id	sid	tid	token	lemma	pos
iajs-825	1	1	ibn	ibn	PROPN
iajs-825	1	2	alhaitham	alhaitham	NOUN
iajs-825	1	3	j.	j.	PROPN
iajs-825	1	4	for	for	ADP
iajs-825	1	5	pure	pure	ADJ
iajs-825	1	6	&	&	CCONJ
iajs-825	1	7	appl	appl	PROPN
iajs-825	1	8	.	.	PUNCT
iajs-825	2	1	sci	sci	PROPN
iajs-825	2	2	.	.	PUNCT
iajs-825	2	3	vol.24	vol.24	NOUN
iajs-825	2	4	(	(	PUNCT
iajs-825	2	5	3	3	NUM
iajs-825	2	6	)	)	PUNCT
iajs-825	2	7	2011	2011	NUM
iajs-825	2	8	some	some	PRON
iajs-825	2	9	results	result	VERB
iajs-825	2	10	on	on	ADP
iajs-825	2	11	the	the	DET
iajs-825	2	12	complete	complete	ADJ
iajs-825	2	13	arcs	arc	NOUN
iajs-825	2	14	in	in	ADP
iajs-825	2	15	three	three	NUM
iajs-825	2	16	dimensional	dimensional	ADJ
iajs-825	2	17	projective	projective	ADJ
iajs-825	2	18	space	space	NOUN
iajs-825	2	19	over	over	ADP
iajs-825	2	20	galois	galois	PROPN
iajs-825	2	21	field	field	NOUN
iajs-825	2	22	a.sh	a.sh	PROPN
iajs-825	2	23	.	.	PROPN
iajs-825	2	24	almukhtar	almukhtar	PROPN
iajs-825	2	25	department	department	PROPN
iajs-825	2	26	of	of	ADP
iajs-825	2	27	mathematics	mathematics	PROPN
iajs-825	2	28	,	,	PUNCT
iajs-825	2	29	college	college	NOUN
iajs-825	2	30	of	of	ADP
iajs-825	2	31	education	education	PROPN
iajs-825	2	32	ibn	ibn	PROPN
iajs-825	2	33	-	-	PUNCT
iajs-825	2	34	al	al	PROPN
iajs-825	2	35	-	-	PUNCT
iajs-825	2	36	haitham	haitham	PROPN
iajs-825	2	37	,	,	PUNCT
iajs-825	2	38	university	university	PROPN
iajs-825	2	39	of	of	ADP
iajs-825	2	40	baghdad	baghdad	PROPN
iajs-825	2	41	received	receive	VERB
iajs-825	2	42	in	in	ADP
iajs-825	2	43	:	:	PUNCT
iajs-825	2	44	11	11	NUM
iajs-825	2	45	may	may	AUX
iajs-825	2	46	2011	2011	NUM
iajs-825	2	47	accepted	accept	VERB
iajs-825	2	48	in	in	ADP
iajs-825	2	49	:	:	PUNCT
iajs-825	2	50	16	16	NUM
iajs-825	2	51	june	june	PROPN
iajs-825	2	52	2011	2011	NUM
iajs-825	2	53	abstract	abstract	NOUN
iajs-825	2	54	the	the	DET
iajs-825	2	55	aim	aim	NOUN
iajs-825	2	56	of	of	ADP
iajs-825	2	57	this	this	DET
iajs-825	2	58	paper	paper	NOUN
iajs-825	2	59	is	be	AUX
iajs-825	2	60	to	to	PART
iajs-825	2	61	introduce	introduce	VERB
iajs-825	2	62	the	the	DET
iajs-825	2	63	definition	definition	NOUN
iajs-825	2	64	of	of	ADP
iajs-825	2	65	projective	projective	ADJ
iajs-825	2	66	3	3	NUM
iajs-825	2	67	-	-	PUNCT
iajs-825	2	68	space	space	NOUN
iajs-825	2	69	over	over	ADP
iajs-825	2	70	galois	galois	PROPN
iajs-825	2	71	field	field	NOUN
