
iajs-1009	3	2	i.	i.	PROPN
iajs-1009	3	3	vol.23	vol.23	PROPN
iajs-1009	3	4	(	(	PUNCT
iajs-1009	3	5	1	1	NUM
iajs-1009	3	6	)	)	PUNCT
iajs-1009	3	7	2010	2010	NUM
iajs-1009	3	8	the	the	DET
iajs-1009	3	9	maximum	maximum	ADJ
iajs-1009	3	10	complete	complete	ADJ
iajs-1009	3	11	(	(	PUNCT
iajs-1009	3	12	k	k	NOUN
iajs-1009	3	13	,	,	PUNCT
iajs-1009	3	14	n)-arcs	n)-arcs	X
iajs-1009	3	15	in	in	ADP
iajs-1009	3	16	the	the	DET
iajs-1009	3	17	projective	projective	ADJ
iajs-1009	3	18	plane	plane	NOUN
iajs-1009	3	19	pg(2,4	pg(2,4	NOUN
iajs-1009	3	20	)	)	PUNCT
iajs-1009	3	21	by	by	ADP
iajs-1009	3	22	geometric	geometric	ADJ
iajs-1009	3	23	method	method	NOUN
iajs-1009	3	24	s.	s.	PROPN
iajs-1009	3	25	j.	j.	PROPN
iajs-1009	3	26	kadhum	kadhum	PROPN
iajs-1009	3	27	department	department	PROPN
iajs-1009	3	28	of	of	ADP
iajs-1009	3	29	mathematics	mathematics	PROPN
iajs-1009	3	30	,	,	PUNCT
iajs-1009	3	31	college	college	NOUN
iajs-1009	3	32	of	of	ADP
iajs-1009	3	33	education	education	NOUN
iajs-1009	3	34	,	,	PUNCT
iajs-1009	3	35	ibn	ibn	PROPN
iajs-1009	3	36	al	al	PROPN
iajs-1009	3	37	-	-	PUNCT
iajs-1009	3	38	haitham	haitham	PROPN
iajs-1009	3	39	,	,	PUNCT
iajs-1009	3	40	university	university	PROPN
iajs-1009	3	41	of	of	ADP
iajs-1009	3	42	baghdad	baghdad	PROPN
iajs-1009	3	43	abstract	abstract	PROPN
iajs-1009	3	44	a	a	DET
iajs-1009	3	45	(	(	PUNCT
iajs-1009	3	46	k	k	NOUN
iajs-1009	3	47	,	,	PUNCT
iajs-1009	3	48	n)-arc	n)-arc	X
iajs-1009	3	49	a	a	PRON
iajs-1009	3	50	in	in	ADP
iajs-1009	3	51	a	a	DET
iajs-1009	3	52	finite	finite	ADJ
iajs-1009	3	53	projective	projective	ADJ
iajs-1009	3	54	plane	plane	NOUN
iajs-1009	3	55	pg(2,q	pg(2,q	VERB
iajs-1009	3	56	)	)	PUNCT
iajs-1009	3	57	over	over	ADP
iajs-1009	3	58	galois	galois	PROPN
iajs-1009	3	59	field	field	NOUN
iajs-1009	3	60	gf(q	gf(q	NOUN
iajs-1009	3	61	)	)	PUNCT
iajs-1009	3	62	,	,	PUNCT
iajs-1009	3	63	q	q	NOUN
iajs-1009	3	64	=	=	VERB
iajs-1009	3	65	pⁿ	pⁿ	NOUN
iajs-1009	3	66	for	for	ADP
iajs-1009	3	67	same	same	ADJ
iajs-1009	3	68	prime	prime	ADJ
iajs-1009	3	69	number	number	NOUN
iajs-1009	3	70	p	p	NOUN
iajs-1009	3	71	and	and	CCONJ
iajs-1009	3	72	some	some	DET
iajs-1009	3	73	integer	integer	NOUN
iajs-1009	3	74	n≥2	n≥2	PROPN
iajs-1009	3	75	,	,	PUNCT
iajs-1009	3	76	is	be	AUX
iajs-1009	3	77	a	a	DET
iajs-1009	3	78	set	set	NOUN
iajs-1009	3	79	of	of	ADP
iajs-1009	3	80	k	k	PROPN
iajs-1009	3	81	points	point	NOUN
iajs-1009	3	82	,	,	PUNCT
iajs-1009	3	83	no	no	PRON
iajs-1009	3	84	n+1	n+1	PROPN
iajs-1009	3	85	of	of	ADP
iajs-1009	3	86	which	which	PRON
iajs-1009	3	87	are	be	AUX
iajs-1009	3	88	collinear	collinear	VERB
iajs-1009	3	89	.	.	PUNCT
iajs-1009	4	1	a	a	PRON
iajs-1009	4	2	(	(	PUNCT
iajs-1009	4	3	k	k	NOUN
iajs-1009	4	4	,	,	PUNCT
iajs-1009	4	5	n)-arc	n)-arc	X
iajs-1009	4	6	is	be	AUX
iajs-1009	4	7	complete	complete	ADJ
iajs-1009	4	8	if	if	SCONJ
iajs-1009	4	9	it	it	PRON
iajs-1009	4	10	is	be	AUX
iajs-1009	4	11	not	not	PART
iajs-1009	4	12	contained	contain	VERB
iajs-1009	4	13	in	in	ADP
iajs-1009	4	14	a(k+1,n)-arc	a(k+1,n)-arc	PRON
iajs-1009	4	15	.	.	PUNCT
iajs-1009	5	1	in	in	ADP
iajs-1009	5	2	this	this	DET
iajs-1009	5	3	paper	paper	NOUN
iajs-1009	5	4	,	,	PUNCT
iajs-1009	5	5	the	the	DET
iajs-1009	5	6	maximum	maximum	ADJ
iajs-1009	5	7	complete	complete	ADJ
iajs-1009	5	8	(	(	PUNCT
iajs-1009	5	9	k	k	NOUN
iajs-1009	5	10	,	,	PUNCT
iajs-1009	5	11	n)-arcs	n)-arcs	X
iajs-1009	5	12	,	,	PUNCT
iajs-1009	5	13	n=2,3	n=2,3	NOUN
iajs-1009	5	14	in	in	ADP
iajs-1009	5	15	pg(2,4	pg(2,4	NOUN
iajs-1009	5	16	)	)	PUNCT
iajs-1009	5	17	can	can	AUX
iajs-1009	5	18	be	be	AUX
iajs-1009	5	19	constructed	construct	VERB
iajs-1009	5	20	from	from	ADP
iajs-1009	5	21	the	the	DET
iajs-1009	5	22	equation	equation	NOUN
iajs-1009	5	23	of	of	ADP
iajs-1009	5	24	the	the	DET
iajs-1009	5	25	conic	conic	NOUN
iajs-1009	5	26	.	.	PUNCT
iajs-1009	6	1	1	1	X
iajs-1009	6	2	.	.	X
iajs-1009	6	3	introduction	introduction	NOUN
iajs-1009	7	1	[	[	X
iajs-1009	7	2	1	1	NUM
iajs-1009	7	3	]	]	PUNCT
iajs-1009	7	4	,	,	PUNCT
iajs-1009	7	5	found	find	VERB
iajs-1009	7	6	the	the	DET
iajs-1009	7	7	complete	complete	ADJ
iajs-1009	7	8	(	(	PUNCT
iajs-1009	7	9	k,2)-arcs	k,2)-arcs	X
iajs-1009	7	10	in	in	ADP
iajs-1009	7	11	the	the	DET
iajs-1009	7	12	projective	projective	ADJ
iajs-1009	7	13	planes	plane	NOUN
iajs-1009	7	14	over	over	ADP
iajs-1009	7	15	galois	galois	PROPN
iajs-1009	7	16	field	field	NOUN
iajs-1009	7	17	gf(pⁿ	gf(pⁿ	PROPN
iajs-1009	7	18	)	)	PUNCT
iajs-1009	7	19	for	for	ADP
iajs-1009	7	20	some	some	DET
iajs-1009	7	21	prime	prime	ADJ
iajs-1009	7	22	number	number	NOUN
iajs-1009	7	23	p	p	NOUN
iajs-1009	7	24	and	and	CCONJ
iajs-1009	7	25	some	some	DET
iajs-1009	7	26	integer	integer	NOUN
iajs-1009	7	27	n.	n.	NOUN
iajs-1009	8	1	[	[	X
iajs-1009	8	2	2	2	X
iajs-1009	8	3	]	]	PUNCT
iajs-1009	8	4	found	find	VERB
iajs-1009	8	5	an	an	DET
iajs-1009	8	6	algebraic	algebraic	ADJ
iajs-1009	8	7	method	method	NOUN
iajs-1009	8	8	for	for	ADP
iajs-1009	8	9	construction	construction	NOUN
iajs-1009	8	10	of	of	ADP
iajs-1009	8	11	(	(	PUNCT
iajs-1009	8	12	k,4)-arcs	k,4)-arcs	PROPN
iajs-1009	8	13	in	in	ADP
iajs-1009	8	14	the	the	DET
iajs-1009	8	15	projective	projective	ADJ
iajs-1009	8	16	plane	plane	NOUN
iajs-1009	8	17	pg(2,4	pg(2,4	NOUN
iajs-1009	8	18	)	)	PUNCT
iajs-1009	8	19	.	.	PUNCT
iajs-1009	9	1	in	in	ADP
iajs-1009	9	2	this	this	DET
iajs-1009	9	3	paper	paper	NOUN
iajs-1009	9	4	,	,	PUNCT
iajs-1009	9	5	the	the	DET
iajs-1009	9	6	maximum	maximum	ADJ
iajs-1009	9	7	complete	complete	ADJ
iajs-1009	9	8	(	(	PUNCT
iajs-1009	9	9	k	k	NOUN
iajs-1009	9	10	,	,	PUNCT
iajs-1009	9	11	n)-arcs	n)-arcs	X
iajs-1009	9	12	in	in	ADP
iajs-1009	9	13	pg(2,4	pg(2,4	NOUN
iajs-1009	9	14	)	)	PUNCT
iajs-1009	9	15	,	,	PUNCT
iajs-1009	9	16	n=2,3	n=2,3	PROPN
iajs-1009	9	17	are	be	AUX
iajs-1009	9	18	obtained	obtain	VERB
iajs-1009	9	19	from	from	ADP
iajs-1009	9	20	the	the	DET
iajs-1009	9	21	equation	equation	NOUN
iajs-1009	9	22	of	of	ADP
iajs-1009	9	23	the	the	DET
iajs-1009	9	24	conic	conic	NOUN
iajs-1009	9	25	by	by	ADP
iajs-1009	9	26	geometric	geometric	ADJ
iajs-1009	9	27	method	method	NOUN
iajs-1009	9	28	.	.	PUNCT
iajs-1009	10	1	a	a	DET
iajs-1009	10	2	projective	projective	ADJ
iajs-1009	10	3	plane	plane	NOUN
iajs-1009	10	4	pg(2,q	pg(2,q	VERB
iajs-1009	10	5	)	)	PUNCT
iajs-1009	10	6	over	over	ADP
iajs-1009	10	7	gf(q	gf(q	NOUN
iajs-1009	10	8	)	)	PUNCT
iajs-1009	10	9	consists	consist	VERB
iajs-1009	10	10	of	of	ADP
iajs-1009	10	11	1+q+q	1+q+q	NUM
iajs-1009	10	12	2	2	NUM
iajs-1009	10	13	points	point	NOUN
iajs-1009	10	14	and	and	CCONJ
iajs-1009	10	15	1+q+q2	1+q+q2	NUM
iajs-1009	10	16	of	of	ADP
iajs-1009	10	17	lines	line	NOUN
iajs-1009	10	18	,	,	PUNCT
iajs-1009	10	19	every	every	DET
iajs-1009	10	20	line	line	NOUN
iajs-1009	10	21	contains	contain	VERB
iajs-1009	10	22	1+q	1+q	NUM
iajs-1009	10	23	points	point	NOUN
iajs-1009	10	24	end	end	NOUN
iajs-1009	10	25	every	every	DET
iajs-1009	10	26	point	point	NOUN
iajs-1009	10	27	is	be	AUX
iajs-1009	10	28	on	on	ADP
iajs-1009	10	29	1+q	1+q	NUM
iajs-1009	10	30	lines	line	NOUN
iajs-1009	10	31	.	.	PUNCT
iajs-1009	11	1	any	any	DET
iajs-1009	11	2	point	point	NOUN
iajs-1009	11	3	of	of	ADP
iajs-1009	11	4	the	the	DET
iajs-1009	11	5	plane	plane	NOUN
iajs-1009	11	6	has	have	VERB
iajs-1009	11	7	the	the	DET
iajs-1009	11	8	form	form	NOUN
iajs-1009	11	9	of	of	ADP
iajs-1009	11	10	triple	triple	ADJ
iajs-1009	11	11	(	(	PUNCT
iajs-1009	11	12	x0,x1,x2	x0,x1,x2	PROPN
iajs-1009	11	13	)	)	PUNCT
iajs-1009	11	14	,	,	PUNCT
iajs-1009	11	15	where	where	SCONJ
iajs-1009	11	16	x0,x1,x2	x0,x1,x2	PROPN
iajs-1009	11	17	are	be	AUX
iajs-1009	11	18	elements	element	NOUN
iajs-1009	11	19	of	of	ADP
iajs-1009	11	20	gf(q	gf(q	NOUN
iajs-1009	11	21	)	)	PUNCT
iajs-1009	11	22	with	with	ADP
iajs-1009	11	23	the	the	DET
iajs-1009	11	24	exception	exception	NOUN
iajs-1009	11	25	of	of	ADP
iajs-1009	11	26	a	a	DET
iajs-1009	11	27	triple	triple	NOUN
iajs-1009	11	28	consisting	consist	VERB
iajs-1009	11	29	of	of	ADP
iajs-1009	11	30	three	three	NUM
iajs-1009	11	31	zero	zero	NUM
iajs-1009	11	32	elements	element	NOUN
iajs-1009	11	33	,	,	PUNCT
iajs-1009	11	34	two	two	NUM
iajs-1009	11	35	triples	triple	NOUN
iajs-1009	11	36	represent	represent	VERB
iajs-1009	11	37	the	the	DET
iajs-1009	11	38	same	same	ADJ
iajs-1009	11	39	point	point	NOUN
iajs-1009	11	40	if	if	SCONJ
iajs-1009	11	41	there	there	PRON
iajs-1009	11	42	exists	exist	VERB
iajs-1009	11	43	λ	λ	PROPN
iajs-1009	11	44	in	in	ADP
iajs-1009	11	45	gf(q)\	gf(q)\	NOUN
iajs-1009	11	46	{	{	PUNCT
iajs-1009	11	47	0	0	NUM
iajs-1009	11	48	}	}	PUNCT
iajs-1009	11	49	,	,	PUNCT
iajs-1009	11	50	s.t	s.t	PROPN
iajs-1009	11	51	.	.	PUNCT
iajs-1009	12	1	(	(	PUNCT
iajs-1009	12	2	y0,y1,y2	y0,y1,y2	INTJ
iajs-1009	12	3	)	)	PUNCT
iajs-1009	13	1	=	=	PUNCT
iajs-1009	13	2	λ	λ	PROPN
iajs-1009	13	3	(	(	PUNCT
iajs-1009	13	4	x0,x1,x2	x0,x1,x2	PROPN
iajs-1009	13	5	)	)	PUNCT
iajs-1009	13	6	.	.	PUNCT
iajs-1009	14	1	similarly	similarly	ADV
iajs-1009	14	2	,	,	PUNCT
iajs-1009	14	3	any	any	DET
iajs-1009	14	4	line	line	NOUN
iajs-1009	14	5	of	of	ADP
iajs-1009	14	6	the	the	DET
iajs-1009	14	7	plane	plane	NOUN
iajs-1009	14	8	has	have	VERB
iajs-1009	14	9	the	the	DET
iajs-1009	14	10	from	from	ADP
iajs-1009	14	11	of	of	ADP
iajs-1009	14	12	a	a	DET
iajs-1009	14	13	triple	triple	ADJ
iajs-1009	14	14	[	[	PUNCT
iajs-1009	14	15	x0,x1,x2	x0,x1,x2	X
iajs-1009	14	16	]	]	PUNCT
iajs-1009	14	17	,	,	PUNCT
iajs-1009	14	18	x0,x1,x2	x0,x1,x2	PROPN
iajs-1009	14	19	are	be	AUX
iajs-1009	14	20	in	in	ADP
iajs-1009	14	21	gf(q	gf(q	NOUN
iajs-1009	14	22	)	)	PUNCT
iajs-1009	14	23	with	with	ADP
iajs-1009	14	24	the	the	DET
iajs-1009	14	25	exception	exception	NOUN
iajs-1009	14	26	of	of	ADP
iajs-1009	14	27	a	a	DET
iajs-1009	14	28	triple	triple	ADJ
iajs-1009	14	29	consisting	consist	VERB
iajs-1009	14	30	three	three	NUM
iajs-1009	14	31	zero	zero	NUM
iajs-1009	14	32	elements	element	NOUN
iajs-1009	14	33	.	.	PUNCT
iajs-1009	15	1	two	two	NUM
iajs-1009	15	2	lines	line	NOUN
iajs-1009	15	3	[	[	X
iajs-1009	15	4	x0,x1,x2	x0,x1,x2	X
iajs-1009	15	5	]	]	PUNCT
iajs-1009	15	6	and	and	CCONJ
iajs-1009	15	7	[	[	X
iajs-1009	15	8	y0,y1,y2	y0,y1,y2	X
iajs-1009	15	9	]	]	PUNCT
iajs-1009	15	10	represent	represent	VERB
iajs-1009	15	11	the	the	DET
iajs-1009	15	12	same	same	ADJ
iajs-1009	15	13	line	line	NOUN
iajs-1009	15	14	if	if	SCONJ
iajs-1009	15	15	there	there	PRON
iajs-1009	15	16	exists	exist	VERB
iajs-1009	15	17	λ	λ	PROPN
iajs-1009	15	18	in	in	ADP
iajs-1009	15	19	gp(q)\{0	gp(q)\{0	PROPN
iajs-1009	15	20	}	}	PUNCT
iajs-1009	15	21	s.t	s.t	PROPN
iajs-1009	15	22	.	.	PUNCT
iajs-1009	16	1	[	[	X
iajs-1009	16	2	x0,x1,x2	x0,x1,x2	X
iajs-1009	16	3	]	]	X
iajs-1009	17	1	=	=	SYM
iajs-1009	17	2	λ[y	λ[y	X
iajs-1009	17	3	0,y1,y2	0,y1,y2	NUM
iajs-1009	17	4	]	]	PUNCT
iajs-1009	17	5	.	.	PUNCT
iajs-1009	18	1	the	the	DET
iajs-1009	18	2	point	point	NOUN
iajs-1009	18	3	(	(	PUNCT
iajs-1009	18	4	x0,x1,x2	x0,x1,x2	PROPN
iajs-1009	18	5	)	)	PUNCT
iajs-1009	18	6	is	be	AUX
iajs-1009	18	7	incident	incident	NOUN
iajs-1009	18	8	with	with	ADP
iajs-1009	18	9	line	line	NOUN
iajs-1009	19	1	[	[	X
iajs-1009	19	2	y0,y1,y2	y0,y1,y2	X
iajs-1009	19	3	]	]	X
iajs-1009	19	4	if	if	SCONJ
iajs-1009	19	5	x0y0+x1y1+x2y2	x0y0+x1y1+x2y2	PUNCT
iajs-1009	19	6	=	=	SYM
iajs-1009	19	7	0	0	X
iajs-1009	19	8	.	.	PUNCT
iajs-1009	20	1	ibn	ibn	PROPN
iajs-1009	20	2	alhaitham	alhaitham	PROPN
iajs-1009	21	1	j.	j.	PROPN
iajs-1009	22	1	fo	fo	ADP
iajs-1009	22	2	r	r	NOUN
iajs-1009	22	3	pure	pure	ADJ
iajs-1009	22	4	&	&	CCONJ
iajs-1009	22	5	appl	appl	PROPN
iajs-1009	22	6	.	.	PUNCT
iajs-1009	23	1	sc	sc	PROPN
iajs-1009	23	2	i.	i.	PROPN
iajs-1009	23	3	vol.23	vol.23	PROPN
iajs-1009	23	4	(	(	PUNCT
iajs-1009	23	5	1	1	NUM
iajs-1009	23	6	)	)	PUNCT
iajs-1009	23	7	2010	2010	NUM
iajs-1009	23	8	2	2	NUM
iajs-1009	23	9	.	.	PUNCT
iajs-1009	23	10	basic	basic	ADJ
iajs-1009	23	11	definitions	definition	NOUN
iajs-1009	23	12	and	and	CCONJ
iajs-1009	23	13	theorems	theorem	VERB
iajs-1009	23	14	2.1	2.1	NUM
iajs-1009	23	15	definition	definition	NOUN
iajs-1009	23	16	[	[	X
iajs-1009	23	17	3	3	X
iajs-1009	23	18	]	]	X
iajs-1009	23	19	a	a	DET
iajs-1009	23	20	(	(	PUNCT
iajs-1009	23	21	k	k	NOUN
iajs-1009	23	22	,	,	PUNCT
iajs-1009	23	23	n)-arc	n)-arc	X
iajs-1009	23	24	in	in	ADP
iajs-1009	23	25	a	a	DET
iajs-1009	23	26	finite	finite	ADJ
iajs-1009	23	27	projective	projective	ADJ
iajs-1009	23	28	plane	plane	NOUN
iajs-1009	23	29	as	as	ADP
iajs-1009	23	30	a	a	DET
iajs-1009	23	31	set	set	NOUN
iajs-1009	23	32	of	of	ADP
iajs-1009	23	33	k	k	PROPN
iajs-1009	23	34	points	point	NOUN
iajs-1009	23	35	no	no	PRON
iajs-1009	23	36	n+1	n+1	PROPN
iajs-1009	23	37	of	of	ADP
iajs-1009	23	38	which	which	PRON
iajs-1009	23	39	are	be	AUX
iajs-1009	23	40	collinear	collinear	VERB
iajs-1009	23	41	.	.	PUNCT
iajs-1009	24	1	2.2	2.2	NUM
iajs-1009	24	2	definition	definition	NOUN
iajs-1009	24	3	[	[	X
iajs-1009	24	4	4	4	X
iajs-1009	24	5	]	]	X
iajs-1009	24	6	a	a	DET
iajs-1009	24	7	(	(	PUNCT
iajs-1009	24	8	k	k	NOUN
iajs-1009	24	9	,	,	PUNCT
iajs-1009	24	10	n)-arc	n)-arc	X
iajs-1009	24	11	is	be	AUX
iajs-1009	24	12	a	a	DET
iajs-1009	24	13	set	set	NOUN
iajs-1009	24	14	of	of	ADP
iajs-1009	24	15	k	k	PROPN
iajs-1009	24	16	point	point	NOUN
iajs-1009	24	17	,	,	PUNCT
iajs-1009	24	18	no	no	DET
iajs-1009	24	19	three	three	NUM
iajs-1009	24	20	of	of	ADP
iajs-1009	24	21	them	they	PRON
iajs-1009	24	22	are	be	AUX
iajs-1009	24	23	collinear	collinear	ADJ
iajs-1009	24	24	,	,	PUNCT
iajs-1009	24	25	we	we	PRON
iajs-1009	24	26	denote	denote	VERB
iajs-1009	24	27	this	this	PRON
iajs-1009	24	28	by	by	ADP
iajs-1009	24	29	k	k	PROPN
iajs-1009	24	30	-	-	NOUN
iajs-1009	24	31	arc	arc	NOUN
iajs-1009	24	32	.	.	PUNCT
iajs-1009	25	1	2.3	2.3	NUM