iajs-825	2	72	gf(q	gf(q	NOUN
iajs-825	2	73	)	)	PUNCT
iajs-825	2	74	,	,	PUNCT
iajs-825	2	75	q	q	NOUN
iajs-825	2	76	=	=	PUNCT
iajs-825	2	77	pm	pm	NOUN
iajs-825	2	78	,	,	PUNCT
iajs-825	2	79	for	for	ADP
iajs-825	2	80	some	some	DET
iajs-825	2	81	prime	prime	ADJ
iajs-825	2	82	number	number	NOUN
iajs-825	2	83	p	p	NOUN
iajs-825	2	84	and	and	CCONJ
iajs-825	2	85	some	some	DET
iajs-825	2	86	integer	integer	NOUN
iajs-825	2	87	m.	m.	NOUN
iajs-825	2	88	also	also	ADV
iajs-825	2	89	the	the	DET
iajs-825	2	90	definitions	definition	NOUN
iajs-825	2	91	of	of	ADP
iajs-825	2	92	(	(	PUNCT
iajs-825	2	93	k	k	NOUN
iajs-825	2	94	,	,	PUNCT
iajs-825	2	95	n)-arcs	n)-arcs	X
iajs-825	2	96	,	,	PUNCT
iajs-825	2	97	complete	complete	ADJ
iajs-825	2	98	arcs	arc	NOUN
iajs-825	2	99	,	,	PUNCT
iajs-825	2	100	n	n	CCONJ
iajs-825	2	101	-	-	PUNCT
iajs-825	2	102	secants	secant	NOUN
iajs-825	2	103	,	,	PUNCT
iajs-825	2	104	the	the	DET
iajs-825	2	105	index	index	NOUN
iajs-825	2	106	of	of	ADP
iajs-825	2	107	the	the	DET
iajs-825	2	108	point	point	NOUN
iajs-825	2	109	and	and	CCONJ
iajs-825	2	110	the	the	DET
iajs-825	2	111	projectively	projectively	ADV
iajs-825	2	112	equivalent	equivalent	ADJ
iajs-825	2	113	arcs	arc	NOUN
iajs-825	2	114	are	be	AUX
iajs-825	2	115	given	give	VERB
iajs-825	2	116	.	.	PUNCT
iajs-825	3	1	moreover	moreover	ADV
iajs-825	3	2	some	some	DET
iajs-825	3	3	theorems	theorem	NOUN
iajs-825	3	4	about	about	ADP
iajs-825	3	5	these	these	DET
iajs-825	3	6	notations	notation	NOUN
iajs-825	3	7	are	be	AUX
iajs-825	3	8	proved	prove	VERB
iajs-825	3	9	.	.	PUNCT
iajs-825	4	1	keywords	keyword	NOUN
iajs-825	4	2	:	:	PUNCT
iajs-825	4	3	arcs	arc	NOUN
iajs-825	4	4	,	,	PUNCT
iajs-825	4	5	index	index	NOUN
iajs-825	4	6	,	,	PUNCT
iajs-825	4	7	plane	plane	NOUN
iajs-825	4	8	.	.	PUNCT
iajs-825	5	1	introduction	introduction	NOUN
iajs-825	5	2	:	:	PUNCT
iajs-825	6	1	[	[	X
iajs-825	6	2	1	1	X
iajs-825	6	3	]	]	PUNCT
iajs-825	6	4	a	a	DET
iajs-825	6	5	projective	projective	ADJ
iajs-825	6	6	3	3	NUM
iajs-825	6	7	–	–	PUNCT
iajs-825	6	8	space	space	NOUN
iajs-825	6	9	pg(3,k	pg(3,k	NOUN
iajs-825	6	10	)	)	PUNCT
iajs-825	6	11	over	over	ADP
iajs-825	6	12	a	a	DET
iajs-825	6	13	field	field	NOUN
iajs-825	6	14	k	k	X
iajs-825	6	15	is	be	AUX
iajs-825	6	16	a	a	DET
iajs-825	6	17	3	3	NUM
iajs-825	6	18	–	–	PUNCT
iajs-825	6	19	dimensional	dimensional	ADJ
iajs-825	6	20	projective	projective	ADJ