iajs-1009	25	2	definition	definition	NOUN
iajs-1009	25	3	[	[	X
iajs-1009	25	4	5	5	NUM
iajs-1009	25	5	]	]	X
iajs-1009	25	6	a	a	PRON
iajs-1009	25	7	(	(	PUNCT
iajs-1009	25	8	k	k	NOUN
iajs-1009	25	9	,	,	PUNCT
iajs-1009	25	10	n)-arc	n)-arc	X
iajs-1009	25	11	is	be	AUX
iajs-1009	25	12	said	say	VERB
iajs-1009	25	13	to	to	PART
iajs-1009	25	14	be	be	AUX
iajs-1009	25	15	complete	complete	ADJ
iajs-1009	25	16	if	if	SCONJ
iajs-1009	25	17	it	it	PRON
iajs-1009	25	18	is	be	AUX
iajs-1009	25	19	not	not	PART
iajs-1009	25	20	contained	contain	VERB
iajs-1009	25	21	in	in	ADP
iajs-1009	25	22	a	a	DET
iajs-1009	25	23	(	(	PUNCT
iajs-1009	25	24	k+1,n)-arc	k+1,n)-arc	NOUN
iajs-1009	25	25	.	.	PUNCT
iajs-1009	26	1	we	we	PRON
iajs-1009	26	2	denote	denote	VERB
iajs-1009	26	3	by	by	ADP
iajs-1009	26	4	m(2,p	m(2,p	PROPN
iajs-1009	26	5	)	)	PUNCT
iajs-1009	26	6	the	the	DET
iajs-1009	26	7	maximum	maximum	ADJ
iajs-1009	26	8	number	number	NOUN
iajs-1009	26	9	of	of	ADP
iajs-1009	26	10	points	point	NOUN
iajs-1009	26	11	in	in	ADP
iajs-1009	26	12	pg(2,p	pg(2,p	NOUN
iajs-1009	26	13	)	)	PUNCT
iajs-1009	26	14	that	that	SCONJ
iajs-1009	26	15	a	a	PRON
iajs-1009	26	16	(	(	PUNCT
iajs-1009	26	17	k	k	NOUN
iajs-1009	26	18	,	,	PUNCT
iajs-1009	26	19	n)-arc	n)-arc	PRON
iajs-1009	26	20	can	can	AUX
iajs-1009	26	21	have	have	VERB
iajs-1009	26	22	.	.	PUNCT
iajs-1009	27	1	2.4	2.4	NUM
iajs-1009	27	2	theorem	theorem	NOUN
iajs-1009	27	3	[	[	X
iajs-1009	27	4	6	6	NUM
iajs-1009	27	5	]	]	X
iajs-1009	27	6	a	a	DET
iajs-1009	27	7	(	(	PUNCT
iajs-1009	27	8	k	k	NOUN
iajs-1009	27	9	,	,	PUNCT
iajs-1009	27	10	n)-arc	n)-arc	ADV
iajs-1009	27	11	in	in	ADP
iajs-1009	27	12	pg(2,p	pg(2,p	NOUN
iajs-1009	27	13	)	)	PUNCT
iajs-1009	27	14	is	be	AUX
iajs-1009	27	15	complete	complete	ADJ
iajs-1009	27	16	if	if	SCONJ
iajs-1009	27	17	and	and	CCONJ
iajs-1009	27	18	only	only	ADV
iajs-1009	27	19	if	if	SCONJ
iajs-1009	27	20	c0	c0	PROPN
iajs-1009	27	21	=	=	NOUN
iajs-1009	27	22	0	0	X
iajs-1009	27	23	.	.	X
iajs-1009	28	1	proof	proof	NOUN
iajs-1009	28	2	:	:	PUNCT
iajs-1009	28	3	(	(	PUNCT
iajs-1009	28	4			NOUN
iajs-1009	28	5	)	)	PUNCT
iajs-1009	28	6	let	let	VERB
iajs-1009	28	7	a	a	DET
iajs-1009	28	8	(	(	PUNCT
iajs-1009	28	9	k	k	NOUN
iajs-1009	28	10	,	,	PUNCT
iajs-1009	28	11	n)-arc	n)-arc	PRON
iajs-1009	28	12	k	k	X
iajs-1009	28	13	be	be	AUX
iajs-1009	28	14	a	a	DET
iajs-1009	28	15	complete	complete	ADJ
iajs-1009	28	16	arc	arc	NOUN
iajs-1009	28	17	in	in	ADP
iajs-1009	28	18	pg(2,p	pg(2,p	NOUN
iajs-1009	28	19	)	)	PUNCT
iajs-1009	28	20	suppose	suppose	VERB
iajs-1009	28	21	that	that	SCONJ
iajs-1009	28	22	c0	c0	PROPN
iajs-1009	28	23	≠	≠	PROPN
iajs-1009	28	24	0	0	NUM
iajs-1009	28	25	,	,	PUNCT
iajs-1009	28	26	then	then	ADV
iajs-1009	28	27	there	there	PRON
iajs-1009	28	28	is	be	VERB
iajs-1009	28	29	at	at	SCONJ
iajs-1009	28	30	lest	lest	SCONJ
iajs-1009	28	31	one	one	NUM
iajs-1009	28	32	point	point	NOUN
iajs-1009	28	33	say	say	VERB
iajs-1009	28	34	n	n	PRON
iajs-1009	28	35	has	have	VERB
iajs-1009	28	36	index	index	NOUN
iajs-1009	28	37	zero	zero	NUM
iajs-1009	28	38	and	and	CCONJ
iajs-1009	28	39	n	n	PROPN
iajs-1009	28	40			PROPN
iajs-1009	28	41	k.	k.	PROPN
iajs-1009	29	1	then	then	ADV
iajs-1009	29	2	k	k	PROPN
iajs-1009	29	3			X
iajs-1009	29	4	{	{	PUNCT
iajs-1009	29	5	n	n	CCONJ
iajs-1009	29	6	}	}	PUNCT
iajs-1009	29	7	is	be	AUX
iajs-1009	29	8	an	an	DET
iajs-1009	29	9	arc	arc	NOUN
iajs-1009	29	10	in	in	ADP
iajs-1009	29	11	pg(2,p	pg(2,p	NOUN
iajs-1009	29	12	)	)	PUNCT
iajs-1009	29	13	.	.	PUNCT
iajs-1009	30	1	hence	hence	ADV
iajs-1009	30	2	k	k	PROPN
iajs-1009	30	3			PROPN
iajs-1009	30	4	k	k	PROPN
iajs-1009	30	5			X
iajs-1009	30	6	{	{	PUNCT
iajs-1009	30	7	n	n	CCONJ
iajs-1009	30	8	}	}	PUNCT
iajs-1009	30	9	,	,	PUNCT
iajs-1009	30	10	which	which	PRON
iajs-1009	30	11	implies	imply	VERB
iajs-1009	30	12	(	(	PUNCT
iajs-1009	30	13	k	k	X
iajs-1009	30	14	,	,	PUNCT
iajs-1009	30	15	n)-arc	n)-arc	X
iajs-1009	30	16	k	k	X
iajs-1009	30	17	is	be	AUX
iajs-1009	30	18	incomplete	incomplete	ADJ
iajs-1009	30	19	(	(	PUNCT
iajs-1009	30	20	contradiction	contradiction	NOUN
iajs-1009	30	21	)	)	PUNCT
iajs-1009	30	22	.	.	PUNCT
iajs-1009	31	1	(	(	PUNCT
iajs-1009	31	2			NOUN
iajs-1009	31	3	)	)	PUNCT
iajs-1009	31	4	suppose	suppose	VERB
iajs-1009	31	5	that	that	SCONJ
iajs-1009	31	6	c0=0	c0=0	PROPN
iajs-1009	31	7	for	for	ADP
iajs-1009	31	8	the	the	DET
iajs-1009	31	9	(	(	PUNCT
iajs-1009	31	10	k	k	NOUN
iajs-1009	31	11	,	,	PUNCT
iajs-1009	31	12	n)-arc	n)-arc	X
iajs-1009	31	13	k	k	NOUN
iajs-1009	31	14	,	,	PUNCT
iajs-1009	31	15	then	then	ADV
iajs-1009	31	16	there	there	PRON
iajs-1009	31	17	are	be	VERB
iajs-1009	31	18	no	no	DET
iajs-1009	31	19	points	point	NOUN
iajs-1009	31	20	of	of	ADP
iajs-1009	31	21	index	index	NOUN
iajs-1009	31	22	zero	zero	NUM
iajs-1009	31	23	,	,	PUNCT
iajs-1009	31	24	then	then	ADV
iajs-1009	31	25	the	the	DET
iajs-1009	31	26	(	(	PUNCT
iajs-1009	31	27	k	k	NOUN
iajs-1009	31	28	,	,	PUNCT
iajs-1009	31	29	n)arc	n)arc	PROPN
iajs-1009	31	30	k	k	PROPN
iajs-1009	31	31	is	be	AUX
iajs-1009	31	32	complete	complete	ADJ
iajs-1009	31	33	.	.	PUNCT
iajs-1009	32	1	2.5	2.5	NUM
iajs-1009	32	2	definition	definition	NOUN
iajs-1009	32	3	[	[	X
iajs-1009	32	4	4	4	X
iajs-1009	32	5	]	]	PUNCT
iajs-1009	32	6	a	a	DET
iajs-1009	32	7	k	k	NOUN
iajs-1009	32	8	-	-	PUNCT
iajs-1009	32	9	arc	arc	NOUN
iajs-1009	32	10	is	be	AUX
iajs-1009	32	11	called	call	VERB
iajs-1009	32	12	an	an	DET
iajs-1009	32	13	oval	oval	NOUN
iajs-1009	32	14	when	when	SCONJ
iajs-1009	32	15	k	k	PROPN
iajs-1009	32	16	=	=	PRON
iajs-1009	32	17	(	(	PUNCT
iajs-1009	32	18	2,p	2,p	PROPN
iajs-1009	32	19	)	)	PUNCT
iajs-1009	32	20	.	.	PUNCT
iajs-1009	33	1	2.6	2.6	NUM
iajs-1009	33	2	definition	definition	NOUN
iajs-1009	33	3	[	[	X
iajs-1009	33	4	7	7	X
iajs-1009	33	5	]	]	X
iajs-1009	33	6	let	let	VERB
iajs-1009	33	7	ℓ	ℓ	NOUN
iajs-1009	33	8	be	be	AUX
iajs-1009	33	9	any	any	DET
iajs-1009	33	10	line	line	NOUN
iajs-1009	33	11	in	in	ADP
iajs-1009	33	12	pg(2,p	pg(2,p	NOUN
iajs-1009	33	13	)	)	PUNCT
iajs-1009	33	14	if	if	SCONJ
iajs-1009	33	15	ℓ	ℓ	NOUN
iajs-1009	33	16	intersects	intersect	VERB
iajs-1009	33	17	a	a	DET
iajs-1009	33	18	k	k	NOUN
iajs-1009	33	19	-	-	NOUN
iajs-1009	33	20	arc	arc	NOUN
iajs-1009	33	21	in	in	ADP
iajs-1009	33	22	i	i	PROPN
iajs-1009	33	23	-	-	PUNCT
iajs-1009	33	24	points	point	NOUN
iajs-1009	33	25	,	,	PUNCT
iajs-1009	33	26	|	|	NOUN
iajs-1009	33	27	ℓ	ℓ	NOUN
iajs-1009	33	28	∩	∩	X
iajs-1009	33	29	k	k	PROPN
iajs-1009	34	1	|	|	NOUN
iajs-1009	34	2	=	=	SYM
iajs-1009	34	3	i	i	PROPN
iajs-1009	34	4	,	,	PUNCT
iajs-1009	34	5	then	then	ADV
iajs-1009	34	6	ℓ	ℓ	PROPN
iajs-1009	34	7	is	be	AUX
iajs-1009	34	8	called	call	VERB
iajs-1009	34	9	an	an	DET
iajs-1009	34	10	i	i	PROPN
iajs-1009	34	11	-	-	PUNCT
iajs-1009	34	12	secant	secant	NOUN
iajs-1009	34	13	of	of	ADP
iajs-1009	34	14	k	k	PROPN
iajs-1009	34	15	,	,	PUNCT
iajs-1009	34	16	then	then	ADV
iajs-1009	34	17	2	2	NUM
iajs-1009	34	18	-	-	PUNCT
iajs-1009	34	19	secont	secont	NOUN
iajs-1009	34	20	of	of	ADP
iajs-1009	34	21	k	k	PROPN
iajs-1009	34	22	is	be	AUX
iajs-1009	34	23	called	call	VERB
iajs-1009	34	24	a	a	DET
iajs-1009	34	25	bisecant	bisecant	NOUN
iajs-1009	34	26	of	of	ADP
iajs-1009	34	27	k	k	PROPN
iajs-1009	34	28	then	then	ADV
iajs-1009	34	29	1	1	NUM
iajs-1009	34	30	-	-	PUNCT
iajs-1009	34	31	secont	secont	NOUN
iajs-1009	34	32	of	of	ADP
iajs-1009	34	33	k	k	PROPN
iajs-1009	34	34	is	be	AUX
iajs-1009	34	35	called	call	VERB
iajs-1009	34	36	a	a	DET
iajs-1009	34	37	unisecant	unisecant	NOUN
iajs-1009	34	38	of	of	ADP
iajs-1009	34	39	k	k	PROPN
iajs-1009	34	40	then	then	ADV
iajs-1009	34	41	0	0	NUM
iajs-1009	34	42	-	-	PUNCT
iajs-1009	34	43	secont	secont	NOUN
iajs-1009	34	44	of	of	ADP
iajs-1009	34	45	k	k	PROPN
iajs-1009	34	46	is	be	AUX
iajs-1009	34	47	called	call	VERB
iajs-1009	34	48	an	an	DET
iajs-1009	34	49	external	external	NOUN
iajs-1009	34	50	of	of	ADP
iajs-1009	34	51	k.	k.	PROPN
iajs-1009	34	52	2.7	2.7	NUM
iajs-1009	34	53	definition	definition	NOUN
iajs-1009	34	54	[	[	X
iajs-1009	34	55	3	3	X
iajs-1009	34	56	]	]	X
iajs-1009	34	57	let	let	VERB
iajs-1009	34	58	n	n	PRON
iajs-1009	34	59	be	be	AUX
iajs-1009	34	60	a	a	DET
iajs-1009	34	61	point	point	NOUN
iajs-1009	34	62	in	in	ADP
iajs-1009	34	63	pg(2,p	pg(2,p	NOUN
iajs-1009	34	64	)	)	PUNCT
iajs-1009	34	65	and	and	CCONJ
iajs-1009	34	66	n	n	PRON
iajs-1009	34	67	is	be	AUX
iajs-1009	34	68	not	not	PART
iajs-1009	34	69	on	on	ADP
iajs-1009	34	70	a	a	DET
iajs-1009	34	71	k	k	NOUN
iajs-1009	34	72	-	-	PUNCT
iajs-1009	34	73	arc	arc	NOUN
iajs-1009	34	74	,	,	PUNCT
iajs-1009	34	75	then	then	ADV
iajs-1009	34	76	we	we	PRON
iajs-1009	34	77	say	say	VERB
iajs-1009	34	78	n	n	PRON
iajs-1009	34	79	is	be	AUX
iajs-1009	34	80	a	a	DET
iajs-1009	34	81	point	point	NOUN
iajs-1009	34	82	of	of	ADP
iajs-1009	34	83	index	index	NOUN
iajs-1009	35	1	i	i	PRON
iajs-1009	35	2	if	if	SCONJ
iajs-1009	35	3	there	there	PRON
iajs-1009	35	4	are	be	VERB
iajs-1009	35	5	exactly	exactly	ADV
iajs-1009	35	6	i	i	NOUN
iajs-1009	35	7	-	-	PUNCT
iajs-1009	35	8	bisecant	bisecant	ADJ
iajs-1009	35	9	through	through	ADP
iajs-1009	35	10	n	n	PROPN
iajs-1009	35	11	.	.	PUNCT
iajs-1009	36	1	2.8	2.8	NUM
iajs-1009	36	2	definition	definition	NOUN
iajs-1009	36	3	[	[	X
iajs-1009	36	4	5	5	NUM
iajs-1009	36	5	]	]	PUNCT
iajs-1009	36	6	the	the	DET
iajs-1009	36	7	set	set	NOUN
iajs-1009	36	8	ci	ci	PROPN
iajs-1009	36	9	consists	consist	VERB
iajs-1009	36	10	of	of	ADP
iajs-1009	36	11	all	all	DET
iajs-1009	36	12	points	point	NOUN
iajs-1009	36	13	of	of	ADP
iajs-1009	36	14	index	index	NOUN
iajs-1009	36	15	i	i	NOUN
iajs-1009	36	16	ci	ci	NOUN
iajs-1009	37	1	=	=	PUNCT
iajs-1009	37	2	|	|	ADV
iajs-1009	37	3	ci	ci	NOUN
iajs-1009	38	1	|	|	NOUN
iajs-1009	38	2	=	=	NOUN
iajs-1009	39	1	#	#	NOUN
iajs-1009	39	2	the	the	DET
iajs-1009	39	3	number	number	NOUN
iajs-1009	39	4	of	of	ADP
iajs-1009	39	5	points	point	NOUN
iajs-1009	39	6	in	in	ADP
iajs-1009	39	7	ci	ci	NOUN
iajs-1009	39	8	and	and	CCONJ
iajs-1009	39	9	#	#	DET
iajs-1009	39	10	the	the	DET
iajs-1009	39	11	number	number	NOUN
iajs-1009	39	12	of	of	ADP
iajs-1009	39	13	index	index	NOUN
iajs-1009	39	14	i.	i.	PROPN
iajs-1009	39	15	2.9	2.9	NUM
iajs-1009	39	16	theorem	theorem	VERB
iajs-1009	39	17	[	[	X
iajs-1009	39	18	5	5	NUM
iajs-1009	39	19	]	]	PUNCT
iajs-1009	39	20	let	let	VERB
iajs-1009	39	21	m	m	PRON
iajs-1009	39	22	be	be	AUX
iajs-1009	39	23	a	a	DET
iajs-1009	39	24	point	point	NOUN
iajs-1009	39	25	of	of	ADP
iajs-1009	39	26	the	the	DET
iajs-1009	39	27	k	k	NOUN
iajs-1009	39	28	-	-	PUNCT
iajs-1009	39	29	arc	arc	NOUN
iajs-1009	39	30	of	of	ADP
iajs-1009	39	31	pg(2,k	pg(2,k	NOUN
iajs-1009	39	32	)	)	PUNCT
iajs-1009	39	33	and	and	CCONJ
iajs-1009	39	34	t(m	t(m	PROPN
iajs-1009	39	35	)	)	PUNCT
iajs-1009	39	36	be	be	AUX
iajs-1009	39	37	the	the	DET
iajs-1009	39	38	number	number	NOUN
iajs-1009	39	39	of	of	ADP
iajs-1009	39	40	the	the	DET
iajs-1009	39	41	unisecants	unisecant	NOUN
iajs-1009	39	42	of	of	ADP
iajs-1009	39	43	k	k	PROPN
iajs-1009	39	44	through	through	ADP
iajs-1009	39	45	m	m	PROPN
iajs-1009	39	46	,	,	PUNCT
iajs-1009	39	47	then	then	ADV
iajs-1009	39	48	t(m	t(m	PROPN
iajs-1009	39	49	)	)	PUNCT
iajs-1009	40	1	=	=	PUNCT
iajs-1009	40	2	p+2	p+2	PROPN
iajs-1009	40	3	-	-	PUNCT
iajs-1009	40	4	k	k	PROPN
iajs-1009	40	5	=	=	PROPN
iajs-1009	40	6	t	t	PROPN
iajs-1009	40	7	.	.	PUNCT
iajs-1009	41	1	ibn	ibn	PROPN
iajs-1009	41	2	alhaitham	alhaitham	PROPN
iajs-1009	42	1	j.	j.	PROPN
iajs-1009	43	1	fo	fo	ADP
iajs-1009	43	2	r	r	NOUN
iajs-1009	43	3	pure	pure	ADJ
iajs-1009	43	4	&	&	CCONJ
iajs-1009	43	5	appl	appl	PROPN
iajs-1009	43	6	.	.	PUNCT
iajs-1009	44	1	sc	sc	PROPN
iajs-1009	44	2	i.	i.	PROPN
iajs-1009	44	3	vol.23	vol.23	PROPN
iajs-1009	44	4	(	(	PUNCT
iajs-1009	44	5	1	1	NUM
iajs-1009	44	6	)	)	PUNCT
iajs-1009	44	7	2010	2010	NUM
iajs-1009	44	8	proof	proof	NOUN
iajs-1009	44	9	:	:	PUNCT
iajs-1009	44	10	the	the	DET
iajs-1009	44	11	number	number	NOUN
iajs-1009	44	12	of	of	ADP
iajs-1009	44	13	lines	line	NOUN
iajs-1009	44	14	in	in	ADP
iajs-1009	44	15	pg(2,p	pg(2,p	NOUN
iajs-1009	44	16	)	)	PUNCT
iajs-1009	44	17	through	through	ADP
iajs-1009	44	18	any	any	DET
iajs-1009	44	19	point	point	NOUN
iajs-1009	44	20	is	be	AUX
iajs-1009	44	21	p+1	p+1	NOUN
iajs-1009	44	22	there	there	PRON
iajs-1009	44	23	are	be	VERB
iajs-1009	44	24	exactly	exactly	ADV
iajs-1009	44	25	p+1	p+1	PRON
iajs-1009	44	26	lines	line	NOUN
iajs-1009	44	27	through	through	ADP
iajs-1009	44	28	m	m	PRON
iajs-1009	44	29	the	the	DET
iajs-1009	44	30	point	point	NOUN
iajs-1009	44	31	m	m	VERB
iajs-1009	44	32	with	with	ADP
iajs-1009	44	33	any	any	DET
iajs-1009	44	34	other	other	ADJ
iajs-1009	44	35	point	point	NOUN
iajs-1009	44	36	of	of	ADP
iajs-1009	44	37	the	the	DET
iajs-1009	44	38	k	k	ADJ
iajs-1009	44	39	-	-	PUNCT
iajs-1009	44	40	arc	arc	NOUN
iajs-1009	44	41	determine	determine	VERB
iajs-1009	44	42	a	a	DET
iajs-1009	44	43	bisecant	bisecant	NOUN
iajs-1009	44	44	of	of	ADP
iajs-1009	44	45	k	k	PROPN
iajs-1009	44	46	since	since	SCONJ
iajs-1009	44	47	there	there	PRON
iajs-1009	44	48	are	be	VERB
iajs-1009	44	49	(	(	PUNCT
iajs-1009	44	50	k-1	k-1	PROPN
iajs-1009	44	51	)	)	PUNCT
iajs-1009	44	52	points	point	NOUN
iajs-1009	44	53	of	of	ADP
iajs-1009	44	54	k	k	PROPN
iajs-1009	44	55	other	other	ADJ
iajs-1009	45	1	then	then	ADV
iajs-1009	45	2	m	m	PROPN
iajs-1009	45	3	,	,	PUNCT
iajs-1009	45	4	then	then	ADV
iajs-1009	45	5	there	there	PRON
iajs-1009	45	6	are	be	VERB
iajs-1009	45	7	exactly	exactly	ADV
iajs-1009	45	8	(	(	PUNCT
iajs-1009	45	9	k-1	k-1	PROPN
iajs-1009	45	10	)	)	PUNCT
iajs-1009	45	11	lines	line	NOUN
iajs-1009	45	12	determined	determine	VERB
iajs-1009	45	13	from	from	ADP
iajs-1009	45	14	m	m	PROPN
iajs-1009	45	15	and	and	CCONJ