iajs-825	6	21	space	space	NOUN
iajs-825	6	22	which	which	PRON
iajs-825	6	23	consists	consist	VERB
iajs-825	6	24	of	of	ADP
iajs-825	6	25	points	point	NOUN
iajs-825	6	26	,	,	PUNCT
iajs-825	6	27	lines	line	NOUN
iajs-825	6	28	and	and	CCONJ
iajs-825	6	29	planes	plane	NOUN
iajs-825	6	30	with	with	ADP
iajs-825	6	31	the	the	DET
iajs-825	6	32	incidence	incidence	NOUN
iajs-825	6	33	relation	relation	NOUN
iajs-825	6	34	between	between	ADP
iajs-825	6	35	them	they	PRON
iajs-825	6	36	.	.	PUNCT
iajs-825	7	1	the	the	DET
iajs-825	7	2	projective	projective	ADJ
iajs-825	7	3	3	3	NUM
iajs-825	7	4	–	–	PUNCT
iajs-825	7	5	space	space	NOUN
iajs-825	7	6	satisfies	satisfy	VERB
iajs-825	7	7	the	the	DET
iajs-825	7	8	following	follow	VERB
iajs-825	7	9	axioms	axiom	NOUN
iajs-825	7	10	:	:	PUNCT
iajs-825	7	11	a.	a.	NOUN
iajs-825	7	12	any	any	DET
iajs-825	7	13	two	two	NUM
iajs-825	7	14	distinct	distinct	ADJ
iajs-825	7	15	points	point	NOUN
iajs-825	7	16	are	be	AUX
iajs-825	7	17	contained	contain	VERB
iajs-825	7	18	in	in	ADP
iajs-825	7	19	a	a	DET
iajs-825	7	20	unique	unique	ADJ
iajs-825	7	21	line	line	NOUN
iajs-825	7	22	.	.	PUNCT
iajs-825	8	1	b.	b.	VERB
iajs-825	9	1	any	any	DET
iajs-825	9	2	three	three	NUM
iajs-825	9	3	distinct	distinct	ADJ
iajs-825	9	4	non	non	ADJ
iajs-825	9	5	-	-	ADJ
iajs-825	9	6	collinear	collinear	ADJ
iajs-825	9	7	points	point	NOUN
iajs-825	9	8	,	,	PUNCT
iajs-825	9	9	also	also	ADV
iajs-825	9	10	any	any	DET
iajs-825	9	11	line	line	NOUN
iajs-825	9	12	and	and	CCONJ
iajs-825	9	13	point	point	VERB
iajs-825	9	14	not	not	PART
iajs-825	9	15	on	on	ADP
iajs-825	9	16	the	the	DET
iajs-825	9	17	line	line	NOUN
iajs-825	9	18	are	be	AUX
iajs-825	9	19	contained	contain	VERB
iajs-825	9	20	in	in	ADP
iajs-825	9	21	a	a	DET
iajs-825	9	22	unique	unique	ADJ
iajs-825	9	23	plane	plane	NOUN
iajs-825	9	24	.	.	PUNCT
iajs-825	10	1	c.	c.	NOUN
iajs-825	11	1	any	any	DET
iajs-825	11	2	two	two	NUM
iajs-825	11	3	distinct	distinct	ADJ
iajs-825	11	4	coplanar	coplanar	ADJ
iajs-825	11	5	lines	line	NOUN
iajs-825	11	6	intersect	intersect	ADJ
iajs-825	11	7	in	in	ADP
iajs-825	11	8	a	a	DET
iajs-825	11	9	unique	unique	ADJ
iajs-825	11	10	point	point	NOUN
iajs-825	11	11	.	.	PUNCT
iajs-825	12	1	d.	d.	NOUN
iajs-825	12	2	any	any	DET
iajs-825	12	3	line	line	NOUN
iajs-825	12	4	not	not	PART
iajs-825	12	5	on	on	ADP
iajs-825	12	6	a	a	DET
iajs-825	12	7	given	give	VERB