iajs-1009	45	16	the	the	DET
iajs-1009	45	17	other	other	ADJ
iajs-1009	45	18	point	point	NOUN
iajs-1009	45	19	of	of	ADP
iajs-1009	45	20	k	k	PROPN
iajs-1009	45	21	which	which	PRON
iajs-1009	45	22	are	be	AUX
iajs-1009	45	23	the	the	DET
iajs-1009	45	24	bisecants	bisecant	NOUN
iajs-1009	45	25	of	of	ADP
iajs-1009	45	26	k	k	PROPN
iajs-1009	45	27	through	through	ADP
iajs-1009	45	28	m	m	PROPN
iajs-1009	45	29	since	since	SCONJ
iajs-1009	45	30	any	any	DET
iajs-1009	45	31	line	line	NOUN
iajs-1009	45	32	through	through	ADP
iajs-1009	45	33	m	m	PROPN
iajs-1009	45	34	is	be	AUX
iajs-1009	45	35	either	either	CCONJ
iajs-1009	45	36	a	a	DET
iajs-1009	45	37	bisecant	bisecant	ADJ
iajs-1009	45	38	or	or	CCONJ
iajs-1009	45	39	a	a	DET
iajs-1009	45	40	unisecant	unisecant	ADJ
iajs-1009	45	41	,	,	PUNCT
iajs-1009	45	42	then	then	ADV
iajs-1009	45	43	the	the	DET
iajs-1009	45	44	number	number	NOUN
iajs-1009	45	45	of	of	ADP
iajs-1009	45	46	unisecants	unisecant	NOUN
iajs-1009	45	47	of	of	ADP
iajs-1009	45	48	k	k	PROPN
iajs-1009	45	49	through	through	ADP
iajs-1009	45	50	m	m	NOUN
iajs-1009	45	51	=	=	ADJ
iajs-1009	45	52	p+1-(k-1	p+1-(k-1	NOUN
iajs-1009	45	53	)	)	PUNCT
iajs-1009	45	54	=	=	PUNCT
iajs-1009	46	1	p+2	p+2	PROPN
iajs-1009	46	2	-	-	PUNCT
iajs-1009	46	3	k	k	PROPN
iajs-1009	46	4	=	=	PROPN
iajs-1009	46	5	t	t	PROPN
iajs-1009	46	6	.	.	PUNCT
iajs-1009	47	1	2.10	2.10	NUM
iajs-1009	47	2	notation	notation	NOUN
iajs-1009	47	3	:	:	PUNCT
iajs-1009	47	4	ti	ti	X
iajs-1009	47	5	=	=	NOUN
iajs-1009	47	6	the	the	DET
iajs-1009	47	7	number	number	NOUN
iajs-1009	47	8	of	of	ADP
iajs-1009	47	9	i	i	PROPN
iajs-1009	47	10	-	-	PUNCT
iajs-1009	47	11	secant	secant	NOUN
iajs-1009	47	12	of	of	ADP
iajs-1009	47	13	a	a	DET
iajs-1009	47	14	k	k	NOUN
iajs-1009	47	15	-	-	PUNCT
iajs-1009	47	16	arc	arc	NOUN
iajs-1009	47	17	,	,	PUNCT
iajs-1009	47	18	t2	t2	NOUN
iajs-1009	47	19	=	=	PUNCT
iajs-1009	47	20	the	the	DET
iajs-1009	47	21	number	number	NOUN
iajs-1009	47	22	of	of	ADP
iajs-1009	47	23	bisecant	bisecant	ADJ
iajs-1009	47	24	lines	line	NOUN
iajs-1009	47	25	of	of	ADP
iajs-1009	47	26	a	a	DET
iajs-1009	47	27	k	k	NOUN
iajs-1009	47	28	-	-	NOUN
iajs-1009	47	29	arc	arc	NOUN
iajs-1009	47	30	.	.	PUNCT
iajs-1009	48	1	t1	t1	NOUN
iajs-1009	48	2	=	=	NOUN
iajs-1009	49	1	the	the	DET
iajs-1009	49	2	number	number	NOUN
iajs-1009	49	3	of	of	ADP
iajs-1009	49	4	unsecant	unsecant	ADJ
iajs-1009	49	5	lines	line	NOUN
iajs-1009	49	6	of	of	ADP
iajs-1009	49	7	a	a	DET
iajs-1009	49	8	k	k	NOUN
iajs-1009	49	9	-	-	NOUN
iajs-1009	49	10	arc	arc	NOUN
iajs-1009	49	11	.	.	PUNCT
iajs-1009	50	1	t0	t0	NOUN
iajs-1009	51	1	=	=	PUNCT
iajs-1009	52	1	the	the	DET
iajs-1009	52	2	number	number	NOUN
iajs-1009	52	3	of	of	ADP
iajs-1009	52	4	external	external	ADJ
iajs-1009	52	5	lines	line	NOUN
iajs-1009	52	6	of	of	ADP
iajs-1009	52	7	a	a	DET
iajs-1009	52	8	k	k	NOUN
iajs-1009	52	9	-	-	NOUN
iajs-1009	52	10	arc	arc	NOUN
iajs-1009	52	11	.	.	PUNCT
iajs-1009	53	1	2.11	2.11	NUM
iajs-1009	53	2	definition	definition	NOUN
iajs-1009	53	3	[	[	X
iajs-1009	53	4	4	4	X
iajs-1009	53	5	]	]	PUNCT
iajs-1009	53	6	let	let	VERB
iajs-1009	53	7	k	k	PRON
iajs-1009	53	8	be	be	AUX
iajs-1009	53	9	a	a	DET
iajs-1009	53	10	k	k	NOUN
iajs-1009	53	11	-	-	PUNCT
iajs-1009	53	12	arc	arc	NOUN
iajs-1009	53	13	which	which	PRON
iajs-1009	53	14	is	be	AUX
iajs-1009	53	15	an	an	DET
iajs-1009	53	16	oval	oval	NOUN
iajs-1009	53	17	an	an	DET
iajs-1009	53	18	external	external	ADJ
iajs-1009	53	19	point	point	NOUN
iajs-1009	53	20	to	to	ADP
iajs-1009	53	21	an	an	DET
iajs-1009	53	22	oval	oval	NOUN
iajs-1009	53	23	,	,	PUNCT
iajs-1009	53	24	is	be	AUX
iajs-1009	53	25	a	a	DET
iajs-1009	53	26	point	point	NOUN
iajs-1009	53	27	of	of	ADP
iajs-1009	53	28	intersection	intersection	NOUN
iajs-1009	53	29	two	two	NUM
iajs-1009	53	30	unisecants	unisecant	NOUN
iajs-1009	53	31	of	of	ADP
iajs-1009	53	32	k.	k.	PROPN
iajs-1009	53	33	2.12	2.12	NUM
iajs-1009	53	34	theorem	theorem	VERB
iajs-1009	53	35	[	[	X
iajs-1009	53	36	5	5	NUM
iajs-1009	53	37	]	]	X
iajs-1009	53	38	m	m	VERB
iajs-1009	53	39	(	(	PUNCT
iajs-1009	53	40	2	2	NUM
iajs-1009	53	41	,	,	PUNCT
iajs-1009	53	42	p	p	NOUN
iajs-1009	53	43	)	)	PUNCT
iajs-1009	53	44	=	=	PUNCT
iajs-1009	54	1			NOUN
iajs-1009	54	2			NOUN
iajs-1009	54	3			ADP
iajs-1009	54	4			ADV
iajs-1009	54	5			VERB
iajs-1009	54	6	even	even	ADV
iajs-1009	54	7	pfor	pfor	ADP
iajs-1009	54	8	2p	2p	NOUN
iajs-1009	54	9	odd	odd	ADJ
iajs-1009	54	10	pfor	pfor	NOUN
iajs-1009	54	11	1p	1p	NUM
iajs-1009	54	12	2.13	2.13	NUM
iajs-1009	54	13	theorem	theorem	NOUN
iajs-1009	54	14	[	[	X
iajs-1009	54	15	5	5	NUM
iajs-1009	54	16	]	]	PUNCT
iajs-1009	54	17	the	the	DET
iajs-1009	54	18	number	number	NOUN
iajs-1009	54	19	of	of	ADP
iajs-1009	54	20	external	external	ADJ
iajs-1009	54	21	points	point	NOUN
iajs-1009	54	22	of	of	ADP
iajs-1009	54	23	an	an	DET
iajs-1009	54	24	oval	oval	NOUN
iajs-1009	54	25	k	k	NOUN
iajs-1009	54	26	-	-	PUNCT
iajs-1009	54	27	arc	arc	NOUN
iajs-1009	54	28	in	in	ADP
iajs-1009	54	29	pg(2,p	pg(2,p	NOUN
iajs-1009	54	30	)	)	PUNCT
iajs-1009	54	31	is	be	AUX
iajs-1009	54	32	2	2	NUM
iajs-1009	54	33	)	)	SYM
iajs-1009	54	34	1	1	NUM
iajs-1009	54	35	(	(	PUNCT
iajs-1009	54	36	pp	pp	PROPN
iajs-1009	54	37	.	.	PUNCT
iajs-1009	55	1	proof	proof	NOUN
iajs-1009	55	2	:	:	PUNCT
iajs-1009	55	3	if	if	SCONJ
iajs-1009	55	4	k	k	PROPN
iajs-1009	55	5	is	be	AUX
iajs-1009	55	6	an	an	DET
iajs-1009	55	7	0val	0val	PROPN
iajs-1009	55	8	,	,	PUNCT
iajs-1009	55	9	then	then	ADV
iajs-1009	55	10	m	m	VERB
iajs-1009	55	11	(	(	PUNCT
iajs-1009	55	12	2	2	NUM
iajs-1009	55	13	,	,	PUNCT
iajs-1009	55	14	p	p	NOUN
iajs-1009	55	15	)	)	PUNCT
iajs-1009	55	16	=	=	PUNCT
iajs-1009	56	1			NOUN
iajs-1009	56	2			NOUN
iajs-1009	56	3			ADP
iajs-1009	56	4			ADV
iajs-1009	56	5			VERB
iajs-1009	56	6	even	even	ADV
iajs-1009	56	7	pfor	pfor	ADP
iajs-1009	56	8	2p	2p	NOUN
iajs-1009	56	9	odd	odd	ADJ
iajs-1009	56	10	pfor	pfor	NOUN
iajs-1009	57	1	1p	1p	NUM
iajs-1009	58	1	p	p	X
iajs-1009	58	2	is	be	AUX
iajs-1009	58	3	odd	odd	ADJ
iajs-1009	58	4			NOUN
iajs-1009	59	1	k	k	X
iajs-1009	60	1	=	=	PUNCT
iajs-1009	60	2	p+1	p+1	PROPN
iajs-1009	60	3	t	t	NOUN
iajs-1009	60	4	=	=	PUNCT
iajs-1009	60	5	p+2	p+2	PROPN
iajs-1009	60	6	-	-	PUNCT
iajs-1009	60	7	k	k	PROPN
iajs-1009	60	8	=	=	PUNCT
iajs-1009	60	9	p+2-(p+1	p+2-(p+1	NOUN
iajs-1009	60	10	)	)	PUNCT
iajs-1009	60	11	=	=	SYM
iajs-1009	60	12	1	1	NUM
iajs-1009	60	13	t1	t1	NOUN
iajs-1009	60	14	=	=	PUNCT
iajs-1009	60	15	kt	kt	PROPN
iajs-1009	60	16	=	=	PUNCT
iajs-1009	60	17	(	(	PUNCT
iajs-1009	60	18	p+1)*1	p+1)*1	NOUN
iajs-1009	60	19	=	=	SYM
iajs-1009	61	1	p+1	p+1	NOUN
iajs-1009	61	2	=	=	NOUN
iajs-1009	61	3	the	the	DET
iajs-1009	61	4	number	number	NOUN
iajs-1009	61	5	of	of	ADP
iajs-1009	61	6	unisecants	unisecant	NOUN
iajs-1009	61	7	of	of	ADP
iajs-1009	61	8	k	k	PROPN
iajs-1009	61	9	in	in	ADP
iajs-1009	61	10	pg(2,p	pg(2,p	PROPN
iajs-1009	61	11	)	)	PUNCT
iajs-1009	61	12	,	,	PUNCT
iajs-1009	61	13	since	since	SCONJ
iajs-1009	61	14	each	each	DET
iajs-1009	61	15	two	two	NUM
iajs-1009	61	16	unisecants	unisecant	NOUN
iajs-1009	61	17	intersect	intersect	ADJ
iajs-1009	61	18	in	in	ADP
iajs-1009	61	19	an	an	DET
iajs-1009	61	20	external	external	ADJ
iajs-1009	61	21	point	point	NOUN
iajs-1009	61	22	,	,	PUNCT
iajs-1009	61	23	then	then	ADV
iajs-1009	61	24	the	the	DET
iajs-1009	61	25	number	number	NOUN
iajs-1009	61	26	of	of	ADP
iajs-1009	61	27	external	external	ADJ
iajs-1009	61	28	points	point	NOUN
iajs-1009	61	29	=	=	SYM
iajs-1009	61	30			NOUN
iajs-1009	61	31			NOUN
iajs-1009	61	32			PROPN
iajs-1009	61	33			PROPN
iajs-1009	61	34			PROPN
iajs-1009	61	35			NOUN
iajs-1009	61	36			VERB
iajs-1009	61	37	2	2	NUM
iajs-1009	61	38	1p	1p	NUM
iajs-1009	61	39	=	=	PUNCT
iajs-1009	61	40	!	!	PUNCT
iajs-1009	62	1	2)!21	2)!21	NUM
iajs-1009	62	2	(	(	PUNCT
iajs-1009	62	3	)	)	PUNCT
iajs-1009	62	4	!	!	PUNCT
iajs-1009	63	1	1	1	NUM
iajs-1009	63	2	(	(	PUNCT
iajs-1009	63	3			PROPN
iajs-1009	63	4			ADV
iajs-1009	64	1	p	p	X
iajs-1009	64	2	p	p	NOUN
iajs-1009	64	3	=	=	NOUN
iajs-1009	64	4	1	1	NUM
iajs-1009	64	5	*	*	NUM
iajs-1009	64	6	2)!1	2)!1	NUM
iajs-1009	64	7	(	(	PUNCT
iajs-1009	64	8	)	)	PUNCT
iajs-1009	64	9	!	!	PUNCT
iajs-1009	65	1	1()1	1()1	NUM
iajs-1009	66	1	(	(	PUNCT
iajs-1009	66	2			PROPN
iajs-1009	66	3			PROPN
iajs-1009	66	4	p	p	NOUN
iajs-1009	66	5	ppp	ppp	NOUN
iajs-1009	66	6	=	=	SYM
iajs-1009	66	7	2	2	NUM
iajs-1009	66	8	)	)	PUNCT
iajs-1009	66	9	1	1	NUM
iajs-1009	66	10	(	(	PUNCT
iajs-1009	66	11	pp	pp	NOUN
iajs-1009	66	12	.	.	PUNCT
iajs-1009	67	1	2.14	2.14	NUM
iajs-1009	67	2	definition	definition	NOUN
iajs-1009	67	3	[	[	X
iajs-1009	67	4	3	3	X
iajs-1009	67	5	]	]	X
iajs-1009	67	6	an	an	DET
iajs-1009	67	7	internal	internal	ADJ
iajs-1009	67	8	point	point	NOUN
iajs-1009	67	9	to	to	ADP
iajs-1009	67	10	an	an	DET
iajs-1009	67	11	oval	oval	NOUN
iajs-1009	67	12	if	if	SCONJ
iajs-1009	67	13	it	it	PRON
iajs-1009	67	14	is	be	AUX
iajs-1009	67	15	not	not	PART
iajs-1009	67	16	any	any	DET
iajs-1009	67	17	unisecant	unisecant	ADJ
iajs-1009	67	18	of	of	ADP
iajs-1009	67	19	the	the	DET
iajs-1009	67	20	oval	oval	NOUN
iajs-1009	67	21	which	which	PRON
iajs-1009	67	22	is	be	AUX
iajs-1009	67	23	not	not	PART
iajs-1009	67	24	on	on	ADP
iajs-1009	67	25	the	the	DET
iajs-1009	67	26	oval	oval	NOUN
iajs-1009	67	27	.	.	PUNCT
iajs-1009	68	1	2.15	2.15	NUM
iajs-1009	68	2	theorem	theorem	NOUN
iajs-1009	68	3	[	[	X
iajs-1009	68	4	5	5	NUM
iajs-1009	68	5	]	]	PUNCT
iajs-1009	68	6	the	the	DET
iajs-1009	68	7	number	number	NOUN
iajs-1009	68	8	of	of	ADP
iajs-1009	68	9	the	the	DET
iajs-1009	68	10	internal	internal	ADJ
iajs-1009	68	11	points	point	NOUN
iajs-1009	68	12	to	to	ADP
iajs-1009	68	13	on	on	ADP
iajs-1009	68	14	oval	oval	NOUN
iajs-1009	68	15	is	be	AUX
iajs-1009	68	16	2	2	NUM
iajs-1009	68	17	)	)	SYM
iajs-1009	68	18	1	1	NUM
iajs-1009	68	19	(	(	PUNCT
iajs-1009	68	20	pp	pp	NOUN
iajs-1009	68	21	.	.	PUNCT
iajs-1009	69	1	proof	proof	NOUN
iajs-1009	69	2	:	:	PUNCT
iajs-1009	69	3	the	the	DET
iajs-1009	69	4	number	number	NOUN
iajs-1009	69	5	of	of	ADP
iajs-1009	69	6	the	the	DET
iajs-1009	69	7	external	external	ADJ
iajs-1009	69	8	points	point	NOUN
iajs-1009	69	9	+	+	CCONJ
iajs-1009	69	10	the	the	DET
iajs-1009	69	11	number	number	NOUN
iajs-1009	69	12	of	of	ADP
iajs-1009	69	13	the	the	DET
iajs-1009	69	14	internal	internal	ADJ
iajs-1009	69	15	points	point	NOUN
iajs-1009	69	16	=	=	SYM
iajs-1009	69	17	p2+p+1k	p2+p+1k	NOUN
iajs-1009	69	18	.	.	PUNCT
iajs-1009	70	1	#	#	NOUN
iajs-1009	70	2	of	of	ADP
iajs-1009	70	3	external	external	ADJ
iajs-1009	70	4	points	point	NOUN
iajs-1009	70	5	=	=	SYM
iajs-1009	70	6	2	2	NUM
iajs-1009	70	7	)	)	PUNCT
iajs-1009	70	8	1	1	NUM
iajs-1009	70	9	(	(	PUNCT
iajs-1009	70	10	pp	pp	PROPN
iajs-1009	70	11	ibn	ibn	PROPN
iajs-1009	70	12	alhaitham	alhaitham	NOUN
iajs-1009	70	13	j.	j.	PROPN
iajs-1009	71	1	fo	fo	ADP
iajs-1009	71	2	r	r	NOUN
iajs-1009	71	3	pure	pure	ADJ
iajs-1009	71	4	&	&	CCONJ
iajs-1009	71	5	appl	appl	PROPN
iajs-1009	71	6	.	.	PUNCT
iajs-1009	72	1	sc	sc	PROPN
iajs-1009	72	2	i.	i.	PROPN
iajs-1009	72	3	vol.23	vol.23	PROPN
iajs-1009	72	4	(	(	PUNCT
iajs-1009	72	5	1	1	NUM
iajs-1009	72	6	)	)	PUNCT
iajs-1009	72	7	2010	2010	NUM
iajs-1009	72	8	#	#	NOUN
iajs-1009	72	9	of	of	ADP
iajs-1009	72	10	the	the	DET
iajs-1009	72	11	internal	internal	ADJ
iajs-1009	72	12	points	point	NOUN
iajs-1009	72	13	=	=	NOUN
iajs-1009	72	14	p2	p2	PROPN
iajs-1009	72	15	+	+	CCONJ
iajs-1009	72	16	p	p	X
iajs-1009	73	1	+	+	NOUN
iajs-1009	73	2	1(p+1	1(p+1	NUM
iajs-1009	73	3	)	)	PUNCT
iajs-1009	73	4	2	2	NUM
iajs-1009	73	5	)	)	PUNCT
iajs-1009	73	6	1	1	NUM
iajs-1009	73	7	(	(	PUNCT
iajs-1009	73	8	pp	pp	NOUN
iajs-1009	73	9	=	=	SYM
iajs-1009	73	10	2	2	NUM
iajs-1009	73	11	22222	22222	NUM
iajs-1009	73	12	22	22	NUM
iajs-1009	73	13	ppppp	ppppp	NOUN
iajs-1009	73	14			PUNCT
iajs-1009	73	15	=	=	SYM
iajs-1009	73	16	2	2	NUM
iajs-1009	73	17	2	2	NUM
iajs-1009	73	18	pp	pp	NOUN
iajs-1009	73	19			NOUN
iajs-1009	73	20	=	=	SYM
iajs-1009	73	21	2	2	NUM
iajs-1009	73	22	)	)	PUNCT
iajs-1009	73	23	1	1	NUM
iajs-1009	73	24	(	(	PUNCT
iajs-1009	73	25	pp	pp	NOUN
iajs-1009	73	26	.	.	PUNCT
iajs-1009	74	1	2.16	2.16	NUM
iajs-1009	74	2	theorem	theorem	VERB
iajs-1009	74	3	[	[	X
iajs-1009	74	4	7	7	NUM
iajs-1009	74	5	]	]	PUNCT
iajs-1009	74	6	in	in	ADP
iajs-1009	74	7	pg(2,p	pg(2,p	NOUN
iajs-1009	74	8	)	)	PUNCT
iajs-1009	74	9	with	with	ADP
iajs-1009	74	10	p	p	PROPN
iajs-1009	74	11			NUM
iajs-1009	74	12	4	4	NUM
iajs-1009	74	13	,	,	PUNCT
iajs-1009	74	14	there	there	PRON
iajs-1009	74	15	is	be	VERB
iajs-1009	74	16	a	a	DET
iajs-1009	74	17	unique	unique	ADJ
iajs-1009	74	18	conic	conic	NOUN
iajs-1009	74	19	through	through	ADP
iajs-1009	74	20	a	a	DET
iajs-1009	74	21	5	5	NUM
iajs-1009	74	22	-	-	PUNCT
iajs-1009	74	23	arc	arc	NOUN
iajs-1009	74	24	.	.	PUNCT
iajs-1009	75	1	2.17	2.17	NUM
iajs-1009	75	2	theorem	theorem	VERB
iajs-1009	75	3	[	[	X
iajs-1009	75	4	4,5	4,5	NUM
iajs-1009	75	5	]	]	PUNCT
iajs-1009	75	6	every	every	DET
iajs-1009	75	7	conic	conic	NOUN
iajs-1009	75	8	in	in	ADP
iajs-1009	75	9	pg(2,p	pg(2,p	NOUN
iajs-1009	75	10	)	)	PUNCT
iajs-1009	75	11	is	be	AUX
iajs-1009	75	12	a(p+1)-arc	a(p+1)-arc	PROPN
iajs-1009	75	13	the	the	DET
iajs-1009	75	14	converse	converse	NOUN
iajs-1009	75	15	of	of	ADP
iajs-1009	75	16	theorem	theorem	NOUN
iajs-1009	75	17	is	be	AUX
iajs-1009	75	18	also	also	ADV
iajs-1009	75	19	satisfied	satisfied	ADJ
iajs-1009	75	20	.	.	PUNCT
iajs-1009	76	1	2.18	2.18	NUM
iajs-1009	76	2	theorem	theorem	VERB
iajs-1009	76	3	[	[	X
iajs-1009	76	4	3	3	NUM
iajs-1009	76	5	]	]	PUNCT
iajs-1009	76	6	in	in	ADP
iajs-1009	76	7	pg(2,p	pg(2,p	NOUN
iajs-1009	76	8	)	)	PUNCT
iajs-1009	76	9	,	,	PUNCT
iajs-1009	76	10	with	with	ADP
iajs-1009	76	11	p	p	PRON
iajs-1009	76	12	odd	odd	ADJ