iajs-825	12	8	plane	plane	NOUN
iajs-825	12	9	intersects	intersect	NOUN
iajs-825	12	10	the	the	DET
iajs-825	12	11	plane	plane	NOUN
iajs-825	12	12	in	in	ADP
iajs-825	12	13	a	a	DET
iajs-825	12	14	unique	unique	ADJ
iajs-825	12	15	point	point	NOUN
iajs-825	12	16	.	.	PUNCT
iajs-825	13	1	e.	e.	PROPN
iajs-825	14	1	any	any	DET
iajs-825	14	2	two	two	NUM
iajs-825	14	3	distinct	distinct	ADJ
iajs-825	14	4	planes	plane	NOUN
iajs-825	14	5	intersect	intersect	ADJ
iajs-825	14	6	in	in	ADP
iajs-825	14	7	a	a	DET
iajs-825	14	8	unique	unique	ADJ
iajs-825	14	9	line	line	NOUN
iajs-825	14	10	.	.	PUNCT
iajs-825	15	1	a	a	DET
iajs-825	15	2	projective	projective	ADJ
iajs-825	15	3	space	space	NOUN
iajs-825	15	4	pg(3,q	pg(3,q	NOUN
iajs-825	15	5	)	)	PUNCT
iajs-825	15	6	over	over	ADP
iajs-825	15	7	galois	galois	PROPN
iajs-825	15	8	field	field	NOUN
iajs-825	15	9	gf(q	gf(q	NOUN
iajs-825	15	10	)	)	PUNCT
iajs-825	15	11	,	,	PUNCT
iajs-825	15	12	q	q	NOUN
iajs-825	16	1	=	=	PUNCT
iajs-825	16	2	p	p	NOUN
iajs-825	16	3	m	m	PROPN
iajs-825	16	4	,	,	PUNCT
iajs-825	16	5	for	for	ADP
iajs-825	16	6	some	some	DET
iajs-825	16	7	prime	prime	ADJ
iajs-825	16	8	number	number	NOUN
iajs-825	16	9	p	p	NOUN
iajs-825	16	10	and	and	CCONJ
iajs-825	16	11	some	some	DET
iajs-825	16	12	integer	integer	NOUN
iajs-825	16	13	m	m	PROPN
iajs-825	16	14	,	,	PUNCT
iajs-825	16	15	is	be	AUX
iajs-825	16	16	a	a	DET
iajs-825	16	17	3	3	NUM
iajs-825	16	18	–	–	PUNCT
iajs-825	16	19	dimensional	dimensional	ADJ
iajs-825	16	20	projective	projective	ADJ
iajs-825	16	21	space	space	NOUN
iajs-825	16	22	.	.	PUNCT
iajs-825	17	1	now	now	ADV
iajs-825	17	2	,	,	PUNCT
iajs-825	17	3	some	some	DET
iajs-825	17	4	theorems	theorem	NOUN
iajs-825	17	5	on	on	ADP
iajs-825	17	6	pg(3,q	pg(3,q	NOUN
iajs-825	17	7	)	)	PUNCT
iajs-825	17	8	p	p	NOUN
iajs-825	17	9	roved	rove	VERB
iajs-825	17	10	in	in	ADP
iajs-825	17	11	[	[	X
iajs-825	17	12	1	1	NUM
iajs-825	17	13	]	]	PUNCT
iajs-825	17	14	and	and	CCONJ
iajs-825	17	15	[	[	X
iajs-825	17	16	2	2	NUM
iajs-825	17	17	]	]	PUNCT
iajs-825	17	18	are	be	AUX
iajs-825	17	19	given	give	VERB
iajs-825	17	20	in	in	ADP
iajs-825	17	21	the	the	DET
iajs-825	17	22	following	following	NOUN
iajs-825	17	23	.	.	PUNCT
iajs-825	18	1	theorem	theorem	VERB
iajs-825	18	2	1	1	NUM
iajs-825	18	3	:	:	PUNCT
iajs-825	18	4	every	every	DET
iajs-825	18	5	line	line	NOUN
iajs-825	18	6	in	in	ADP
iajs-825	18	7	pg(3,q	pg(3,q	NOUN