iajs-1009	76	13	,	,	PUNCT
iajs-1009	76	14	every	every	DET
iajs-1009	76	15	oval	oval	NOUN
iajs-1009	76	16	has	have	VERB
iajs-1009	76	17	a	a	DET
iajs-1009	76	18	conic	conic	ADJ
iajs-1009	76	19	.	.	PUNCT
iajs-1009	77	1	2.19	2.19	NUM
iajs-1009	77	2	definition	definition	NOUN
iajs-1009	77	3	[	[	X
iajs-1009	77	4	8	8	X
iajs-1009	77	5	]	]	X
iajs-1009	77	6	a	a	DET
iajs-1009	77	7	complete	complete	ADJ
iajs-1009	77	8	quadrangle	quadrangle	NOUN
iajs-1009	77	9	is	be	AUX
iajs-1009	77	10	a	a	DET
iajs-1009	77	11	set	set	NOUN
iajs-1009	77	12	of	of	ADP
iajs-1009	77	13	four	four	NUM
iajs-1009	77	14	points	point	NOUN
iajs-1009	77	15	a	a	DET
iajs-1009	77	16	,	,	PUNCT
iajs-1009	77	17	b	b	NOUN
iajs-1009	77	18	,	,	PUNCT
iajs-1009	77	19	c	c	PROPN
iajs-1009	77	20	and	and	CCONJ
iajs-1009	77	21	d	d	PROPN
iajs-1009	77	22	in	in	ADP
iajs-1009	77	23	which	which	PRON
iajs-1009	77	24	no	no	DET
iajs-1009	77	25	three	three	NUM
iajs-1009	77	26	of	of	ADP
iajs-1009	77	27	them	they	PRON
iajs-1009	77	28	are	be	AUX
iajs-1009	77	29	collinear	collinear	ADJ
iajs-1009	77	30	,	,	PUNCT
iajs-1009	77	31	the	the	DET
iajs-1009	77	32	points	point	NOUN
iajs-1009	77	33	a	a	DET
iajs-1009	77	34	,	,	PUNCT
iajs-1009	77	35	b	b	NOUN
iajs-1009	77	36	,	,	PUNCT
iajs-1009	77	37	c	c	PROPN
iajs-1009	77	38	and	and	CCONJ
iajs-1009	77	39	d	d	PROPN
iajs-1009	77	40	are	be	AUX
iajs-1009	77	41	called	call	VERB
iajs-1009	77	42	the	the	DET
iajs-1009	77	43	vertices	vertex	NOUN
iajs-1009	77	44	of	of	ADP
iajs-1009	77	45	the	the	DET
iajs-1009	77	46	quadrangle	quadrangle	NOUN
iajs-1009	77	47	,	,	PUNCT
iajs-1009	77	48	the	the	DET
iajs-1009	77	49	lines	line	NOUN
iajs-1009	77	50	joining	join	VERB
iajs-1009	77	51	any	any	DET
iajs-1009	77	52	two	two	NUM
iajs-1009	77	53	vertices	vertex	NOUN
iajs-1009	77	54	are	be	AUX
iajs-1009	77	55	called	call	VERB
iajs-1009	77	56	the	the	DET
iajs-1009	77	57	sides	side	NOUN
iajs-1009	77	58	which	which	PRON
iajs-1009	77	59	are	be	AUX
iajs-1009	77	60	ab	ab	PROPN
iajs-1009	77	61	,	,	PUNCT
iajs-1009	77	62	ac	ac	PROPN
iajs-1009	77	63	,	,	PUNCT
iajs-1009	77	64	bd	bd	PROPN
iajs-1009	77	65	,	,	PUNCT
iajs-1009	77	66	bc	bc	PROPN
iajs-1009	77	67	,	,	PUNCT
iajs-1009	77	68	ad	ad	NOUN
iajs-1009	77	69	,	,	PUNCT
iajs-1009	77	70	cd	cd	PROPN
iajs-1009	77	71	.	.	PUNCT
iajs-1009	78	1	two	two	NUM
iajs-1009	78	2	sides	side	NOUN
iajs-1009	78	3	are	be	AUX
iajs-1009	78	4	said	say	VERB
iajs-1009	78	5	to	to	PART
iajs-1009	78	6	be	be	AUX
iajs-1009	78	7	opposite	opposite	ADJ
iajs-1009	78	8	if	if	SCONJ
iajs-1009	78	9	they	they	PRON
iajs-1009	78	10	have	have	VERB
iajs-1009	78	11	no	no	DET
iajs-1009	78	12	vertex	vertex	NOUN
iajs-1009	78	13	in	in	ADP
iajs-1009	78	14	common	common	ADJ
iajs-1009	78	15	.	.	PUNCT
iajs-1009	79	1	the	the	DET
iajs-1009	79	2	point	point	NOUN
iajs-1009	79	3	of	of	ADP
iajs-1009	79	4	intersection	intersection	NOUN
iajs-1009	79	5	of	of	ADP
iajs-1009	79	6	any	any	DET
iajs-1009	79	7	two	two	NUM
iajs-1009	79	8	opposite	opposite	ADJ
iajs-1009	79	9	sides	side	NOUN
iajs-1009	79	10	is	be	AUX
iajs-1009	79	11	called	call	VERB
iajs-1009	79	12	a	a	DET
iajs-1009	79	13	diagonal	diagonal	ADJ
iajs-1009	79	14	point	point	NOUN
iajs-1009	79	15	the	the	DET
iajs-1009	79	16	diagonal	diagonal	ADJ
iajs-1009	79	17	points	point	NOUN
iajs-1009	79	18	;	;	PUNCT
iajs-1009	79	19	d1	d1	PROPN
iajs-1009	79	20	=	=	PROPN
iajs-1009	79	21	ab	ab	PROPN
iajs-1009	79	22	cd	cd	NUM
iajs-1009	79	23	,	,	PUNCT
iajs-1009	79	24	d2	d2	PROPN
iajs-1009	79	25	=	=	SYM
iajs-1009	79	26	ac	ac	PROPN
iajs-1009	79	27			PROPN
iajs-1009	79	28	bd	bd	PROPN
iajs-1009	79	29	and	and	CCONJ
iajs-1009	79	30	d3	d3	PROPN
iajs-1009	79	31	=	=	SYM
iajs-1009	79	32	ad	ad	PROPN
iajs-1009	79	33			X
iajs-1009	79	34	bc	bc	PROPN
iajs-1009	79	35	.	.	PROPN
iajs-1009	79	36	3	3	NUM
iajs-1009	79	37	.	.	PUNCT
iajs-1009	79	38	maximum	maximum	ADV
iajs-1009	79	39	complete	complete	ADJ
iajs-1009	79	40	(	(	PUNCT
iajs-1009	79	41	k	k	NOUN
iajs-1009	79	42	,	,	PUNCT
iajs-1009	79	43	n)-arcs	n)-arcs	X
iajs-1009	79	44	in	in	ADP
iajs-1009	79	45	pg(2,4	pg(2,4	NOUN
iajs-1009	79	46	)	)	PUNCT
iajs-1009	79	47	3.1	3.1	NUM
iajs-1009	79	48	the	the	DET
iajs-1009	79	49	additions	addition	NOUN
iajs-1009	79	50	and	and	CCONJ
iajs-1009	79	51	multiplications	multiplication	NOUN
iajs-1009	79	52	operations	operation	NOUN
iajs-1009	79	53	of	of	ADP
iajs-1009	79	54	gf(4	gf(4	NOUN
iajs-1009	79	55	)	)	PUNCT
iajs-1009	80	1	[	[	X
iajs-1009	80	2	9	9	NUM
iajs-1009	80	3	]	]	PUNCT
iajs-1009	80	4	to	to	PART
iajs-1009	80	5	find	find	VERB
iajs-1009	80	6	addition	addition	NOUN
iajs-1009	80	7	and	and	CCONJ
iajs-1009	80	8	multiplication	multiplication	NOUN
iajs-1009	80	9	tables	table	NOUN
iajs-1009	80	10	in	in	ADP
iajs-1009	80	11	gf(4	gf(4	NOUN
iajs-1009	80	12	)	)	PUNCT
iajs-1009	80	13	,	,	PUNCT
iajs-1009	80	14	we	we	PRON
iajs-1009	80	15	have	have	VERB
iajs-1009	80	16	the	the	DET
iajs-1009	80	17	order	order	NOUN
iajs-1009	80	18	pairs	pair	NOUN
iajs-1009	80	19	(	(	PUNCT
iajs-1009	80	20	x1,x2	x1,x2	PROPN
iajs-1009	80	21	)	)	PUNCT
iajs-1009	80	22	such	such	ADJ
iajs-1009	80	23	that	that	PRON
iajs-1009	80	24	x1,x2	x1,x2	PROPN
iajs-1009	80	25	in	in	ADP
iajs-1009	80	26	gf(2	gf(2	PROPN
iajs-1009	80	27	)	)	PUNCT
iajs-1009	80	28	,	,	PUNCT
iajs-1009	80	29	as	as	SCONJ
iajs-1009	80	30	follows	follow	VERB
iajs-1009	80	31	:	:	PUNCT
iajs-1009	80	32	0	0	NUM
iajs-1009	80	33			PROPN
iajs-1009	80	34	(	(	PUNCT
iajs-1009	80	35	0,0	0,0	NOUN
iajs-1009	80	36	)	)	PUNCT
iajs-1009	80	37	,	,	PUNCT
iajs-1009	80	38	1	1	NUM
iajs-1009	80	39			PROPN
iajs-1009	80	40	(	(	PUNCT
iajs-1009	80	41	1,0	1,0	NUM
iajs-1009	80	42	)	)	PUNCT
iajs-1009	80	43	,	,	PUNCT
iajs-1009	80	44	2	2	NUM
iajs-1009	80	45			PROPN
iajs-1009	80	46	(	(	PUNCT
iajs-1009	80	47	0,1	0,1	NUM
iajs-1009	80	48	)	)	PUNCT
iajs-1009	80	49	,	,	PUNCT
iajs-1009	80	50	3	3	NUM
iajs-1009	80	51			PROPN
iajs-1009	80	52	(	(	PUNCT
iajs-1009	80	53	1,1	1,1	NUM
iajs-1009	80	54	)	)	PUNCT
iajs-1009	80	55	.	.	PUNCT
iajs-1009	81	1	put	put	VERB
iajs-1009	81	2	these	these	DET
iajs-1009	81	3	points	point	NOUN
iajs-1009	81	4	in	in	ADP
iajs-1009	81	5	one	one	NUM
iajs-1009	81	6	ibn	ibn	PROPN
iajs-1009	81	7	alhaitham	alhaitham	NOUN
iajs-1009	81	8	j.	j.	PROPN
iajs-1009	82	1	fo	fo	ADP
iajs-1009	82	2	r	r	NOUN
iajs-1009	82	3	pure	pure	ADJ
iajs-1009	82	4	&	&	CCONJ
iajs-1009	82	5	appl	appl	PROPN
iajs-1009	82	6	.	.	PUNCT
iajs-1009	83	1	sc	sc	PROPN
iajs-1009	83	2	i.	i.	PROPN
iajs-1009	83	3	vol.23	vol.23	PROPN
iajs-1009	83	4	(	(	PUNCT
iajs-1009	83	5	1	1	NUM
iajs-1009	83	6	)	)	PUNCT
iajs-1009	83	7	2010	2010	NUM
iajs-1009	83	8	orbit	orbit	NOUN
iajs-1009	83	9	,	,	PUNCT
iajs-1009	83	10	(	(	PUNCT
iajs-1009	83	11	1,0	1,0	NUM
iajs-1009	83	12	)	)	PUNCT
iajs-1009	83	13	at	at	ADP
iajs-1009	83	14	the	the	DET
iajs-1009	83	15	first	first	ADJ
iajs-1009	83	16	point	point	NOUN
iajs-1009	83	17	and	and	CCONJ
iajs-1009	83	18	by	by	ADP
iajs-1009	83	19	the	the	DET
iajs-1009	83	20	principle	principle	NOUN
iajs-1009	83	21	of	of	ADP
iajs-1009	83	22	(	(	PUNCT
iajs-1009	83	23	1,0)ai	1,0)ai	NUM
iajs-1009	83	24	,	,	PUNCT
iajs-1009	83	25	i=0,1,2,3	i=0,1,2,3	NOUN
iajs-1009	83	26	and	and	CCONJ
iajs-1009	83	27	a=	a=	ADJ
iajs-1009	83	28			PROPN
iajs-1009	83	29			PROPN
iajs-1009	83	30			X
iajs-1009	83	31			NOUN
iajs-1009	83	32			VERB
iajs-1009	83	33			PROPN
iajs-1009	83	34	11	11	NUM
iajs-1009	83	35	01	01	NUM
iajs-1009	83	36	,	,	PUNCT
iajs-1009	83	37	(	(	PUNCT
iajs-1009	83	38	1,0)a=(0,1	1,0)a=(0,1	NUM
iajs-1009	83	39	)	)	PUNCT
iajs-1009	83	40	and	and	CCONJ
iajs-1009	83	41	(	(	PUNCT
iajs-1009	83	42	1,0)a2=	1,0)a2=	NUM
iajs-1009	83	43	(	(	PUNCT
iajs-1009	83	44	1,1	1,1	NUM
iajs-1009	83	45	)	)	PUNCT
iajs-1009	83	46	,	,	PUNCT
iajs-1009	83	47	so	so	CCONJ
iajs-1009	83	48	(	(	PUNCT
iajs-1009	83	49	1,0	1,0	NUM
iajs-1009	83	50	)	)	PUNCT
iajs-1009	83	51			PROPN
iajs-1009	83	52			PROPN
iajs-1009	83	53			PRON
iajs-1009	83	54			NOUN
iajs-1009	83	55			VERB
iajs-1009	83	56			PROPN
iajs-1009	83	57	11	11	NUM
iajs-1009	83	58	01	01	NUM
iajs-1009	83	59	)	)	PUNCT
iajs-1009	83	60	1,1	1,1	NUM
iajs-1009	83	61	(	(	PUNCT
iajs-1009	83	62	)	)	PUNCT
iajs-1009	83	63	1,0	1,0	NUM
iajs-1009	83	64	(	(	PUNCT
iajs-1009	83	65	.	.	PUNCT
iajs-1009	84	1	now	now	ADV
iajs-1009	84	2	,	,	PUNCT
iajs-1009	84	3	in	in	ADP
iajs-1009	84	4	the	the	DET
iajs-1009	84	5	left	left	NOUN
iajs-1009	84	6	of	of	ADP
iajs-1009	84	7	the	the	DET
iajs-1009	84	8	following	follow	VERB
iajs-1009	84	9	table	table	NOUN
iajs-1009	84	10	,	,	PUNCT
iajs-1009	84	11	m	m	VERB
iajs-1009	84	12	is	be	AUX
iajs-1009	84	13	the	the	DET
iajs-1009	84	14	operation	operation	NOUN
iajs-1009	84	15	of	of	ADP
iajs-1009	84	16	multiplication	multiplication	NOUN
iajs-1009	84	17	and	and	CCONJ
iajs-1009	84	18	in	in	ADP
iajs-1009	84	19	the	the	DET
iajs-1009	84	20	right	right	NOUN
iajs-1009	85	1	n	n	NOUN
iajs-1009	85	2	is	be	AUX
iajs-1009	85	3	the	the	DET
iajs-1009	85	4	operation	operation	NOUN
iajs-1009	85	5	of	of	ADP
iajs-1009	85	6	addition	addition	NOUN
iajs-1009	85	7	,	,	PUNCT
iajs-1009	85	8	in	in	ADP
iajs-1009	85	9	multiplication	multiplication	NOUN
iajs-1009	85	10	side	side	NOUN
iajs-1009	85	11	we	we	PRON
iajs-1009	85	12	write	write	VERB
iajs-1009	85	13	the	the	DET
iajs-1009	85	14	numeration	numeration	NOUN
iajs-1009	85	15	of	of	ADP
iajs-1009	85	16	point	point	NOUN
iajs-1009	85	17	as	as	ADP
iajs-1009	85	18	last	last	ADJ
iajs-1009	85	19	,	,	PUNCT
iajs-1009	85	20	and	and	CCONJ
iajs-1009	85	21	the	the	DET
iajs-1009	85	22	addition	addition	NOUN
iajs-1009	85	23	side	side	NOUN
iajs-1009	85	24	takes	take	VERB
iajs-1009	85	25	the	the	DET
iajs-1009	85	26	normal	normal	ADJ
iajs-1009	85	27	sequence	sequence	NOUN
iajs-1009	85	28	.	.	PUNCT
iajs-1009	86	1	m	m	PUNCT
iajs-1009	86	2	(	(	PUNCT
iajs-1009	86	3	*	*	PUNCT
iajs-1009	86	4	)	)	PUNCT
iajs-1009	86	5	(	(	PUNCT
iajs-1009	86	6	+	+	NOUN
iajs-1009	86	7	)	)	PUNCT
iajs-1009	86	8	n	n	NOUN
iajs-1009	86	9	=	=	SYM
iajs-1009	86	10	f(m	f(m	PROPN
iajs-1009	86	11	)	)	PUNCT
iajs-1009	86	12	1	1	NUM
iajs-1009	86	13	(	(	PUNCT
iajs-1009	86	14	1,0	1,0	NUM
iajs-1009	86	15	)	)	PUNCT
iajs-1009	86	16	0	0	NUM
iajs-1009	86	17	2	2	NUM
iajs-1009	86	18	(	(	PUNCT
iajs-1009	86	19	0,1	0,1	NUM
iajs-1009	86	20	)	)	PUNCT
iajs-1009	86	21	1	1	NUM
iajs-1009	86	22	3	3	NUM
iajs-1009	86	23	(	(	PUNCT
iajs-1009	86	24	1,1	1,1	NUM
iajs-1009	86	25	)	)	PUNCT
iajs-1009	86	26	2	2	NUM
iajs-1009	86	27	mod	mod	NOUN
iajs-1009	86	28	3	3	NUM
iajs-1009	86	29	in	in	ADP
iajs-1009	86	30	addition	addition	NOUN
iajs-1009	86	31	table	table	NOUN
iajs-1009	86	32	,	,	PUNCT
iajs-1009	86	33	we	we	PRON
iajs-1009	86	34	have	have	VERB
iajs-1009	86	35	the	the	DET
iajs-1009	86	36	following	follow	VERB
iajs-1009	86	37	relation	relation	NOUN
iajs-1009	86	38	:	:	PUNCT
iajs-1009	86	39	(	(	PUNCT
iajs-1009	86	40	x1,x2	x1,x2	PROPN
iajs-1009	86	41	)	)	PUNCT
iajs-1009	87	1	+	+	CCONJ
iajs-1009	87	2	(	(	PUNCT
iajs-1009	87	3	y1,y2	y1,y2	PROPN
iajs-1009	87	4	)	)	PUNCT
iajs-1009	87	5	=	=	PRON
iajs-1009	87	6	(	(	PUNCT
iajs-1009	87	7	z1,z2	z1,z2	PROPN
iajs-1009	87	8	)	)	PUNCT
iajs-1009	87	9	where	where	SCONJ
iajs-1009	87	10	zi	zi	NOUN
iajs-1009	87	11	=	=	PUNCT
iajs-1009	87	12	(	(	PUNCT
iajs-1009	87	13	y	y	PROPN
iajs-1009	87	14	i+	i+	NOUN
iajs-1009	87	15	xi	xi	NOUN
iajs-1009	87	16	)	)	PUNCT
iajs-1009	87	17	mod(2	mod(2	NOUN
iajs-1009	87	18	)	)	PUNCT
iajs-1009	87	19	for	for	ADP
iajs-1009	87	20	i	i	PROPN
iajs-1009	87	21	=	=	NOUN
iajs-1009	87	22	1,2	1,2	NUM
iajs-1009	87	23	in	in	ADP
iajs-1009	87	24	multiplication	multiplication	NOUN
iajs-1009	87	25	table	table	NOUN
iajs-1009	87	26	we	we	PRON
iajs-1009	87	27	have	have	VERB
iajs-1009	87	28	the	the	DET
iajs-1009	87	29	following	follow	VERB
iajs-1009	87	30	relation	relation	NOUN
iajs-1009	87	31	:	:	PUNCT
iajs-1009	87	32	(	(	PUNCT
iajs-1009	87	33	(	(	PUNCT
iajs-1009	87	34	1,0	1,0	NUM
iajs-1009	87	35	)	)	PUNCT
iajs-1009	87	36	a	a	DET
iajs-1009	87	37	f(m	f(m	PROPN
iajs-1009	87	38	1	1	NUM
iajs-1009	87	39	)	)	PUNCT
iajs-1009	87	40	)	)	PUNCT
iajs-1009	87	41	a	a	DET
iajs-1009	87	42	f(m2	f(m2	NOUN
iajs-1009	87	43	)	)	PUNCT
iajs-1009	87	44			ADP
iajs-1009	87	45	m1*m2	m1*m2	PROPN
iajs-1009	87	46	=	=	SYM
iajs-1009	87	47	m3	m3	PROPN
iajs-1009	87	48	=(	=(	NOUN
iajs-1009	87	49	1,0	1,0	NUM
iajs-1009	87	50	)	)	PUNCT
iajs-1009	87	51	a(f(m	a(f(m	PROPN
iajs-1009	87	52	1	1	NUM
iajs-1009	87	53	)	)	PUNCT
iajs-1009	87	54	+	+	NOUN
iajs-1009	87	55	f(m	f(m	PROPN
iajs-1009	87	56	2	2	NUM
iajs-1009	87	57	)	)	PUNCT
iajs-1009	87	58	)	)	PUNCT
iajs-1009	87	59	(	(	PUNCT
iajs-1009	87	60	m	m	VERB
iajs-1009	87	61	od	od	PROPN
iajs-1009	87	62	3	3	NUM
iajs-1009	87	63	)	)	PUNCT
iajs-1009	87	64	=	=	PRON
iajs-1009	87	65	(	(	PUNCT
iajs-1009	87	66	x1,x2	x1,x2	PROPN
iajs-1009	87	67	)	)	PUNCT
iajs-1009	87	68	for	for	ADP
iajs-1009	87	69	example	example	NOUN
iajs-1009	87	70	:	:	PUNCT
iajs-1009	87	71	2	2	NUM
iajs-1009	87	72	*	*	SYM
iajs-1009	87	73	3	3	NUM
iajs-1009	87	74	=	=	SYM
iajs-1009	87	75	1	1	NUM
iajs-1009	87	76			X
iajs-1009	87	77	(	(	PUNCT
iajs-1009	87	78	(	(	PUNCT
iajs-1009	87	79	1,0)a1)a2	1,0)a1)a2	NUM
iajs-1009	87	80	=	=	SYM
iajs-1009	87	81	(	(	PUNCT
iajs-1009	87	82	1,0)a3	1,0)a3	X
iajs-1009	87	83	=	=	SYM
iajs-1009	87	84	(	(	PUNCT
iajs-1009	87	85	1,0)a0	1,0)a0	NOUN
iajs-1009	87	86	=	=	SYM
iajs-1009	87	87	(	(	PUNCT
iajs-1009	87	88	1,0	1,0	NUM
iajs-1009	87	89	)	)	PUNCT
iajs-1009	87	90	,	,	PUNCT
iajs-1009	87	91	where	where	SCONJ
iajs-1009	87	92	(	(	PUNCT
iajs-1009	87	93	1,0	1,0	NUM
iajs-1009	87	94	)	)	PUNCT
iajs-1009	87	95	is	be	AUX
iajs-1009	87	96	equal	equal	ADJ
iajs-1009	87	97	to	to	ADP
iajs-1009	87	98	1	1	NUM
iajs-1009	87	99	in	in	ADP
iajs-1009	87	100	multiplication	multiplication	NOUN
iajs-1009	87	101	tables	table	NOUN
iajs-1009	87	102	.	.	PUNCT
iajs-1009	88	1	the	the	DET
iajs-1009	88	2	additions	addition	NOUN
iajs-1009	88	3	and	and	CCONJ
iajs-1009	88	4	multiplications	multiplication	NOUN
iajs-1009	88	5	operations	operation	NOUN
iajs-1009	88	6	of	of	ADP
iajs-1009	88	7	gf(4	gf(4	NOUN
iajs-1009	88	8	)	)	PUNCT
iajs-1009	88	9	are	be	AUX
iajs-1009	88	10	in	in	ADP
iajs-1009	88	11	table	table	NOUN
iajs-1009	88	12	(	(	PUNCT
iajs-1009	88	13	1	1	NUM
iajs-1009	88	14	)	)	PUNCT
iajs-1009	88	15	.	.	PUNCT
iajs-1009	89	1	3.2	3.2	NUM
iajs-1009	89	2	the	the	DET
iajs-1009	89	3	projective	projective	ADJ
iajs-1009	89	4	plane	plane	NOUN
iajs-1009	89	5	pg(2,4	pg(2,4	NOUN
iajs-1009	89	6	)	)	PUNCT
iajs-1009	89	7	the	the	DET
iajs-1009	89	8	projective	projective	ADJ
iajs-1009	89	9	plane	plane	NOUN
iajs-1009	89	10	pg(2,4	pg(2,4	NOUN
iajs-1009	89	11	)	)	PUNCT
iajs-1009	89	12	contains	contain	VERB
iajs-1009	89	13	21	21	NUM
iajs-1009	89	14	points	point	NOUN
iajs-1009	89	15	,	,	PUNCT
iajs-1009	89	16	21	21	NUM
iajs-1009	89	17	lines	line	NOUN
iajs-1009	89	18	,	,	PUNCT
iajs-1009	89	19	5	5	NUM
iajs-1009	89	20	points	point	NOUN
iajs-1009	89	21	on	on	ADP
iajs-1009	89	22	every	every	DET
iajs-1009	89	23	line	line	NOUN
iajs-1009	89	24	and	and	CCONJ
iajs-1009	89	25	5	5	NUM
iajs-1009	89	26	lines	line	NOUN
iajs-1009	89	27	through	through	ADP
iajs-1009	89	28	every	every	DET
iajs-1009	89	29	point	point	NOUN
iajs-1009	89	30	.	.	PUNCT
iajs-1009	90	1	let	let	VERB
iajs-1009	90	2	pi	pi	NOUN
iajs-1009	90	3	and	and	CCONJ
iajs-1009	90	4	li	li	PROPN
iajs-1009	90	5	,	,	PUNCT
iajs-1009	90	6	i=1,2,---,21	i=1,2,---,21	PRON
iajs-1009	90	7	be	be	VERB
iajs-1009	90	8	points	point	NOUN
iajs-1009	90	9	and	and	CCONJ
iajs-1009	90	10	the	the	DET
iajs-1009	90	11	lines	line	NOUN
iajs-1009	90	12	of	of	ADP
iajs-1009	90	13	pg(2,4	pg(2,4	NOUN
iajs-1009	90	14	)	)	PUNCT
iajs-1009	90	15	respectively	respectively	ADV
iajs-1009	90	16	,	,	PUNCT
iajs-1009	90	17	the	the	DET
iajs-1009	90	18	points	point	NOUN
iajs-1009	90	19	and	and	CCONJ
iajs-1009	90	20	lines	line	NOUN
iajs-1009	90	21	of	of	ADP
iajs-1009	90	22	pg(2,4	pg(2,4	NOUN
iajs-1009	90	23	)	)	PUNCT
iajs-1009	90	24	are	be	AUX
iajs-1009	90	25	in	in	ADP
iajs-1009	90	26	table	table	NOUN
iajs-1009	90	27	(	(	PUNCT
iajs-1009	90	28	2	2	NUM
iajs-1009	90	29	)	)	PUNCT
iajs-1009	90	30	.	.	PUNCT
iajs-1009	91	1	3.3	3.3	NUM
iajs-1009	91	2	the	the	DET
iajs-1009	91	3	construction	construction	NOUN
iajs-1009	91	4	of	of	ADP
iajs-1009	91	5	k	k	NOUN
iajs-1009	91	6	-	-	NOUN
iajs-1009	91	7	arc	arc	NOUN
iajs-1009	91	8	in	in	ADP
iajs-1009	91	9	pg(2,4	pg(2,4	NOUN
iajs-1009	91	10	)	)	PUNCT
iajs-1009	91	11	let	let	VERB
iajs-1009	91	12	a={1,2,6,11	a={1,2,6,11	X
iajs-1009	91	13	}	}	PUNCT
iajs-1009	91	14	,	,	PUNCT
iajs-1009	91	15	be	be	AUX
iajs-1009	91	16	the	the	DET
iajs-1009	91	17	reference	reference	NOUN
iajs-1009	91	18	and	and	CCONJ
iajs-1009	91	19	unit	unit	NOUN
iajs-1009	91	20	points	point	NOUN
iajs-1009	91	21	of	of	ADP
iajs-1009	91	22	pg(2,4	pg(2,4	NOUN
iajs-1009	91	23	)	)	PUNCT
iajs-1009	91	24	where	where	SCONJ
iajs-1009	91	25	1=(1,0,0	1=(1,0,0	NOUN
iajs-1009	91	26	)	)	PUNCT
iajs-1009	91	27	,	,	PUNCT
iajs-1009	91	28	2=(0,1,0	2=(0,1,0	NUM
iajs-1009	91	29	)	)	PUNCT
iajs-1009	91	30	,	,	PUNCT
iajs-1009	91	31	6=(0,0,1	6=(0,0,1	NOUN
iajs-1009	91	32	)	)	PUNCT
iajs-1009	91	33	,	,	PUNCT
iajs-1009	91	34	11=(1,1,1	11=(1,1,1	NUM
iajs-1009	91	35	)	)	PUNCT
iajs-1009	91	36	.	.	PUNCT
iajs-1009	92	1	a	a	PRON
iajs-1009	92	2	is	be	AUX
iajs-1009	92	3	(	(	PUNCT
iajs-1009	92	4	4,2)-arc	4,2)-arc	NUM
iajs-1009	92	5	since	since	SCONJ
iajs-1009	92	6	it	it	PRON
iajs-1009	92	7	contains	contain	VERB
iajs-1009	92	8	four	four	NUM
iajs-1009	92	9	points	point	NOUN
iajs-1009	92	10	no	no	DET
iajs-1009	92	11	three	three	NUM
iajs-1009	92	12	of	of	ADP
iajs-1009	92	13	them	they	PRON
iajs-1009	92	14	are	be	AUX
iajs-1009	92	15	collinear	collinear	ADJ
iajs-1009	92	16	.	.	PUNCT
iajs-1009	93	1	there	there	PRON
iajs-1009	93	2	are	be	VERB
iajs-1009	93	3	six	six	NUM
iajs-1009	93	4	lines	line	NOUN
iajs-1009	93	5	from	from	ADP
iajs-1009	93	6	the	the	DET
iajs-1009	93	7	joining	joining	NOUN
iajs-1009	93	8	of	of	ADP
iajs-1009	93	9	these	these	DET
iajs-1009	93	10	points	point	NOUN
iajs-1009	93	11	which	which	PRON
iajs-1009	93	12	are	be	AUX
iajs-1009	93	13	ℓ1	ℓ1	ADJ
iajs-1009	93	14	=	=	PUNCT
iajs-1009	94	1	[	[	X
iajs-1009	94	2	1,2]={1,2,3,4,5	1,2]={1,2,3,4,5	NUM
iajs-1009	94	3	}	}	PUNCT
iajs-1009	94	4	ℓ2	ℓ2	NOUN
iajs-1009	94	5	=	=	PUNCT
iajs-1009	95	1	[	[	X
iajs-1009	95	2	1,6]={1,6,7,8,9	1,6]={1,6,7,8,9	NUM
iajs-1009	95	3	}	}	PUNCT
iajs-1009	95	4	ℓ3	ℓ3	NOUN
iajs-1009	95	5	=	=	PUNCT
iajs-1009	96	1	[	[	X
iajs-1009	96	2	1,11]={1,10,11,12,13	1,11]={1,10,11,12,13	NUM
iajs-1009	96	3	}	}	PUNCT
iajs-1009	96	4	ℓ4	ℓ4	NOUN
iajs-1009	96	5	=	=	PUNCT
iajs-1009	97	1	[	[	X
iajs-1009	97	2	2,6]={2,6,10,14,18	2,6]={2,6,10,14,18	NUM
iajs-1009	97	3	}	}	PUNCT
iajs-1009	97	4	ℓ5	ℓ5	NOUN
iajs-1009	97	5	=	=	PUNCT
iajs-1009	98	1	[	[	X
iajs-1009	98	2	2,11]={2,7,11,15,19	2,11]={2,7,11,15,19	NUM
iajs-1009	98	3	}	}	PUNCT
iajs-1009	98	4	ℓ6	ℓ6	NOUN
iajs-1009	98	5	=	=	PUNCT
iajs-1009	99	1	[	[	X
iajs-1009	99	2	6,11]={3,6,11,16,21	6,11]={3,6,11,16,21	NUM
iajs-1009	99	3	}	}	PUNCT
iajs-1009	99	4	the	the	DET
iajs-1009	99	5	diagonal	diagonal	ADJ
iajs-1009	99	6	points	point	NOUN
iajs-1009	99	7	of	of	ADP
iajs-1009	99	8	a	a	PRON
iajs-1009	99	9	are	be	AUX
iajs-1009	99	10	the	the	DET
iajs-1009	99	11	points	point	NOUN
iajs-1009	99	12	{	{	PUNCT
iajs-1009	99	13	3,7,10	3,7,10	NUM
iajs-1009	99	14	}	}	PUNCT
iajs-1009	99	15	where	where	SCONJ
iajs-1009	99	16	ℓ1	ℓ1	VERB
iajs-1009	99	17			PUNCT
iajs-1009	99	18	ℓ6	ℓ6	NOUN
iajs-1009	99	19	=	=	SYM
iajs-1009	99	20	3	3	NUM
iajs-1009	99	21	,	,	PUNCT
iajs-1009	99	22	ℓ2	ℓ2	NOUN
iajs-1009	99	23			PUNCT
iajs-1009	99	24	ℓ5	ℓ5	NOUN
iajs-1009	99	25	=	=	SYM
iajs-1009	99	26	7	7	NUM
iajs-1009	99	27	,	,	PUNCT
iajs-1009	99	28	ℓ4	ℓ4	NOUN
iajs-1009	99	29			ADJ
iajs-1009	99	30	ℓ3	ℓ3	NOUN
iajs-1009	99	31	=	=	PUNCT
iajs-1009	99	32	10	10	NUM
iajs-1009	99	33	.	.	PUNCT
iajs-1009	100	1	the	the	DET
iajs-1009	100	2	points	point	NOUN
iajs-1009	100	3	of	of	ADP
iajs-1009	100	4	pg(2,4	pg(2,4	NOUN
iajs-1009	100	5	)	)	PUNCT
iajs-1009	100	6	are	be	AUX
iajs-1009	100	7	classified	classify	VERB
iajs-1009	100	8	with	with	ADP
iajs-1009	100	9	respect	respect	NOUN
iajs-1009	100	10	to	to	ADP
iajs-1009	100	11	the	the	DET
iajs-1009	100	12	lines	line	NOUN
iajs-1009	100	13	through	through	ADP
iajs-1009	100	14	the	the	DET
iajs-1009	100	15	reference	reference	NOUN
iajs-1009	100	16	and	and	CCONJ
iajs-1009	100	17	unit	unit	NOUN
iajs-1009	100	18	points	point	NOUN
iajs-1009	100	19	as	as	SCONJ
iajs-1009	100	20	follows	follow	VERB
iajs-1009	100	21	:	:	PUNCT
iajs-1009	101	1	ibn	ibn	NOUN
iajs-1009	101	2	alhaitham	alhaitham	NOUN
iajs-1009	101	3	j.	j.	PROPN
iajs-1009	102	1	fo	fo	ADP
iajs-1009	102	2	r	r	NOUN
iajs-1009	102	3	pure	pure	ADJ
iajs-1009	102	4	&	&	CCONJ
iajs-1009	102	5	appl	appl	PROPN
iajs-1009	102	6	.	.	PUNCT
iajs-1009	103	1	sc	sc	PROPN
iajs-1009	103	2	i.	i.	PROPN
iajs-1009	103	3	vol.23	vol.23	PROPN
iajs-1009	103	4	(	(	PUNCT
iajs-1009	103	5	1	1	NUM
iajs-1009	103	6	)	)	PUNCT
iajs-1009	103	7	2010	2010	NUM
iajs-1009	103	8	1	1	NUM
iajs-1009	103	9	.	.	PUNCT
iajs-1009	104	1	the	the	DET
iajs-1009	104	2	number	number	NOUN
iajs-1009	104	3	of	of	ADP
iajs-1009	104	4	points	point	NOUN
iajs-1009	104	5	on	on	ADP
iajs-1009	104	6	these	these	DET
iajs-1009	104	7	lines	line	NOUN
iajs-1009	104	8	is	be	AUX
iajs-1009	104	9	19	19	NUM
iajs-1009	104	10	.	.	NOUN
iajs-1009	104	11	2	2	NUM
iajs-1009	104	12	.	.	X
iajs-1009	105	1	there	there	PRON
iajs-1009	105	2	exists	exist	VERB
iajs-1009	105	3	two	two	NUM
iajs-1009	105	4	points	point	NOUN
iajs-1009	105	5	of	of	ADP
iajs-1009	105	6	index	index	NOUN
iajs-1009	105	7	zero	zero	NUM
iajs-1009	105	8	for	for	ADP
iajs-1009	105	9	a	a	PRON
iajs-1009	105	10	,	,	PUNCT
iajs-1009	105	11	which	which	PRON
iajs-1009	105	12	are	be	AUX
iajs-1009	105	13	the	the	DET
iajs-1009	105	14	point	point	NOUN
iajs-1009	105	15	17	17	NUM
iajs-1009	105	16	and	and	CCONJ
iajs-1009	105	17	the	the	DET
iajs-1009	105	18	point	point	NOUN
iajs-1009	105	19	20	20	NUM
iajs-1009	105	20	not	not	PART
iajs-1009	105	21	on	on	ADP
iajs-1009	105	22	any	any	PRON
iajs-1009	105	23	of	of	ADP
iajs-1009	105	24	these	these	DET
iajs-1009	105	25	lines	line	NOUN
iajs-1009	105	26	,	,	PUNCT
iajs-1009	105	27	then	then	ADV
iajs-1009	105	28	the	the	DET
iajs-1009	105	29	4	4	NUM
iajs-1009	105	30	-	-	PUNCT
iajs-1009	105	31	arc	arc	NOUN
iajs-1009	105	32	a	a	NOUN
iajs-1009	105	33	is	be	AUX
iajs-1009	105	34	incomplete	incomplete	ADJ
iajs-1009	105	35	.	.	PUNCT
iajs-1009	106	1	3.4	3.4	NUM
iajs-1009	106	2	the	the	DET
iajs-1009	106	3	conic	conic	NOUN
iajs-1009	106	4	in	in	ADP
iajs-1009	106	5	pg(2,4	pg(2,4	NOUN
iajs-1009	106	6	)	)	PUNCT
iajs-1009	106	7	through	through	ADP
iajs-1009	106	8	the	the	DET
iajs-1009	106	9	reference	reference	NOUN
iajs-1009	106	10	and	and	CCONJ
iajs-1009	106	11	unit	unit	NOUN
iajs-1009	106	12	points	point	NOUN
iajs-1009	106	13	.	.	PUNCT
iajs-1009	107	1	the	the	DET
iajs-1009	107	2	general	general	ADJ
iajs-1009	107	3	equation	equation	NOUN
iajs-1009	107	4	of	of	ADP
iajs-1009	107	5	the	the	DET
iajs-1009	107	6	conic	conic	NOUN
iajs-1009	107	7	is	be	AUX
iajs-1009	107	8	:	:	PUNCT
iajs-1009	107	9	2	2	NUM
iajs-1009	107	10	2	2	NUM
iajs-1009	107	11	2	2	NUM
iajs-1009	107	12	1	1	NUM
iajs-1009	107	13	1	1	NUM
iajs-1009	107	14	2	2	NUM
iajs-1009	107	15	2	2	NUM
iajs-1009	107	16	3	3	NUM
iajs-1009	107	17	3	3	NUM
iajs-1009	107	18	4	4	NUM
iajs-1009	107	19	1	1	NUM
iajs-1009	107	20	2	2	NUM
iajs-1009	107	21	5	5	NUM
iajs-1009	107	22	1	1	NUM
iajs-1009	107	23	3	3	NUM
iajs-1009	107	24	6	6	NUM
iajs-1009	107	25	2	2	NUM
iajs-1009	107	26	3a	3a	NUM
iajs-1009	107	27	x	x	SYM
iajs-1009	107	28	a	a	PRON
iajs-1009	107	29	x	x	SYM
iajs-1009	107	30	a	a	DET
iajs-1009	107	31	x	x	SYM
iajs-1009	107	32	a	a	X
iajs-1009	107	33	x	x	X
iajs-1009	107	34	x	x	X
iajs-1009	107	35	a	a	X
iajs-1009	107	36	x	x	X
iajs-1009	107	37	x	x	X
iajs-1009	107	38	a	a	X
iajs-1009	107	39	x	x	X
iajs-1009	107	40	x	x	SYM
iajs-1009	107	41	0	0	NOUN
iajs-1009	107	42			PROPN
iajs-1009	107	43			PROPN
iajs-1009	107	44			PUNCT
iajs-1009	107	45			PUNCT
iajs-1009	107	46			PROPN
iajs-1009	107	47	…	…	PUNCT
iajs-1009	107	48	..	..	PUNCT
iajs-1009	107	49	…	…	PUNCT
iajs-1009	107	50	…	…	PUNCT
iajs-1009	107	51	…	…	SYM
iajs-1009	107	52	.	.	PUNCT
iajs-1009	107	53	…	…	PUNCT
iajs-1009	107	54	(1	(1	X
iajs-1009	107	55	)	)	PUNCT
iajs-1009	107	56	by	by	ADP
iajs-1009	107	57	substituting	substitute	VERB
iajs-1009	107	58	the	the	DET
iajs-1009	107	59	points	point	NOUN
iajs-1009	107	60	of	of	ADP
iajs-1009	107	61	the	the	DET
iajs-1009	107	62	arc	arc	NOUN
iajs-1009	107	63	a	a	DET
iajs-1009	107	64	in	in	ADP
iajs-1009	107	65	(	(	PUNCT
iajs-1009	107	66	1	1	NUM
iajs-1009	107	67	)	)	PUNCT
iajs-1009	107	68	,	,	PUNCT
iajs-1009	107	69	we	we	PRON
iajs-1009	107	70	get	get	VERB
iajs-1009	107	71	:	:	PUNCT
iajs-1009	107	72	1	1	NUM
iajs-1009	107	73	=	=	SYM
iajs-1009	107	74	(	(	PUNCT
iajs-1009	107	75	1,0,0	1,0,0	NUM
iajs-1009	107	76	)	)	PUNCT
iajs-1009	107	77			NOUN
iajs-1009	107	78	a1	a1	NOUN
iajs-1009	107	79	=	=	SYM
iajs-1009	107	80	0	0	NUM
iajs-1009	107	81	,	,	PUNCT
iajs-1009	107	82	2	2	NUM
iajs-1009	107	83	=	=	SYM
iajs-1009	107	84	(	(	PUNCT
iajs-1009	107	85	0,1,0	0,1,0	NUM
iajs-1009	107	86	)	)	PUNCT
iajs-1009	107	87			PROPN
iajs-1009	107	88	a2	a2	PROPN
iajs-1009	107	89	=	=	PROPN
iajs-1009	107	90	0	0	PROPN
iajs-1009	107	91	,	,	PUNCT
iajs-1009	107	92	6	6	NUM
iajs-1009	107	93	=	=	SYM
iajs-1009	107	94	(	(	PUNCT
iajs-1009	107	95	0,0,1	0,0,1	NOUN
iajs-1009	107	96	)	)	PUNCT
iajs-1009	107	97			PROPN
iajs-1009	107	98	a3	a3	NOUN
iajs-1009	107	99	=	=	SYM
iajs-1009	107	100	0	0	NUM
iajs-1009	107	101	,	,	PUNCT
iajs-1009	107	102	11	11	NUM
iajs-1009	107	103	=	=	SYM
iajs-1009	107	104	(	(	PUNCT
iajs-1009	107	105	1,1,1	1,1,1	NUM
iajs-1009	107	106	)	)	PUNCT
iajs-1009	107	107			NOUN
iajs-1009	107	108	a4	a4	NOUN
iajs-1009	107	109	+	+	CCONJ
iajs-1009	107	110	a5	a5	NOUN
iajs-1009	107	111	+	+	CCONJ
iajs-1009	107	112	a6	a6	NOUN
iajs-1009	107	113	=	=	SYM
iajs-1009	107	114	0	0	X
iajs-1009	107	115	.	.	PUNCT
iajs-1009	108	1	so	so	ADV
iajs-1009	108	2	(	(	PUNCT
iajs-1009	108	3	1	1	X
iajs-1009	108	4	)	)	PUNCT
iajs-1009	108	5	becomes	become	VERB
iajs-1009	108	6	:	:	PUNCT
iajs-1009	108	7	a4	a4	NOUN
iajs-1009	108	8	x1	x1	NOUN
iajs-1009	108	9	x2	x2	PROPN
iajs-1009	109	1	+	+	CCONJ
iajs-1009	109	2	a5	a5	PROPN
iajs-1009	109	3	x1	x1	NUM
iajs-1009	109	4	x3	x3	PROPN
iajs-1009	109	5	+	+	CCONJ
iajs-1009	110	1	a6	a6	ADJ
iajs-1009	110	2	x2	x2	NOUN
iajs-1009	110	3	x3	x3	PROPN
iajs-1009	110	4	=	=	SYM
iajs-1009	110	5	0	0	NUM
iajs-1009	110	6	…	…	PUNCT
iajs-1009	110	7	…	…	SYM
iajs-1009	110	8	……	……	NOUN
iajs-1009	110	9	…	…	PUNCT
iajs-1009	110	10	…	…	SYM
iajs-1009	110	11	…	…	PUNCT
iajs-1009	110	12	…	…	PUNCT
iajs-1009	110	13	…	…	PUNCT
iajs-1009	110	14	…	…	PUNCT
iajs-1009	110	15	…	…	PUNCT
iajs-1009	110	16	…	…	PUNCT
iajs-1009	110	17	…	…	PUNCT
iajs-1009	110	18	…	…	PUNCT
iajs-1009	110	19	...	...	PUNCT
iajs-1009	110	20	(	(	PUNCT
iajs-1009	110	21	2	2	X
iajs-1009	110	22	)	)	PUNCT
iajs-1009	110	23	if	if	SCONJ
iajs-1009	110	24	a4	a4	NOUN
iajs-1009	110	25	=	=	SYM
iajs-1009	110	26	0	0	NUM
iajs-1009	110	27	,	,	PUNCT
iajs-1009	110	28	then	then	ADV
iajs-1009	110	29	a5	a5	PROPN
iajs-1009	110	30	x1	x1	PROPN
iajs-1009	110	31	x3	x3	PROPN
iajs-1009	111	1	+	+	CCONJ
iajs-1009	111	2	a6	a6	ADJ
iajs-1009	111	3	x2	x2	NOUN
iajs-1009	111	4	x3	x3	PROPN
iajs-1009	111	5	=	=	SYM
iajs-1009	111	6	0	0	NUM
iajs-1009	111	7	,	,	PUNCT
iajs-1009	111	8	and	and	CCONJ