iajs-825	18	8	)	)	PUNCT
iajs-825	18	9	contains	contain	VERB
iajs-825	18	10	exactly	exactly	ADV
iajs-825	18	11	q	q	PUNCT
iajs-825	18	12	+	+	CCONJ
iajs-825	18	13	1	1	NUM
iajs-825	18	14	points	point	NOUN
iajs-825	18	15	.	.	PUNCT
iajs-825	19	1	theorem	theorem	VERB
iajs-825	19	2	2	2	NUM
iajs-825	19	3	:	:	PUNCT
iajs-825	19	4	every	every	DET
iajs-825	19	5	point	point	NOUN
iajs-825	19	6	in	in	ADP
iajs-825	19	7	pg(3,q	pg(3,q	NOUN
iajs-825	19	8	)	)	PUNCT
iajs-825	19	9	is	be	AUX
iajs-825	19	10	on	on	ADP
iajs-825	19	11	exactly	exactly	ADV
iajs-825	19	12	q	q	ADJ
iajs-825	19	13	+	+	CCONJ
iajs-825	19	14	1	1	NUM
iajs-825	19	15	lines	line	NOUN
iajs-825	19	16	.	.	PUNCT
iajs-825	20	1	theorem	theorem	VERB
iajs-825	20	2	3	3	NUM
iajs-825	20	3	:	:	PUNCT
iajs-825	20	4	every	every	DET
iajs-825	20	5	plane	plane	NOUN
iajs-825	20	6	in	in	ADP
iajs-825	20	7	pg(3,q	pg(3,q	NOUN
iajs-825	20	8	)	)	PUNCT
iajs-825	20	9	contains	contain	VERB
iajs-825	20	10	exactly	exactly	ADV
iajs-825	20	11	q	q	ADJ
iajs-825	20	12	2	2	NUM
iajs-825	20	13	+	+	CCONJ
iajs-825	20	14	q	q	NOUN
iajs-825	20	15	+	+	CCONJ
iajs-825	20	16	1	1	NUM
iajs-825	20	17	points	point	NOUN
iajs-825	20	18	.	.	PUNCT
iajs-825	21	1	theorem	theorem	VERB
iajs-825	21	2	4	4	NUM
iajs-825	21	3	:	:	PUNCT
iajs-825	21	4	every	every	DET
iajs-825	21	5	plane	plane	NOUN
iajs-825	21	6	in	in	ADP
iajs-825	21	7	pg(3,q	pg(3,q	NOUN
iajs-825	21	8	)	)	PUNCT
iajs-825	21	9	contains	contain	VERB
iajs-825	21	10	exactly	exactly	ADV
iajs-825	21	11	q	q	ADJ
iajs-825	21	12	2	2	NUM
iajs-825	21	13	+	+	CCONJ
iajs-825	21	14	q	q	ADJ
iajs-825	21	15	+	+	CCONJ
iajs-825	21	16	1	1	NUM
iajs-825	21	17	lines	line	NOUN
iajs-825	21	18	.	.	PUNCT
iajs-825	22	1	ibn	ibn	PROPN
iajs-825	22	2	alhaitham	alhaitham	PROPN
iajs-825	22	3	j.	j.	PROPN
iajs-825	22	4	for	for	ADP
iajs-825	22	5	pure	pure	ADJ
iajs-825	22	6	&	&	CCONJ
iajs-825	22	7	appl	appl	PROPN
iajs-825	22	8	.	.	PUNCT
iajs-825	23	1	sci	sci	PROPN
iajs-825	23	2	.	.	PUNCT
iajs-825	23	3	vol.24	vol.24	NOUN
iajs-825	23	4	(	(	PUNCT
iajs-825	23	5	3	3	NUM
iajs-825	23	6	)	)	PUNCT
iajs-825	23	7	2011	2011	NUM
iajs-825	23	8	theorem	theorem	VERB
iajs-825	23	9	5	5	NUM
iajs-825	23	10	:	:	PUNCT
iajs-825	23	11	every	every	DET
iajs-825	23	12	point	point	NOUN
iajs-825	23	13	in	in	ADP
iajs-825	23	14	pg(3,q	pg(3,q	NOUN
iajs-825	23	15	)	)	PUNCT
iajs-825	23	16	is	be	AUX
iajs-825	23	17	on	on	ADP