iajs-1009	111	9	hence	hence	ADV
iajs-1009	111	10	(	(	PUNCT
iajs-1009	111	11	a5	a5	PROPN
iajs-1009	111	12	x1	x1	PROPN
iajs-1009	111	13	+	+	PUNCT
iajs-1009	111	14	a6	a6	NOUN
iajs-1009	111	15	x2	x2	NOUN
iajs-1009	111	16	)	)	PUNCT
iajs-1009	111	17	x3=	x3=	PUNCT
iajs-1009	111	18	0	0	PUNCT
iajs-1009	112	1	then	then	ADV
iajs-1009	112	2	the	the	DET
iajs-1009	112	3	conic	conic	NOUN
iajs-1009	112	4	is	be	AUX
iajs-1009	112	5	degenerated	degenerated	ADJ
iajs-1009	112	6	,	,	PUNCT
iajs-1009	112	7	therefore	therefore	ADV
iajs-1009	112	8	for	for	ADP
iajs-1009	112	9	a4	a4	NOUN
iajs-1009	112	10			NOUN
iajs-1009	112	11	0	0	NUM
iajs-1009	112	12	,	,	PUNCT
iajs-1009	112	13	similarly	similarly	ADV
iajs-1009	112	14	a5	a5	PROPN
iajs-1009	112	15			PROPN
iajs-1009	112	16	0	0	NUM
iajs-1009	112	17	and	and	CCONJ
iajs-1009	112	18	a6	a6	PROPN
iajs-1009	112	19			NOUN
iajs-1009	112	20	0	0	X
iajs-1009	112	21	.	.	X
iajs-1009	113	1	dividing	divide	VERB
iajs-1009	113	2	equation	equation	NOUN
iajs-1009	113	3	(	(	PUNCT
iajs-1009	113	4	2	2	NUM
iajs-1009	113	5	)	)	PUNCT
iajs-1009	113	6	by	by	ADP
iajs-1009	113	7	a4	a4	NUM
iajs-1009	113	8	,	,	PUNCT
iajs-1009	113	9	we	we	PRON
iajs-1009	113	10	get	get	VERB
iajs-1009	113	11	:	:	PUNCT
iajs-1009	114	1	x1	x1	PROPN
iajs-1009	114	2	x2	x2	PROPN
iajs-1009	115	1	+	+	PUNCT
iajs-1009	115	2			X
iajs-1009	115	3	x1	x1	NUM
iajs-1009	115	4	x3	x3	PROPN
iajs-1009	115	5	+	+	CCONJ
iajs-1009	116	1			NOUN
iajs-1009	116	2	x2	x2	NOUN
iajs-1009	116	3	x3	x3	NOUN
iajs-1009	116	4	=	=	SYM
iajs-1009	116	5	0	0	NUM
iajs-1009	116	6	…	…	PUNCT
iajs-1009	116	7	…	…	PUNCT
iajs-1009	116	8	…	…	PUNCT
iajs-1009	116	9	…	…	PUNCT
iajs-1009	116	10	…	…	PUNCT
iajs-1009	116	11	…	…	PUNCT
iajs-1009	116	12	…	…	PUNCT
iajs-1009	116	13	…	…	PUNCT
iajs-1009	116	14	…	…	PUNCT
iajs-1009	116	15	…	…	PUNCT
iajs-1009	116	16	…	…	PUNCT
iajs-1009	116	17	…	…	PUNCT
iajs-1009	116	18	…	…	PUNCT
iajs-1009	116	19	…	…	PUNCT
iajs-1009	116	20	…	…	PUNCT
iajs-1009	116	21	..	..	PUNCT
iajs-1009	116	22	…	…	PUNCT
iajs-1009	116	23	(	(	PUNCT
iajs-1009	116	24	3	3	NUM
iajs-1009	116	25	)	)	PUNCT
iajs-1009	116	26	where	where	SCONJ
iajs-1009	116	27	5	5	NUM
iajs-1009	116	28	6	6	NUM
iajs-1009	116	29	1	1	NUM
iajs-1009	116	30	2	2	NUM
iajs-1009	116	31	1	1	NUM
iajs-1009	116	32	3	3	NUM
iajs-1009	116	33	2	2	NUM
iajs-1009	116	34	3	3	NUM
iajs-1009	116	35	4	4	NUM
iajs-1009	116	36	4	4	NUM
iajs-1009	116	37	a	a	DET
iajs-1009	116	38	a	a	DET
iajs-1009	116	39	x	x	NOUN
iajs-1009	116	40	x	x	SYM
iajs-1009	116	41	x	x	SYM
iajs-1009	116	42	x	x	PUNCT
iajs-1009	116	43	x	x	PUNCT
iajs-1009	116	44	x	x	SYM
iajs-1009	116	45	0	0	PUNCT
iajs-1009	116	46	a	a	PRON
iajs-1009	116	47	a	a	DET
iajs-1009	116	48			ADJ
iajs-1009	116	49			X
iajs-1009	116	50			PROPN
iajs-1009	116	51	where	where	SCONJ
iajs-1009	116	52	5	5	NUM
iajs-1009	116	53	6	6	NUM
iajs-1009	116	54	4	4	NUM
iajs-1009	116	55	4	4	NUM
iajs-1009	116	56	a	a	DET
iajs-1009	116	57	a	a	NOUN
iajs-1009	116	58	,	,	PUNCT
iajs-1009	116	59	a	a	DET
iajs-1009	116	60	a	a	DET
iajs-1009	116	61			NOUN
iajs-1009	116	62			VERB
iajs-1009	116	63			PROPN
iajs-1009	116	64	,	,	PUNCT
iajs-1009	116	65	then	then	ADV
iajs-1009	116	66			PROPN
iajs-1009	116	67	=	=	SYM
iajs-1009	116	68	–	–	PUNCT
iajs-1009	116	69	(	(	PUNCT
iajs-1009	116	70	1	1	NUM
iajs-1009	116	71	+	+	NUM
iajs-1009	116	72			NOUN
iajs-1009	116	73	)	)	PUNCT
iajs-1009	116	74	since	since	SCONJ
iajs-1009	116	75	1	1	NUM
iajs-1009	116	76	+	+	NUM
iajs-1009	116	77			NOUN
iajs-1009	116	78	+	+	NOUN
iajs-1009	116	79			NOUN
iajs-1009	116	80	=	=	SYM
iajs-1009	116	81	0	0	NUM
iajs-1009	116	82	(	(	PUNCT
iajs-1009	116	83	mod.4	mod.4	NOUN
iajs-1009	116	84	)	)	PUNCT
iajs-1009	117	1	so	so	CCONJ
iajs-1009	117	2	x1	x1	PROPN
iajs-1009	117	3	x2	x2	PROPN
iajs-1009	118	1	+	+	PUNCT
iajs-1009	118	2			X
iajs-1009	118	3	x1	x1	PROPN
iajs-1009	118	4	x3	x3	ADJ
iajs-1009	118	5	–	–	PUNCT
iajs-1009	118	6	(	(	PUNCT
iajs-1009	118	7	1	1	NUM
iajs-1009	118	8	+	+	NUM
iajs-1009	118	9			NOUN
iajs-1009	118	10	)	)	PUNCT
iajs-1009	119	1	x2	x2	NOUN
iajs-1009	119	2	x3	x3	NOUN
iajs-1009	119	3	=	=	SYM
iajs-1009	119	4	0	0	NUM
iajs-1009	119	5	…	…	PUNCT
iajs-1009	119	6	…	…	PUNCT
iajs-1009	119	7	…	…	PUNCT
iajs-1009	119	8	…	…	PUNCT
iajs-1009	119	9	…	…	PUNCT
iajs-1009	119	10	…	…	PUNCT
iajs-1009	119	11	…	…	PUNCT
iajs-1009	119	12	…	…	PUNCT
iajs-1009	119	13	…	…	PUNCT
iajs-1009	119	14	…	…	PUNCT
iajs-1009	119	15	…	…	PUNCT
iajs-1009	119	16	…	…	PUNCT
iajs-1009	119	17	..	..	PUNCT
iajs-1009	119	18	…	…	PUNCT
iajs-1009	119	19	(	(	PUNCT
iajs-1009	119	20	4	4	NUM
iajs-1009	119	21	)	)	PUNCT
iajs-1009	119	22	where	where	SCONJ
iajs-1009	119	23			NOUN
iajs-1009	119	24			NOUN
iajs-1009	119	25	0	0	NUM
iajs-1009	119	26	and	and	CCONJ
iajs-1009	119	27			NOUN
iajs-1009	119	28			NOUN
iajs-1009	119	29	1	1	NUM
iajs-1009	119	30	for	for	ADP
iajs-1009	119	31	if	if	SCONJ
iajs-1009	119	32			NOUN
iajs-1009	119	33	=	=	SYM
iajs-1009	119	34	0	0	NUM
iajs-1009	119	35	or	or	CCONJ
iajs-1009	119	36			NOUN
iajs-1009	119	37	=	=	SYM
iajs-1009	119	38	1	1	NUM
iajs-1009	119	39	,	,	PUNCT
iajs-1009	119	40	we	we	PRON
iajs-1009	119	41	get	get	VERB
iajs-1009	119	42	a	a	DET
iajs-1009	119	43	degenerated	degenerated	ADJ
iajs-1009	119	44	conics	conic	NOUN
iajs-1009	119	45	,	,	PUNCT
iajs-1009	119	46	i.e.	i.e.	X
iajs-1009	119	47			X
iajs-1009	119	48	=	=	SYM
iajs-1009	119	49	2	2	NUM
iajs-1009	119	50	,	,	PUNCT
iajs-1009	119	51	3	3	NUM
iajs-1009	119	52	.	.	NOUN
iajs-1009	119	53	3.5	3.5	NUM
iajs-1009	119	54	the	the	DET
iajs-1009	119	55	equation	equation	NOUN
iajs-1009	119	56	of	of	ADP
iajs-1009	119	57	the	the	DET
iajs-1009	119	58	conics	conic	NOUN
iajs-1009	119	59	of	of	ADP
iajs-1009	119	60	pg(2,4	pg(2,4	NOUN
iajs-1009	119	61	)	)	PUNCT
iajs-1009	119	62	and	and	CCONJ
iajs-1009	119	63	the	the	DET
iajs-1009	119	64	complete	complete	ADJ
iajs-1009	119	65	arcs	arc	NOUN
iajs-1009	119	66	for	for	ADP
iajs-1009	119	67	any	any	DET
iajs-1009	119	68	value	value	NOUN
iajs-1009	119	69	of	of	ADP
iajs-1009	119	70			NOUN
iajs-1009	119	71	there	there	PRON
iajs-1009	119	72	is	be	VERB
iajs-1009	119	73	a	a	DET
iajs-1009	119	74	unique	unique	ADJ
iajs-1009	119	75	conic	conic	NOUN
iajs-1009	119	76	contains	contain	VERB
iajs-1009	119	77	the	the	DET
iajs-1009	119	78	reference	reference	NOUN
iajs-1009	119	79	and	and	CCONJ
iajs-1009	119	80	the	the	DET
iajs-1009	119	81	unit	unit	NOUN
iajs-1009	119	82	points	point	VERB
iajs-1009	119	83	.	.	PUNCT
iajs-1009	120	1	1	1	X
iajs-1009	120	2	.	.	X
iajs-1009	121	1	if	if	SCONJ
iajs-1009	121	2			NOUN
iajs-1009	121	3	=	=	SYM
iajs-1009	121	4	2	2	NUM
iajs-1009	121	5	,	,	PUNCT
iajs-1009	121	6	then	then	ADV
iajs-1009	121	7	the	the	DET
iajs-1009	121	8	equation	equation	NOUN
iajs-1009	121	9	of	of	ADP
iajs-1009	121	10	the	the	DET
iajs-1009	121	11	conic	conic	ADJ
iajs-1009	121	12	c1	c1	NOUN
iajs-1009	121	13	is	be	AUX
iajs-1009	121	14	x1	x1	PROPN
iajs-1009	121	15	x2	x2	PROPN
iajs-1009	122	1	+	+	CCONJ
iajs-1009	122	2	2	2	NUM
iajs-1009	122	3	x1	x1	NUM
iajs-1009	122	4	x3	x3	ADJ
iajs-1009	123	1	+	+	CCONJ
iajs-1009	123	2	x2	x2	ADJ
iajs-1009	123	3	x3	x3	NOUN
iajs-1009	123	4	=	=	SYM
iajs-1009	123	5	0	0	NUM
iajs-1009	123	6	,	,	PUNCT
iajs-1009	123	7	the	the	DET
iajs-1009	123	8	points	point	NOUN
iajs-1009	123	9	of	of	ADP
iajs-1009	123	10	c1	c1	PROPN
iajs-1009	123	11	are	be	AUX
iajs-1009	123	12	{	{	PUNCT
iajs-1009	123	13	1,2,6,11,12,21	1,2,6,11,12,21	NUM
iajs-1009	123	14	}	}	PUNCT
iajs-1009	123	15	,	,	PUNCT
iajs-1009	123	16	which	which	PRON
iajs-1009	123	17	is	be	AUX
iajs-1009	123	18	not	not	PART
iajs-1009	123	19	a	a	DET
iajs-1009	123	20	complete	complete	ADJ
iajs-1009	123	21	(	(	PUNCT
iajs-1009	123	22	k,3)-arc	k,3)-arc	X
iajs-1009	123	23	,	,	PUNCT
iajs-1009	123	24	since	since	SCONJ
iajs-1009	123	25	there	there	PRON
iajs-1009	123	26	exist	exist	VERB
iajs-1009	123	27	the	the	DET
iajs-1009	123	28	points	point	NOUN
iajs-1009	123	29	{	{	PUNCT
iajs-1009	123	30	4,5,7,8,9,14,15,17,18,19,20	4,5,7,8,9,14,15,17,18,19,20	NUM
iajs-1009	123	31	}	}	PUNCT
iajs-1009	123	32	which	which	PRON
iajs-1009	123	33	are	be	AUX
iajs-1009	123	34	the	the	DET
iajs-1009	123	35	points	point	NOUN
iajs-1009	123	36	of	of	ADP
iajs-1009	123	37	index	index	NOUN
iajs-1009	123	38	zero	zero	NUM
iajs-1009	123	39	for	for	ADP
iajs-1009	123	40	c1	c1	PROPN
iajs-1009	123	41	.	.	PUNCT
iajs-1009	124	1	now	now	ADV
iajs-1009	124	2	,	,	PUNCT
iajs-1009	124	3	we	we	PRON
iajs-1009	124	4	add	add	VERB
iajs-1009	124	5	to	to	ADP
iajs-1009	124	6	c1	c1	PROPN
iajs-1009	124	7	three	three	NUM
iajs-1009	124	8	points	point	NOUN
iajs-1009	124	9	of	of	ADP
iajs-1009	124	10	index	index	NOUN
iajs-1009	124	11	zero	zero	NUM
iajs-1009	124	12	which	which	PRON
iajs-1009	124	13	are	be	AUX
iajs-1009	124	14	{	{	PUNCT
iajs-1009	124	15	4,7,8	4,7,8	NOUN
iajs-1009	124	16	}	}	PUNCT
iajs-1009	124	17	.	.	PUNCT
iajs-1009	125	1	then	then	ADV
iajs-1009	125	2	1c	1c	NUM
iajs-1009	125	3	=	=	SYM
iajs-1009	125	4	{	{	PUNCT
iajs-1009	125	5	1,2,6,11,12,21,4,7,8	1,2,6,11,12,21,4,7,8	NUM
iajs-1009	125	6	}	}	PUNCT
iajs-1009	125	7	is	be	AUX
iajs-1009	125	8	a	a	DET
iajs-1009	125	9	complete	complete	ADJ
iajs-1009	125	10	(	(	PUNCT
iajs-1009	125	11	9,3)-arc	9,3)-arc	NUM
iajs-1009	125	12	,	,	PUNCT
iajs-1009	125	13	since	since	SCONJ
iajs-1009	125	14	c0	c0	PROPN
iajs-1009	125	15	=	=	PROPN
iajs-1009	125	16	0	0	PUNCT
iajs-1009	125	17	and	and	CCONJ
iajs-1009	125	18	1c	1c	NUM
iajs-1009	125	19	is	be	AUX
iajs-1009	125	20	maximum	maximum	ADJ
iajs-1009	125	21	arc	arc	NOUN
iajs-1009	125	22	.	.	PUNCT
iajs-1009	126	1	2	2	X
iajs-1009	126	2	.	.	X
iajs-1009	126	3	if	if	SCONJ
iajs-1009	126	4			NOUN
iajs-1009	126	5	=	=	SYM
iajs-1009	126	6	3	3	NUM
iajs-1009	126	7	,	,	PUNCT
iajs-1009	126	8	then	then	ADV
iajs-1009	126	9	the	the	DET
iajs-1009	126	10	equation	equation	NOUN
iajs-1009	126	11	of	of	ADP
iajs-1009	126	12	the	the	DET
iajs-1009	126	13	conic	conic	ADJ
iajs-1009	126	14	c2	c2	PROPN
iajs-1009	126	15	is	be	AUX
iajs-1009	126	16	x1	x1	PROPN
iajs-1009	126	17	x2	x2	PROPN
iajs-1009	127	1	+	+	CCONJ
iajs-1009	127	2	3	3	NUM
iajs-1009	127	3	x1	x1	NUM
iajs-1009	127	4	x3	x3	ADJ
iajs-1009	127	5	+	+	CCONJ
iajs-1009	127	6	2	2	NUM
iajs-1009	127	7	x2	x2	NOUN
iajs-1009	127	8	x3	x3	NOUN
iajs-1009	127	9	=	=	SYM
iajs-1009	127	10	0	0	NUM
iajs-1009	127	11	,	,	PUNCT
iajs-1009	127	12	the	the	DET
iajs-1009	127	13	points	point	NOUN
iajs-1009	127	14	of	of	ADP
iajs-1009	127	15	c2	c2	PROPN
iajs-1009	127	16	are	be	AUX
iajs-1009	127	17	{	{	PUNCT
iajs-1009	127	18	1,2,6,11,17	1,2,6,11,17	NUM
iajs-1009	127	19	}	}	PUNCT
iajs-1009	127	20	,	,	PUNCT
iajs-1009	127	21	which	which	PRON
iajs-1009	127	22	is	be	AUX
iajs-1009	127	23	not	not	PART
iajs-1009	127	24	a	a	DET
iajs-1009	127	25	complete	complete	ADJ
iajs-1009	127	26	(	(	PUNCT
iajs-1009	127	27	k,2)-arc	k,2)-arc	NOUN
iajs-1009	127	28	,	,	PUNCT
iajs-1009	127	29	since	since	SCONJ
iajs-1009	127	30	there	there	PRON
iajs-1009	127	31	exist	exist	VERB
iajs-1009	127	32	one	one	NUM
iajs-1009	127	33	point	point	NOUN
iajs-1009	127	34	{	{	PUNCT
iajs-1009	127	35	20	20	NUM
iajs-1009	127	36	}	}	PUNCT
iajs-1009	127	37	which	which	PRON
iajs-1009	127	38	is	be	AUX
iajs-1009	127	39	the	the	DET
iajs-1009	127	40	point	point	NOUN
iajs-1009	127	41	of	of	ADP
iajs-1009	127	42	index	index	NOUN
iajs-1009	127	43	zero	zero	NUM
iajs-1009	127	44	for	for	ADP
iajs-1009	127	45	c2	c2	PROPN
iajs-1009	127	46	.	.	PUNCT
iajs-1009	128	1	now	now	ADV
iajs-1009	128	2	,	,	PUNCT
iajs-1009	128	3	we	we	PRON
iajs-1009	128	4	add	add	VERB
iajs-1009	128	5	to	to	ADP
iajs-1009	128	6	c2	c2	PROPN
iajs-1009	128	7	one	one	NUM
iajs-1009	128	8	point	point	NOUN
iajs-1009	128	9	of	of	ADP
iajs-1009	128	10	index	index	NOUN
iajs-1009	128	11	zero	zero	NUM
iajs-1009	128	12	{	{	PUNCT
iajs-1009	128	13	20	20	NUM
iajs-1009	128	14	}	}	PUNCT
iajs-1009	128	15	.	.	PUNCT
iajs-1009	129	1	then	then	ADV
iajs-1009	129	2	2c	2c	NUM
iajs-1009	129	3	=	=	SYM
iajs-1009	129	4	{	{	PUNCT
iajs-1009	129	5	1,2,6,11,17,20	1,2,6,11,17,20	PROPN
iajs-1009	129	6	}	}	PUNCT
iajs-1009	129	7	is	be	AUX
iajs-1009	129	8	a	a	DET
iajs-1009	129	9	complete	complete	ADJ
iajs-1009	129	10	(	(	PUNCT
iajs-1009	129	11	6,2)-arc	6,2)-arc	NUM
iajs-1009	129	12	,	,	PUNCT
iajs-1009	129	13	since	since	SCONJ
iajs-1009	129	14	c0	c0	PROPN
iajs-1009	129	15	=	=	PROPN
iajs-1009	129	16	0	0	X
iajs-1009	129	17	.	.	X
iajs-1009	130	1	conclusion	conclusion	NOUN
iajs-1009	130	2	:	:	PUNCT
iajs-1009	131	1	1	1	X
iajs-1009	131	2	.	.	X
iajs-1009	131	3	each	each	PRON
iajs-1009	131	4	of	of	ADP
iajs-1009	131	5	c1	c1	PROPN
iajs-1009	131	6	and	and	CCONJ
iajs-1009	131	7	c2	c2	PROPN
iajs-1009	131	8	is	be	AUX
iajs-1009	131	9	not	not	PART
iajs-1009	131	10	complete	complete	ADJ
iajs-1009	131	11	(	(	PUNCT
iajs-1009	131	12	k,2)-arc	k,2)-arc	NOUN
iajs-1009	131	13	.	.	PROPN
iajs-1009	132	1	2	2	X
iajs-1009	132	2	.	.	X
iajs-1009	132	3	we	we	PRON
iajs-1009	132	4	add	add	VERB
iajs-1009	132	5	the	the	DET
iajs-1009	132	6	points	point	NOUN
iajs-1009	132	7	of	of	ADP
iajs-1009	132	8	index	index	NOUN
iajs-1009	132	9	zero	zero	NUM
iajs-1009	132	10	for	for	ADP
iajs-1009	132	11	each	each	PRON
iajs-1009	132	12	of	of	ADP
iajs-1009	132	13	them	they	PRON
iajs-1009	132	14	for	for	ADP
iajs-1009	132	15	completeness	completeness	NOUN
iajs-1009	132	16	.	.	PUNCT
iajs-1009	133	1	3	3	X
iajs-1009	133	2	.	.	X
iajs-1009	133	3	the	the	DET
iajs-1009	133	4	points	point	NOUN
iajs-1009	133	5	of	of	ADP
iajs-1009	133	6	index	index	NOUN
iajs-1009	133	7	zero	zero	NUM
iajs-1009	133	8	of	of	ADP
iajs-1009	133	9	pg(2,4	pg(2,4	NOUN
iajs-1009	133	10	)	)	PUNCT
iajs-1009	133	11	with	with	ADP
iajs-1009	133	12	respect	respect	NOUN
iajs-1009	133	13	to	to	ADP
iajs-1009	133	14	4	4	NUM
iajs-1009	133	15	-	-	PUNCT