iajs-825	23	18	exactly	exactly	ADV
iajs-825	23	19	q2	q2	NOUN
iajs-825	23	20	+	+	CCONJ
iajs-825	23	21	q	q	PUNCT
iajs-825	24	1	+	+	NUM
iajs-825	24	2	1	1	NUM
iajs-825	24	3	p	p	NOUN
iajs-825	24	4	lanes	lane	NOUN
iajs-825	24	5	.	.	PUNCT
iajs-825	25	1	theorem	theorem	VERB
iajs-825	25	2	6	6	NUM
iajs-825	25	3	:	:	PUNCT
iajs-825	25	4	there	there	PRON
iajs-825	25	5	exist	exist	VERB
iajs-825	25	6	q	q	PROPN
iajs-825	25	7	3	3	NUM
iajs-825	25	8	+	+	NUM
iajs-825	25	9	q2	q2	NOUN
iajs-825	25	10	+	+	CCONJ
iajs-825	25	11	q	q	PUNCT
iajs-825	26	1	+	+	NUM
iajs-825	26	2	1	1	NUM
iajs-825	26	3	points	point	NOUN
iajs-825	26	4	in	in	ADP
iajs-825	26	5	pg(3,q	pg(3,q	NOUN
iajs-825	26	6	)	)	PUNCT
iajs-825	26	7	.	.	PUNCT
iajs-825	27	1	theorem	theorem	VERB
iajs-825	27	2	7	7	NUM
iajs-825	27	3	:	:	PUNCT
iajs-825	27	4	there	there	PRON
iajs-825	27	5	exist	exist	VERB
iajs-825	27	6	q3	q3	NOUN
iajs-825	27	7	+	+	CCONJ
iajs-825	27	8	q2	q2	NOUN
iajs-825	27	9	+	+	CCONJ
iajs-825	27	10	q	q	PUNCT
iajs-825	28	1	+	+	NUM
iajs-825	28	2	1	1	NUM
iajs-825	28	3	p	p	NOUN
iajs-825	28	4	lanes	lane	NOUN
iajs-825	28	5	in	in	ADP
iajs-825	28	6	pg(3,q	pg(3,q	NOUN
iajs-825	28	7	)	)	PUNCT
iajs-825	28	8	.	.	PUNCT
iajs-825	29	1	theorem	theorem	VERB
iajs-825	29	2	8	8	NUM
iajs-825	29	3	:	:	PUNCT
iajs-825	29	4	any	any	DET
iajs-825	29	5	line	line	NOUN
iajs-825	29	6	in	in	ADP
iajs-825	29	7	pg(3,q	pg(3,q	NOUN
iajs-825	29	8	)	)	PUNCT
iajs-825	29	9	is	be	AUX
iajs-825	29	10	on	on	ADP
iajs-825	29	11	exactly	exactly	ADV
iajs-825	29	12	q	q	ADJ
iajs-825	29	13	+1	+1	ADJ
iajs-825	29	14	planes	plane	NOUN
iajs-825	29	15	.	.	PUNCT
iajs-825	30	1	definition	definition	NOUN
iajs-825	30	2	1	1	NUM
iajs-825	30	3	:	:	PUNCT
iajs-825	31	1	[	[	X
iajs-825	31	2	1	1	X
iajs-825	31	3	]	]	X
iajs-825	31	4	a	a	DET
iajs-825	31	5	(	(	PUNCT
iajs-825	31	6	k	k	NOUN
iajs-825	31	7	,	,	PUNCT
iajs-825	31	8	n	n	CCONJ
iajs-825	31	9	)	)	PUNCT
iajs-825	31	10	–	–	PUNCT
iajs-825	31	11	arc	arc	VERB
iajs-825	31	12	a	a	PRON
iajs-825	31	13	in	in	ADP
iajs-825	31	14	pg(3,q	pg(3,q	NOUN
iajs-825	31	15	)	)	PUNCT
iajs-825	31	16	is	be	AUX
iajs-825	31	17	a	a	DET
iajs-825	31	18	set	set	NOUN
iajs-825	31	19	of	of	ADP
iajs-825	31	20	k	k	PROPN
iajs-825	31	21	points	point	NOUN
iajs-825	31	22	such	such	ADJ
iajs-825	31	23	that	that	SCONJ
iajs-825	31	24	at	at	ADP
iajs-825	31	25	most	most	ADJ
iajs-825	31	26	n	n	NUM
iajs-825	31	27	points	point	NOUN