iajs-1009	133	16	arc	arc	NOUN
iajs-1009	133	17	a	a	NOUN
iajs-1009	133	18	are	be	AUX
iajs-1009	133	19	in	in	ADP
iajs-1009	133	20	the	the	DET
iajs-1009	133	21	same	same	ADJ
iajs-1009	133	22	line	line	NOUN
iajs-1009	133	23	=	=	PUNCT
iajs-1009	133	24	{	{	PUNCT
iajs-1009	133	25	17,20	17,20	NOUN
iajs-1009	133	26	}	}	PUNCT
iajs-1009	133	27	.	.	PUNCT
iajs-1009	134	1	ibn	ibn	PROPN
iajs-1009	134	2	alhaitham	alhaitham	NOUN
iajs-1009	135	1	j.	j.	PROPN
iajs-1009	136	1	fo	fo	ADP
iajs-1009	136	2	r	r	NOUN
iajs-1009	136	3	pure	pure	ADJ
iajs-1009	136	4	&	&	CCONJ
iajs-1009	136	5	appl	appl	PROPN
iajs-1009	136	6	.	.	PUNCT
iajs-1009	137	1	sc	sc	PROPN
iajs-1009	137	2	i.	i.	PROPN
iajs-1009	137	3	vol.23	vol.23	PROPN
iajs-1009	137	4	(	(	PUNCT
iajs-1009	137	5	1	1	NUM
iajs-1009	137	6	)	)	PUNCT
iajs-1009	137	7	2010	2010	NUM
iajs-1009	137	8	3.6	3.6	NUM
iajs-1009	137	9	the	the	DET
iajs-1009	137	10	construction	construction	NOUN
iajs-1009	137	11	of	of	ADP
iajs-1009	137	12	complete	complete	ADJ
iajs-1009	137	13	and	and	CCONJ
iajs-1009	137	14	maximum	maximum	ADJ
iajs-1009	137	15	(	(	PUNCT
iajs-1009	137	16	k,3)-arc	k,3)-arc	VERB
iajs-1009	137	17	in	in	ADP
iajs-1009	137	18	pg(2,4	pg(2,4	NOUN
iajs-1009	137	19	)	)	PUNCT
iajs-1009	137	20	we	we	PRON
iajs-1009	137	21	will	will	AUX
iajs-1009	137	22	try	try	VERB
iajs-1009	137	23	to	to	PART
iajs-1009	137	24	get	get	VERB
iajs-1009	137	25	a	a	DET
iajs-1009	137	26	complete	complete	ADJ
iajs-1009	137	27	(	(	PUNCT
iajs-1009	137	28	k,3)-arc	k,3)-arc	VERB
iajs-1009	137	29	by	by	ADP
iajs-1009	137	30	taking	take	VERB
iajs-1009	137	31	the	the	DET
iajs-1009	137	32	complete	complete	ADJ
iajs-1009	137	33	(	(	PUNCT
iajs-1009	137	34	k,2)-arc	k,2)-arc	NOUN
iajs-1009	137	35	,	,	PUNCT
iajs-1009	137	36	say	say	VERB
iajs-1009	137	37	2c	2c	NUM
iajs-1009	137	38	and	and	CCONJ
iajs-1009	137	39	denoted	denote	VERB
iajs-1009	137	40	by	by	ADP
iajs-1009	137	41	b	b	NOUN
iajs-1009	137	42	,	,	PUNCT
iajs-1009	137	43	we	we	PRON
iajs-1009	137	44	notice	notice	VERB
iajs-1009	137	45	that	that	SCONJ
iajs-1009	137	46	b={1,2,6,11,17,20,5	b={1,2,6,11,17,20,5	PROPN
iajs-1009	137	47	}	}	PUNCT
iajs-1009	137	48	is	be	AUX
iajs-1009	137	49	incomplete	incomplete	ADJ
iajs-1009	137	50	(	(	PUNCT
iajs-1009	137	51	k,3)-arc	k,3)-arc	NOUN
iajs-1009	137	52	,	,	PUNCT
iajs-1009	137	53	since	since	SCONJ
iajs-1009	137	54	there	there	PRON
iajs-1009	137	55	exists	exist	VERB
iajs-1009	137	56	the	the	DET
iajs-1009	137	57	points	point	NOUN
iajs-1009	137	58	{	{	PUNCT
iajs-1009	137	59	7,9,10,12,14,16,19,21	7,9,10,12,14,16,19,21	NUM
iajs-1009	137	60	}	}	PUNCT
iajs-1009	137	61	which	which	PRON
iajs-1009	137	62	are	be	AUX
iajs-1009	137	63	the	the	DET
iajs-1009	137	64	points	point	NOUN
iajs-1009	137	65	of	of	ADP
iajs-1009	137	66	index	index	NOUN
iajs-1009	137	67	zero	zero	NUM
iajs-1009	137	68	for	for	ADP
iajs-1009	137	69	b.	b.	PROPN
iajs-1009	137	70	now	now	ADV
iajs-1009	137	71	,	,	PUNCT
iajs-1009	137	72	we	we	PRON
iajs-1009	137	73	add	add	VERB
iajs-1009	137	74	two	two	NUM
iajs-1009	137	75	points	point	NOUN
iajs-1009	137	76	of	of	ADP
iajs-1009	137	77	index	index	NOUN
iajs-1009	137	78	zero	zero	NUM
iajs-1009	137	79	which	which	PRON
iajs-1009	137	80	are	be	AUX
iajs-1009	137	81	{	{	PUNCT
iajs-1009	137	82	9,10	9,10	NUM
iajs-1009	137	83	}	}	PUNCT
iajs-1009	137	84	.	.	PUNCT
iajs-1009	138	1	then	then	ADV
iajs-1009	138	2	b={1,2,6,11,17,20,5,9,10	b={1,2,6,11,17,20,5,9,10	VERB
iajs-1009	138	3	}	}	PUNCT
iajs-1009	138	4	is	be	AUX
iajs-1009	138	5	a	a	DET
iajs-1009	138	6	complete	complete	ADJ
iajs-1009	138	7	(	(	PUNCT
iajs-1009	138	8	9,3)-arc	9,3)-arc	NUM
iajs-1009	138	9	,	,	PUNCT
iajs-1009	138	10	since	since	SCONJ
iajs-1009	138	11	c0	c0	PROPN
iajs-1009	138	12	=	=	SYM
iajs-1009	138	13	0	0	PUNCT
iajs-1009	138	14	and	and	CCONJ
iajs-1009	138	15	b	b	NOUN
iajs-1009	138	16	is	be	AUX
iajs-1009	138	17	a	a	DET
iajs-1009	138	18	maximum	maximum	ADJ
iajs-1009	138	19	arc	arc	NOUN
iajs-1009	138	20	.	.	PUNCT
iajs-1009	139	1	3.7	3.7	NUM
iajs-1009	139	2	the	the	DET
iajs-1009	139	3	construction	construction	NOUN
iajs-1009	139	4	of	of	ADP
iajs-1009	139	5	complete	complete	ADJ
iajs-1009	139	6	(	(	PUNCT
iajs-1009	139	7	k,4)-arc	k,4)-arc	X
iajs-1009	140	1	we	we	PRON
iajs-1009	140	2	try	try	VERB
iajs-1009	140	3	to	to	PART
iajs-1009	140	4	get	get	VERB
iajs-1009	140	5	a	a	DET
iajs-1009	140	6	complete	complete	ADJ
iajs-1009	140	7	(	(	PUNCT
iajs-1009	140	8	k,4)-arc	k,4)-arc	X
iajs-1009	140	9	by	by	ADP
iajs-1009	140	10	taking	take	VERB
iajs-1009	140	11	the	the	DET
iajs-1009	140	12	union	union	NOUN
iajs-1009	140	13	of	of	ADP
iajs-1009	140	14	two	two	NUM
iajs-1009	140	15	maximum	maximum	ADJ
iajs-1009	140	16	complete	complete	ADJ
iajs-1009	140	17	(	(	PUNCT
iajs-1009	140	18	k,3)-arcs	k,3)-arcs	INTJ
iajs-1009	140	19	,	,	PUNCT
iajs-1009	140	20	say	say	VERB
iajs-1009	140	21	1c	1c	NUM
iajs-1009	140	22	and	and	CCONJ
iajs-1009	140	23	b	b	NOUN
iajs-1009	140	24	denoted	denote	VERB
iajs-1009	140	25	by	by	ADP
iajs-1009	140	26	d	d	PROPN
iajs-1009	140	27	,	,	PUNCT
iajs-1009	140	28	we	we	PRON
iajs-1009	140	29	notice	notice	VERB
iajs-1009	140	30	that	that	SCONJ
iajs-1009	140	31	d	d	PROPN
iajs-1009	140	32	=	=	SYM
iajs-1009	140	33	{	{	PUNCT
iajs-1009	140	34	1,2,6,11,12,21,4,7,18,17,20,5,9,10	1,2,6,11,12,21,4,7,18,17,20,5,9,10	NUM
iajs-1009	140	35	}	}	PUNCT
iajs-1009	140	36	is	be	AUX
iajs-1009	140	37	incomplete	incomplete	ADJ
iajs-1009	140	38	(	(	PUNCT
iajs-1009	140	39	k,4)-arc	k,4)-arc	NOUN
iajs-1009	140	40	,	,	PUNCT
iajs-1009	140	41	since	since	SCONJ
iajs-1009	140	42	there	there	PRON
iajs-1009	140	43	exists	exist	VERB
iajs-1009	140	44	two	two	NUM
iajs-1009	140	45	points	point	NOUN
iajs-1009	140	46	{	{	PUNCT
iajs-1009	140	47	15,16	15,16	NUM
iajs-1009	140	48	}	}	PUNCT
iajs-1009	140	49	which	which	PRON
iajs-1009	140	50	are	be	AUX
iajs-1009	140	51	points	point	NOUN
iajs-1009	140	52	of	of	ADP
iajs-1009	140	53	index	index	NOUN
iajs-1009	140	54	zero	zero	NUM
iajs-1009	140	55	for	for	ADP
iajs-1009	140	56	d.	d.	PROPN
iajs-1009	140	57	now	now	ADV
iajs-1009	140	58	,	,	PUNCT
iajs-1009	140	59	we	we	PRON
iajs-1009	140	60	add	add	VERB
iajs-1009	140	61	the	the	DET
iajs-1009	140	62	two	two	NUM
iajs-1009	140	63	points	point	NOUN
iajs-1009	140	64	of	of	ADP
iajs-1009	140	65	index	index	NOUN
iajs-1009	140	66	zero	zero	NUM
iajs-1009	140	67	.	.	PUNCT
iajs-1009	141	1	then	then	ADV
iajs-1009	141	2	d	d	VERB
iajs-1009	141	3	=	=	SYM
iajs-1009	141	4	{	{	PUNCT
iajs-1009	141	5	1,2,6,11,12,21,4,7,18,17,20,5,9,10,15,16	1,2,6,11,12,21,4,7,18,17,20,5,9,10,15,16	NUM
iajs-1009	141	6	}	}	PUNCT
iajs-1009	141	7	is	be	AUX
iajs-1009	141	8	a	a	DET
iajs-1009	141	9	complete	complete	ADJ
iajs-1009	141	10	(	(	PUNCT
iajs-1009	141	11	16,4)-arc	16,4)-arc	NUM
iajs-1009	141	12	since	since	SCONJ
iajs-1009	141	13	c0	c0	PROPN
iajs-1009	141	14	=	=	PROPN
iajs-1009	141	15	0	0	NUM
iajs-1009	141	16	,	,	PUNCT
iajs-1009	141	17	and	and	CCONJ
iajs-1009	141	18	d	d	NOUN
iajs-1009	141	19	is	be	AUX
iajs-1009	141	20	a	a	DET
iajs-1009	141	21	maximum	maximum	ADJ
iajs-1009	141	22	arc	arc	NOUN
iajs-1009	141	23	.	.	PUNCT
iajs-1009	142	1	conclusion	conclusion	NOUN
iajs-1009	142	2	:	:	PUNCT
iajs-1009	142	3	1	1	X
iajs-1009	142	4	.	.	X
iajs-1009	142	5	there	there	PRON
iajs-1009	142	6	exists	exist	VERB
iajs-1009	142	7	one	one	NUM
iajs-1009	142	8	complete	complete	ADJ
iajs-1009	142	9	and	and	CCONJ
iajs-1009	142	10	maximum	maximum	ADJ
iajs-1009	142	11	(	(	PUNCT
iajs-1009	142	12	16,4)-arc	16,4)-arc	NUM
iajs-1009	142	13	.	.	NOUN
iajs-1009	143	1	2	2	X
iajs-1009	143	2	.	.	X
iajs-1009	143	3	the	the	DET
iajs-1009	143	4	points	point	NOUN
iajs-1009	143	5	of	of	ADP
iajs-1009	143	6	index	index	NOUN
iajs-1009	143	7	zero	zero	NUM
iajs-1009	143	8	of	of	ADP
iajs-1009	143	9	(	(	PUNCT
iajs-1009	143	10	k,4)-arc	k,4)-arc	X
iajs-1009	143	11	with	with	ADP
iajs-1009	143	12	respect	respect	NOUN
iajs-1009	143	13	are	be	AUX
iajs-1009	143	14	in	in	ADP
iajs-1009	143	15	the	the	DET
iajs-1009	143	16	same	same	ADJ
iajs-1009	143	17	line	line	NOUN
iajs-1009	143	18	.	.	PUNCT
iajs-1009	144	1	refrences	refrence	VERB
iajs-1009	144	2	:	:	PUNCT
iajs-1009	145	1	1	1	X
iajs-1009	145	2	.	.	X
iajs-1009	145	3	salih	salih	PROPN
iajs-1009	145	4	,	,	PUNCT
iajs-1009	145	5	r.	r.	PROPN
iajs-1009	145	6	a.	a.	PROPN
iajs-1009	145	7	,	,	PUNCT
iajs-1009	145	8	(	(	PUNCT
iajs-1009	145	9	1999	1999	NUM
iajs-1009	145	10	)	)	PUNCT
iajs-1009	145	11	,	,	PUNCT
iajs-1009	145	12	"	"	PUNCT
iajs-1009	145	13	complete	complete	ADJ
iajs-1009	145	14	arcs	arc	NOUN
iajs-1009	145	15	in	in	ADP
iajs-1009	145	16	projective	projective	ADJ
iajs-1009	145	17	plane	plane	NOUN
iajs-1009	145	18	over	over	ADP
iajs-1009	145	19	galois	galois	PROPN
iajs-1009	145	20	field	field	NOUN
iajs-1009	145	21	"	"	PUNCT
iajs-1009	145	22	,	,	PUNCT
iajs-1009	145	23	m.sc	m.sc	PROPN
iajs-1009	145	24	.	.	PUNCT
iajs-1009	146	1	thesis	thesis	NOUN
iajs-1009	146	2	,	,	PUNCT
iajs-1009	146	3	university	university	NOUN
iajs-1009	146	4	of	of	ADP
iajs-1009	146	5	baghdad	baghdad	PROPN
iajs-1009	146	6	,	,	PUNCT
iajs-1009	146	7	iraq	iraq	PROPN
iajs-1009	146	8	.	.	PUNCT
iajs-1009	147	1	2	2	X
iajs-1009	147	2	.	.	X
iajs-1009	147	3	hassan	hassan	PROPN
iajs-1009	147	4	,	,	PUNCT
iajs-1009	147	5	a.	a.	PROPN
iajs-1009	147	6	s.	s.	PROPN
iajs-1009	147	7	,	,	PUNCT
iajs-1009	147	8	(	(	PUNCT
iajs-1009	147	9	2001	2001	NUM
iajs-1009	147	10	)	)	PUNCT
iajs-1009	147	11	,	,	PUNCT
iajs-1009	147	12	"	"	PUNCT
iajs-1009	147	13	construction	construction	NOUN
iajs-1009	147	14	of	of	ADP
iajs-1009	147	15	(	(	PUNCT
iajs-1009	147	16	k,3	k,3	PROPN
iajs-1009	147	17	)	)	PUNCT
iajs-1009	147	18	–	–	PUNCT
iajs-1009	147	19	arcs	arc	NOUN
iajs-1009	147	20	in	in	ADP
iajs-1009	147	21	projective	projective	ADJ
iajs-1009	147	22	plane	plane	NOUN
iajs-1009	147	23	over	over	ADP
iajs-1009	147	24	galois	galois	PROPN
iajs-1009	147	25	field	field	NOUN
iajs-1009	147	26	gf(q	gf(q	NOUN
iajs-1009	147	27	)	)	PUNCT
iajs-1009	147	28	,	,	PUNCT
iajs-1009	147	29	q	q	NOUN
iajs-1009	148	1	=	=	PUNCT
iajs-1009	148	2	p	p	NOUN
iajs-1009	148	3	h	h	NOUN
iajs-1009	148	4	when	when	SCONJ
iajs-1009	148	5	p	p	PROPN
iajs-1009	148	6	=	=	SYM
iajs-1009	148	7	2	2	NUM
iajs-1009	148	8	and	and	CCONJ
iajs-1009	148	9	h	h	NOUN
iajs-1009	148	10	=	=	SYM
iajs-1009	148	11	2	2	NUM
iajs-1009	148	12	,	,	PUNCT
iajs-1009	148	13	3	3	NUM
iajs-1009	148	14	and	and	CCONJ
iajs-1009	148	15	4	4	NUM
iajs-1009	148	16	,	,	PUNCT
iajs-1009	148	17	m.sc	m.sc	PROPN
iajs-1009	148	18	.	.	PUNCT
iajs-1009	149	1	thesis	thesis	NOUN
iajs-1009	149	2	,	,	PUNCT
iajs-1009	149	3	university	university	NOUN
iajs-1009	149	4	of	of	ADP
iajs-1009	149	5	baghdad	baghdad	PROPN
iajs-1009	149	6	,	,	PUNCT
iajs-1009	149	7	iraq	iraq	PROPN
iajs-1009	149	8	.	.	PUNCT
iajs-1009	150	1	3	3	X
iajs-1009	150	2	.	.	X
iajs-1009	150	3	hirschfeld	hirschfeld	PROPN
iajs-1009	150	4	,	,	PUNCT
iajs-1009	150	5	t.	t.	PROPN
iajs-1009	150	6	w.	w.	PROPN
iajs-1009	150	7	and	and	CCONJ
iajs-1009	150	8	sadeh	sadeh	PROPN
iajs-1009	150	9	,	,	PUNCT
iajs-1009	150	10	a.	a.	PROPN
iajs-1009	150	11	r.	r.	PROPN
iajs-1009	150	12	,	,	PUNCT
iajs-1009	150	13	(	(	PUNCT
iajs-1009	150	14	1984	1984	NUM
iajs-1009	150	15	)	)	PUNCT
iajs-1009	150	16	,	,	PUNCT
iajs-1009	150	17	“	"	PUNCT
iajs-1009	150	18	the	the	DET
iajs-1009	150	19	projective	projective	ADJ
iajs-1009	150	20	plane	plane	NOUN
iajs-1009	150	21	over	over	ADP
iajs-1009	150	22	field	field	NOUN
iajs-1009	150	23	of	of	ADP
iajs-1009	150	24	eleven	eleven	NUM
iajs-1009	150	25	elements	element	NOUN
iajs-1009	150	26	“	"	PUNCT
iajs-1009	150	27	giessan	giessan	VERB
iajs-1009	150	28	.	.	PUNCT
iajs-1009	151	1	4	4	X
iajs-1009	151	2	.	.	X
iajs-1009	151	3	rutter	rutter	PROPN
iajs-1009	151	4	,	,	PUNCT
iajs-1009	151	5	j.	j.	PROPN
iajs-1009	151	6	w.	w.	PROPN
iajs-1009	151	7	,	,	PUNCT
iajs-1009	151	8	(	(	PUNCT
iajs-1009	151	9	2000	2000	NUM
iajs-1009	151	10	)	)	PUNCT
iajs-1009	151	11	,	,	PUNCT
iajs-1009	151	12	"	"	PUNCT
iajs-1009	151	13	geometry	geometry	NOUN
iajs-1009	151	14	of	of	ADP
iajs-1009	151	15	curves	curve	NOUN
iajs-1009	151	16	"	"	PUNCT
iajs-1009	151	17	,	,	PUNCT
iajs-1009	151	18	chapman	chapman	NOUN
iajs-1009	151	19	and	and	CCONJ
iajs-1009	151	20	hall	hall	PROPN
iajs-1009	151	21	/	/	SYM
iajs-1009	151	22	crc	crc	NOUN
iajs-1009	151	23	.	.	PROPN
iajs-1009	152	1	5	5	NUM
iajs-1009	152	2	.	.	X
iajs-1009	153	1	hirschfeld	hirschfeld	PROPN
iajs-1009	153	2	,	,	PUNCT
iajs-1009	153	3	t.	t.	PROPN
iajs-1009	153	4	w.	w.	PROPN
iajs-1009	153	5	,	,	PUNCT
iajs-1009	153	6	(	(	PUNCT
iajs-1009	153	7	1979	1979	NUM
iajs-1009	153	8	)	)	PUNCT
iajs-1009	153	9	,	,	PUNCT
iajs-1009	153	10	“	"	PUNCT
iajs-1009	153	11	projective	projective	ADJ
iajs-1009	153	12	geometrices	geometrice	NOUN
iajs-1009	153	13	over	over	ADP
iajs-1009	153	14	finite	finite	ADJ
iajs-1009	153	15	field	field	NOUN
iajs-1009	153	16	"	"	PUNCT
iajs-1009	153	17	,	,	PUNCT
iajs-1009	153	18	oxford	oxford	PROPN
iajs-1009	153	19	press	press	NOUN
iajs-1009	153	20	.	.	PUNCT
iajs-1009	154	1	6	6	NUM
iajs-1009	154	2	.	.	X
iajs-1009	154	3	thas	thas	PROPN
iajs-1009	154	4	,	,	PUNCT
iajs-1009	154	5	j.	j.	PROPN
iajs-1009	154	6	a.	a.	PROPN
iajs-1009	154	7	,	,	PUNCT
iajs-1009	154	8	(	(	PUNCT
iajs-1009	154	9	1987	1987	NUM
iajs-1009	154	10	)	)	PUNCT
iajs-1009	154	11	,	,	PUNCT
iajs-1009	154	12	"	"	PUNCT
iajs-1009	154	13	complete	complete	ADJ
iajs-1009	154	14	arcs	arc	NOUN
iajs-1009	154	15	and	and	CCONJ
iajs-1009	154	16	algebraic	algebraic	ADJ
iajs-1009	154	17	curves	curve	NOUN
iajs-1009	154	18	in	in	ADP
iajs-1009	154	19	pg(2,p	pg(2,p	NOUN
iajs-1009	154	20	)	)	PUNCT
iajs-1009	154	21	"	"	PUNCT
iajs-1009	154	22	,	,	PUNCT
iajs-1009	154	23	j.	j.	PROPN
iajs-1009	154	24	of	of	ADP
iajs-1009	154	25	algebra	algebra	PROPN
iajs-1009	154	26	,	,	PUNCT
iajs-1009	154	27	106(2	106(2	NUM
iajs-1009	154	28	):	):	PUNCT
iajs-1009	154	29	451	451	NUM
iajs-1009	154	30	-	-	SYM
iajs-1009	154	31	464	464	NUM
iajs-1009	154	32	.	.	PUNCT
iajs-1009	155	1	7	7	X
iajs-1009	155	2	.	.	X
iajs-1009	156	1	hughes	hughe	NOUN
iajs-1009	156	2	,	,	PUNCT
iajs-1009	156	3	d.	d.	PROPN
iajs-1009	156	4	r.	r.	PROPN
iajs-1009	156	5	and	and	CCONJ
iajs-1009	156	6	piper	piper	NOUN
iajs-1009	156	7	,	,	PUNCT
iajs-1009	156	8	f.	f.	PROPN
iajs-1009	156	9	c.	c.	PROPN
iajs-1009	156	10	,	,	PUNCT
iajs-1009	156	11	(	(	PUNCT
iajs-1009	156	12	1973	1973	NUM
iajs-1009	156	13	)	)	PUNCT
iajs-1009	156	14	,	,	PUNCT
iajs-1009	156	15	"	"	PUNCT
iajs-1009	156	16	projective	projective	ADJ
iajs-1009	156	17	planes	plane	NOUN
iajs-1009	156	18	"	"	PUNCT
iajs-1009	156	19	,	,	PUNCT
iajs-1009	156	20	springervelag	springervelag	NOUN
iajs-1009	156	21	,	,	PUNCT
iajs-1009	156	22	new	new	PROPN
iajs-1009	156	23	york	york	PROPN
iajs-1009	156	24	inc	inc	PROPN
iajs-1009	156	25	.	.	PROPN
iajs-1009	156	26	8	8	X
iajs-1009	156	27	.	.	X
iajs-1009	157	1	veblen	veblen	PROPN
iajs-1009	157	2	,	,	PUNCT
iajs-1009	157	3	o.	o.	NOUN
iajs-1009	157	4	and	and	CCONJ
iajs-1009	157	5	young	young	ADJ
iajs-1009	157	6	,	,	PUNCT
iajs-1009	157	7	j.	j.	PROPN
iajs-1009	157	8	w.	w.	PROPN
iajs-1009	157	9	,	,	PUNCT
iajs-1009	157	10	(	(	PUNCT
iajs-1009	157	11	1910	1910	NUM
iajs-1009	157	12	)	)	PUNCT
iajs-1009	157	13	,	,	PUNCT
iajs-1009	157	14	"	"	PUNCT
iajs-1009	157	15	projective	projective	ADJ
iajs-1009	157	16	geometry	geometry	NOUN
iajs-1009	157	17	"	"	PUNCT
iajs-1009	157	18	volment	volment	NOUN
iajs-1009	157	19	,	,	PUNCT
iajs-1009	157	20	ginn	ginn	PROPN
iajs-1009	157	21	.	.	PUNCT
iajs-1009	158	1	9	9	NUM
iajs-1009	158	2	.	.	PUNCT
iajs-1009	158	3	albert	albert	PROPN
iajs-1009	158	4	a.	a.	PROPN
iajs-1009	158	5	a.	a.	PROPN
iajs-1009	158	6	,	,	PUNCT
iajs-1009	158	7	(	(	PUNCT
iajs-1009	158	8	1968	1968	NUM
iajs-1009	158	9	)	)	PUNCT
iajs-1009	158	10	,	,	PUNCT
iajs-1009	158	11	"	"	PUNCT
iajs-1009	158	12	an	an	DET
iajs-1009	158	13	introduction	introduction	NOUN
iajs-1009	158	14	to	to	PART
iajs-1009	158	15	finite	finite	VERB
iajs-1009	158	16	projective	projective	PROPN
iajs-1009	158	17	plane	plane	NOUN
iajs-1009	158	18	"	"	PUNCT
iajs-1009	158	19	,	,	PUNCT
iajs-1009	158	20	holt	holt	PROPN
iajs-1009	158	21	rinehart	rinehart	PROPN
iajs-1009	158	22	and	and	CCONJ
iajs-1009	158	23	winston	winston	PROPN
iajs-1009	158	24	,	,	PUNCT
iajs-1009	158	25	inc	inc	PROPN
iajs-1009	158	26	.	.	PROPN
iajs-1009	158	27	ibn	ibn	PROPN
iajs-1009	158	28	alhaitham	alhaitham	PROPN
iajs-1009	158	29	j.	j.	PROPN
iajs-1009	159	1	fo	fo	ADP
iajs-1009	159	2	r	r	NOUN
iajs-1009	159	3	pure	pure	ADJ
iajs-1009	159	4	&	&	CCONJ
iajs-1009	159	5	appl	appl	PROPN
iajs-1009	159	6	.	.	PUNCT
iajs-1009	160	1	sc	sc	PROPN
iajs-1009	160	2	i.	i.	PROPN
iajs-1009	160	3	vol.23	vol.23	PROPN
iajs-1009	160	4	(	(	PUNCT
iajs-1009	160	5	1	1	NUM
iajs-1009	160	6	)	)	PUNCT
iajs-1009	160	7	2010	2010	NUM
iajs-1009	160	8	table	table	NOUN
iajs-1009	160	9	(	(	PUNCT
iajs-1009	160	10	1	1	NUM
iajs-1009	160	11	)	)	PUNCT
iajs-1009	160	12	the	the	DET
iajs-1009	160	13	addition	addition	NOUN
iajs-1009	160	14	's	's	PART
iajs-1009	160	15	and	and	CCONJ
iajs-1009	160	16	multiplications	multiplication	VERB
iajs-1009	160	17	operations	operation	NOUN
iajs-1009	160	18	of	of	ADP
iajs-1009	160	19	gf(4	gf(4	NOUN
iajs-1009	160	20	)	)	PUNCT
iajs-1009	160	21	table	table	NOUN
iajs-1009	160	22	(	(	PUNCT
iajs-1009	160	23	2	2	X
iajs-1009	160	24	)	)	PUNCT
iajs-1009	160	25	the	the	DET
iajs-1009	160	26	points	point	NOUN
iajs-1009	160	27	and	and	CCONJ
iajs-1009	160	28	lines	line	NOUN
iajs-1009	160	29	of	of	ADP
iajs-1009	160	30	pg(2,4	pg(2,4	NOUN
iajs-1009	160	31	)	)	PUNCT
iajs-1009	160	32	li	li	PROPN
iajs-1009	161	1	pi	pi	PROPN
iajs-1009	161	2	i	i	PRON
iajs-1009	161	3	18	18	NUM
iajs-1009	161	4	14	14	NUM
iajs-1009	161	5	10	10	NUM
iajs-1009	161	6	6	6	NUM
iajs-1009	161	7	2	2	NUM
iajs-1009	161	8	0	0	NUM
iajs-1009	161	9	0	0	NUM
iajs-1009	161	10	1	1	NUM
iajs-1009	161	11	1	1	NUM
iajs-1009	161	12	9	9	NUM
iajs-1009	161	13	8	8	NUM
iajs-1009	161	14	7	7	NUM
iajs-1009	161	15	6	6	NUM
iajs-1009	161	16	1	1	NUM
iajs-1009	161	17	0	0	NUM
iajs-1009	161	18	1	1	NUM
iajs-1009	161	19	0	0	NUM
iajs-1009	161	20	2	2	NUM
iajs-1009	161	21	21	21	NUM
iajs-1009	161	22	16	16	NUM
iajs-1009	161	23	11	11	NUM
iajs-1009	161	24	6	6	NUM
iajs-1009	161	25	3	3	NUM
iajs-1009	161	26	0	0	NUM
iajs-1009	161	27	1	1	NUM
iajs-1009	161	28	1	1	NUM
iajs-1009	161	29	3	3	NUM
iajs-1009	161	30	20	20	NUM
iajs-1009	161	31	15	15	NUM
iajs-1009	161	32	13	13	NUM
iajs-1009	161	33	6	6	NUM
iajs-1009	161	34	5	5	NUM
iajs-1009	161	35	0	0	NUM
iajs-1009	161	36	1	1	NUM
iajs-1009	161	37	2	2	NUM
iajs-1009	161	38	4	4	NUM
iajs-1009	161	39	19	19	NUM
iajs-1009	161	40	17	17	NUM
iajs-1009	161	41	12	12	NUM
iajs-1009	161	42	6	6	NUM
iajs-1009	161	43	4	4	NUM
iajs-1009	161	44	0	0	NUM
iajs-1009	161	45	1	1	NUM
iajs-1009	161	46	3	3	NUM
iajs-1009	161	47	5	5	NUM
iajs-1009	161	48	5	5	NUM
iajs-1009	161	49	4	4	NUM
iajs-1009	161	50	3	3	NUM
iajs-1009	161	51	2	2	NUM
iajs-1009	161	52	1	1	NUM
iajs-1009	161	53	1	1	NUM
iajs-1009	161	54	0	0	NUM
iajs-1009	161	55	0	0	NUM
iajs-1009	161	56	6	6	NUM
iajs-1009	161	57	19	19	NUM
iajs-1009	161	58	15	15	NUM
iajs-1009	161	59	11	11	NUM
iajs-1009	161	60	7	7	NUM
iajs-1009	161	61	2	2	NUM
iajs-1009	161	62	1	1	NUM
iajs-1009	161	63	0	0	NUM
iajs-1009	161	64	1	1	NUM
iajs-1009	161	65	7	7	NUM
iajs-1009	161	66	21	21	NUM
iajs-1009	161	67	17	17	NUM
iajs-1009	161	68	13	13	NUM
iajs-1009	161	69	9	9	NUM
iajs-1009	161	70	2	2	NUM
iajs-1009	161	71	1	1	NUM
iajs-1009	161	72	0	0	NUM
iajs-1009	161	73	2	2	NUM
iajs-1009	161	74	8	8	NUM
iajs-1009	161	75	20	20	NUM
iajs-1009	161	76	16	16	NUM
iajs-1009	161	77	12	12	NUM
iajs-1009	161	78	8	8	NUM
iajs-1009	161	79	2	2	NUM
iajs-1009	161	80	1	1	NUM
iajs-1009	161	81	0	0	NUM
iajs-1009	161	82	3	3	NUM
iajs-1009	161	83	9	9	NUM
iajs-1009	161	84	13	13	NUM
iajs-1009	161	85	12	12	NUM
iajs-1009	161	86	11	11	NUM
iajs-1009	161	87	10	10	NUM
iajs-1009	161	88	1	1	NUM
iajs-1009	161	89	1	1	NUM
iajs-1009	161	90	1	1	NUM
iajs-1009	161	91	0	0	NUM
iajs-1009	161	92	10	10	NUM
iajs-1009	161	93	20	20	NUM
iajs-1009	161	94	17	17	NUM
iajs-1009	161	95	10	10	NUM
iajs-1009	161	96	7	7	NUM
iajs-1009	161	97	3	3	NUM
iajs-1009	161	98	1	1	NUM
iajs-1009	161	99	1	1	NUM
iajs-1009	161	100	1	1	NUM
iajs-1009	161	101	11	11	NUM
iajs-1009	161	102	19	19	NUM
iajs-1009	161	103	16	16	NUM
iajs-1009	161	104	10	10	NUM
iajs-1009	161	105	9	9	NUM
iajs-1009	161	106	5	5	NUM
iajs-1009	161	107	1	1	NUM
iajs-1009	161	108	1	1	NUM
iajs-1009	161	109	2	2	NUM
iajs-1009	161	110	12	12	NUM
iajs-1009	161	111	21	21	NUM
iajs-1009	161	112	15	15	NUM
iajs-1009	161	113	10	10	NUM
iajs-1009	161	114	8	8	NUM
iajs-1009	161	115	4	4	NUM
iajs-1009	161	116	1	1	NUM
iajs-1009	161	117	1	1	NUM
iajs-1009	161	118	3	3	NUM
iajs-1009	161	119	13	13	NUM
iajs-1009	161	120	21	21	NUM
iajs-1009	161	121	20	20	NUM
iajs-1009	161	122	19	19	NUM
iajs-1009	161	123	18	18	NUM
iajs-1009	161	124	1	1	NUM
iajs-1009	161	125	1	1	NUM
iajs-1009	161	126	2	2	NUM
iajs-1009	161	127	0	0	NUM
iajs-1009	161	128	14	14	NUM
iajs-1009	161	129	18	18	NUM
iajs-1009	161	130	16	16	NUM
iajs-1009	161	131	13	13	NUM
iajs-1009	161	132	7	7	NUM
iajs-1009	161	133	4	4	NUM
iajs-1009	161	134	1	1	NUM
iajs-1009	161	135	2	2	NUM
iajs-1009	161	136	1	1	NUM
iajs-1009	161	137	15	15	NUM
iajs-1009	161	138	18	18	NUM
iajs-1009	161	139	15	15	NUM
iajs-1009	161	140	12	12	NUM
iajs-1009	161	141	9	9	NUM
iajs-1009	161	142	3	3	NUM
iajs-1009	161	143	1	1	NUM
iajs-1009	161	144	2	2	NUM
iajs-1009	161	145	2	2	NUM
iajs-1009	161	146	16	16	NUM
iajs-1009	161	147	18	18	NUM
iajs-1009	161	148	17	17	NUM
iajs-1009	161	149	11	11	NUM
iajs-1009	161	150	8	8	NUM
iajs-1009	161	151	5	5	NUM
iajs-1009	161	152	1	1	NUM
iajs-1009	161	153	2	2	NUM
iajs-1009	161	154	3	3	NUM
iajs-1009	161	155	17	17	NUM
iajs-1009	161	156	17	17	NUM
iajs-1009	161	157	16	16	NUM
iajs-1009	161	158	15	15	NUM
iajs-1009	161	159	14	14	NUM
iajs-1009	161	160	1	1	NUM
iajs-1009	161	161	1	1	NUM
iajs-1009	161	162	3	3	NUM
iajs-1009	161	163	0	0	NUM
iajs-1009	161	164	18	18	NUM
iajs-1009	161	165	21	21	NUM
iajs-1009	161	166	14	14	NUM
iajs-1009	161	167	12	12	NUM
iajs-1009	161	168	7	7	NUM
iajs-1009	161	169	5	5	NUM
iajs-1009	161	170	1	1	NUM
iajs-1009	161	171	3	3	NUM
iajs-1009	161	172	1	1	NUM
iajs-1009	161	173	19	19	NUM
iajs-1009	161	174	20	20	NUM
iajs-1009	161	175	14	14	NUM
iajs-1009	161	176	11	11	NUM
iajs-1009	161	177	9	9	NUM
iajs-1009	161	178	4	4	NUM
iajs-1009	161	179	1	1	NUM
iajs-1009	161	180	3	3	NUM
iajs-1009	161	181	2	2	NUM
iajs-1009	161	182	20	20	NUM
iajs-1009	161	183	19	19	NUM
iajs-1009	161	184	14	14	NUM
iajs-1009	161	185	13	13	NUM
iajs-1009	161	186	8	8	NUM
iajs-1009	161	187	3	3	NUM
iajs-1009	161	188	1	1	NUM
iajs-1009	161	189	3	3	NUM
iajs-1009	161	190	3	3	NUM
iajs-1009	161	191	21	21	NUM
iajs-1009	161	192	*	*	SYM
iajs-1009	161	193	1	1	NUM
iajs-1009	161	194	2	2	NUM
iajs-1009	161	195	3	3	NUM
iajs-1009	161	196	1	1	NUM
iajs-1009	161	197	1	1	NUM
iajs-1009	161	198	2	2	NUM
iajs-1009	161	199	3	3	NUM
iajs-1009	161	200	2	2	NUM
iajs-1009	161	201	2	2	NUM
iajs-1009	161	202	3	3	NUM
iajs-1009	161	203	1	1	NUM
iajs-1009	161	204	3	3	NUM
iajs-1009	161	205	3	3	NUM
iajs-1009	161	206	1	1	NUM
iajs-1009	161	207	2	2	NUM
iajs-1009	161	208	+	+	CCONJ
iajs-1009	161	209	0	0	NUM
iajs-1009	161	210	1	1	NUM
iajs-1009	161	211	2	2	NUM
iajs-1009	161	212	3	3	NUM
iajs-1009	161	213	0	0	NUM
iajs-1009	161	214	0	0	NUM
iajs-1009	161	215	1	1	NUM
iajs-1009	161	216	2	2	NUM
iajs-1009	161	217	3	3	NUM
iajs-1009	161	218	1	1	NUM
iajs-1009	161	219	1	1	NUM
iajs-1009	161	220	0	0	NUM
iajs-1009	161	221	3	3	NUM
iajs-1009	161	222	2	2	NUM
iajs-1009	161	223	2	2	NUM
iajs-1009	161	224	2	2	NUM
iajs-1009	161	225	3	3	NUM
iajs-1009	161	226	0	0	NUM
iajs-1009	161	227	1	1	NUM
iajs-1009	161	228	3	3	NUM
iajs-1009	161	229	3	3	NUM
iajs-1009	161	230	2	2	NUM
iajs-1009	161	231	1	1	NUM
iajs-1009	161	232	0	0	NUM
iajs-1009	161	233	\	\	NOUN
iajs-1009	161	234	2010	2010	NUM
iajs-1009	161	235	)	)	PUNCT
iajs-1009	161	236	1	1	NUM
iajs-1009	161	237	(	(	PUNCT
iajs-1009	161	238	23المجلد	23المجلد	NUM
iajs-1009	161	239	مجلة	مجلة	VERB
iajs-1009	161	240	ابن	ابن	PROPN
iajs-1009	161	241	الھیثم	الھیثم	PROPN
iajs-1009	161	242	للعلوم	للعلوم	PROPN
iajs-1009	161	243	الصرفة	الصرفة	PROPN
iajs-1009	161	244	والتطبیقیة	والتطبیقیة	PROPN
iajs-1009	161	245	بطریقة	بطریقة	PROPN
iajs-1009	161	246	هندسیة	هندسیة	PROPN
iajs-1009	161	247	pg)(2,4األقواس	pg)(2,4األقواس	PROPN
iajs-1009	161	248	العظمى	العظمى	AUX
iajs-1009	161	249	الكاملة	الكاملة	VERB
iajs-1009	161	250	في	في	ADP
iajs-1009	161	251	المستوى	المستوى	PROPN
iajs-1009	161	252	االسقاطي	االسقاطي	PROPN
iajs-1009	161	253	سوسن	سوسن	ADP
iajs-1009	161	254	جواد	جواد	NOUN
iajs-1009	161	255	كاظم	كاظم	NOUN
iajs-1009	161	256	قسم	قسم	PROPN
iajs-1009	161	257	الریاضیات	الریاضیات	PROPN
iajs-1009	161	258	،	،	PROPN
iajs-1009	161	259	ابن	ابن	X
iajs-1009	161	260	الهیثم	الهیثم	PROPN
iajs-1009	161	261	،	،	PROPN
iajs-1009	161	262	كلیة	كلیة	PROPN
iajs-1009	161	263	التربیة	التربیة	PROPN
iajs-1009	161	264	،	،	PROPN
iajs-1009	161	265	جامعة	جامعة	PROPN
iajs-1009	161	266	بغداد	بغداد	PROPN
iajs-1009	161	267	الخالصه	الخالصه	PROPN
iajs-1009	161	268	إن	إن	PROPN
iajs-1009	161	269	،	،	PROPN
iajs-1009	161	270	إذ	إذ	PROPN
iajs-1009	161	271	q	q	NOUN
iajs-1009	162	1	=	=	PRON
iajs-1009	162	2	pⁿ	pⁿ	NOUN
iajs-1009	162	3	و	و	PRON
iajs-1009	162	4	pg(q)حول	pg(q)حول	NOUN
iajs-1009	162	5	حقل	حقل	VERB
iajs-1009	162	6	كالوا	كالوا	NOUN
iajs-1009	162	7	pg(2,4)قاطي	pg(2,4)قاطي	PROPN
iajs-1009	162	8	منتهي	منتهي	NOUN
iajs-1009	162	9	في	في	ADP
iajs-1009	162	10	مستوي	مستوي	PROPN
iajs-1009	162	11	إس	إس	PROPN
iajs-1009	162	12	(	(	PUNCT
iajs-1009	162	13	k	k	NOUN
iajs-1009	162	14	,	,	PUNCT
iajs-1009	162	15	n	n	CCONJ
iajs-1009	162	16	)	)	PUNCT
iajs-1009	162	17	األقواس	األقواس	NOUN
iajs-1009	162	18	p	p	PROPN
iajs-1009	162	19	ولعدد	ولعدد	PROPN
iajs-1009	162	20	صحیح	صحیح	VERB
iajs-1009	162	21	أوليعددn	أوليعددn	NOUN
iajs-1009	162	22	≥2	≥2	PROPN
iajs-1009	162	23	,	,	PUNCT
iajs-1009	162	24	هو	هو	PROPN
iajs-1009	162	25	مجموعة	مجموعة	PROPN
iajs-1009	162	26	مكونة	مكونة	PROPN
iajs-1009	162	27	منk	منk	PROPN
iajs-1009	162	28	یوجد	یوجد	PROPN
iajs-1009	162	29	من	من	PRON
iajs-1009	162	30	النقاط	النقاط	PROPN
iajs-1009	162	31	الn+1	الn+1	PROPN
iajs-1009	162	32	منها	منها	NOUN
iajs-1009	162	33	تقع	تقع	VERB
iajs-1009	162	34	على	على	NOUN
iajs-1009	162	35	.مستقیم	.مستقیم	PROPN
iajs-1009	162	36	واحد	واحد	NOUN
iajs-1009	162	37	)	)	PUNCT
iajs-1009	162	38	.(k+1,n	.(k+1,n	NOUN
iajs-1009	163	1	لم	لم	ADP
iajs-1009	163	2	یكن	یكن	VERB
iajs-1009	163	3	محتوى	محتوى	PROPN
iajs-1009	163	4	في	في	ADP
iajs-1009	163	5	القوس	القوس	ADJ
iajs-1009	163	6	إذایكون	إذایكون	PROPN
iajs-1009	163	7	كامل	كامل	NOUN
iajs-1009	163	8	)	)	PUNCT
iajs-1009	163	9	(	(	PUNCT
iajs-1009	163	10	k	k	X
iajs-1009	163	11	,	,	PUNCT
iajs-1009	163	12	n	n	CCONJ
iajs-1009	163	13	–	–	PUNCT
iajs-1009	163	14	القوس	القوس	PROPN
iajs-1009	163	15	من	من	PROPN
iajs-1009	163	16	pg(2,4)في	pg(2,4)في	PROPN
iajs-1009	163	17	المستوي	المستوي	PROPN
iajs-1009	163	18	n=2,3,4العظمى	n=2,3,4العظمى	PROPN
iajs-1009	163	19	الكاملة	الكاملة	PROPN
iajs-1009	163	20	و	و	PRON
iajs-1009	163	21	)	)	PUNCT
iajs-1009	163	22	k	k	NOUN
iajs-1009	163	23	,	,	PUNCT
iajs-1009	163	24	n	n	CCONJ
iajs-1009	163	25	(	(	PUNCT
iajs-1009	163	26	–	–	PUNCT
iajs-1009	163	27	األقواسیتم	األقواسیتم	NOUN
iajs-1009	163	28	بناء	بناء	ADP
iajs-1009	163	29	سفي	سفي	DET
iajs-1009	163	30	هذا	هذا	NOUN
iajs-1009	163	31	البحث	البحث	NOUN
iajs-1009	163	32	.معادلة	.معادلة	PUNCT
iajs-1009	163	33	المخروط	المخروط	PROPN