iajs-825	31	28	of	of	ADP
iajs-825	31	29	which	which	PRON
iajs-825	31	30	lie	lie	NOUN
iajs-825	31	31	in	in	ADP
iajs-825	31	32	any	any	DET
iajs-825	31	33	plane	plane	NOUN
iajs-825	31	34	,	,	PUNCT
iajs-825	31	35	n	n	PROPN
iajs-825	31	36			NUM
iajs-825	31	37	3	3	NUM
iajs-825	31	38	.	.	PUNCT
iajs-825	32	1	n	n	PRON
iajs-825	32	2	is	be	AUX
iajs-825	32	3	called	call	VERB
iajs-825	32	4	the	the	DET
iajs-825	32	5	degree	degree	NOUN
iajs-825	32	6	of	of	ADP
iajs-825	32	7	the	the	DET
iajs-825	32	8	(	(	PUNCT
iajs-825	32	9	k	k	NOUN
iajs-825	32	10	,	,	PUNCT
iajs-825	32	11	n	n	CCONJ
iajs-825	32	12	)	)	PUNCT
iajs-825	32	13	–	–	PUNCT
iajs-825	32	14	arc	arc	NOUN
iajs-825	32	15	.	.	PUNCT
iajs-825	33	1	definition	definition	NOUN
iajs-825	33	2	2	2	NUM
iajs-825	33	3	:	:	PUNCT
iajs-825	33	4	in	in	ADP
iajs-825	33	5	pg(3,q	pg(3,q	NOUN
iajs-825	33	6	)	)	PUNCT
iajs-825	33	7	,	,	PUNCT
iajs-825	33	8	if	if	SCONJ
iajs-825	33	9	a	a	PRON
iajs-825	33	10	is	be	AUX
iajs-825	33	11	any	any	DET
iajs-825	33	12	(	(	PUNCT
iajs-825	33	13	k	k	NOUN
iajs-825	33	14	,	,	PUNCT
iajs-825	33	15	n	n	CCONJ
iajs-825	33	16	)	)	PUNCT
iajs-825	33	17	–	–	PUNCT
iajs-825	33	18	arc	arc	NOUN
iajs-825	33	19	,	,	PUNCT
iajs-825	33	20	then	then	ADV
iajs-825	33	21	an	an	DET
iajs-825	33	22	(	(	PUNCT
iajs-825	33	23	m	m	NOUN
iajs-825	33	24	-	-	NOUN
iajs-825	33	25	secant	secant	ADJ
iajs-825	33	26	)	)	PUNCT
iajs-825	33	27	of	of	ADP
iajs-825	33	28	a	a	PRON
iajs-825	33	29	is	be	AUX
iajs-825	33	30	a	a	DET
iajs-825	33	31	plane	plane	NOUN
iajs-825	33	32	ℓ	ℓ	NOUN
iajs-825	33	33	such	such	ADJ
iajs-825	33	34	that	that	SCONJ
iajs-825	33	35	ℓ	ℓ	PRON
iajs-825	33	36			VERB
iajs-825	33	37	a=	a=	PROPN
iajs-825	33	38	m.	m.	NOUN
iajs-825	33	39	definition	definition	NOUN
iajs-825	33	40	3	3	NUM
iajs-825	33	41	:	:	PUNCT
iajs-825	33	42	[	[	X
iajs-825	33	43	1,2	1,2	NUM
iajs-825	33	44	]	]	PUNCT
iajs-825	33	45	a	a	DET
iajs-825	33	46	point	point	NOUN
iajs-825	33	47	n	n	ADV
iajs-825	33	48	not	not	PART
iajs-825	33	49	on	on	ADP
iajs-825	33	50	a	a	DET
iajs-825	33	51	(	(	PUNCT
iajs-825	33	52	k	k	NOUN
iajs-825	33	53	,	,	PUNCT
iajs-825	33	54	n)-arc	n)-arc	AUX
iajs-825	33	55	a	a	PRON
iajs-825	33	56	has	have	VERB
iajs-825	33	57	index	index	NOUN
iajs-825	33	58	i	i	PRON
iajs-825	33	59	if	if	SCONJ
iajs-825	33	60	there	there	PRON
iajs-825	33	61	exists	exist	VERB
iajs-825	33	62	exactly	exactly	ADV
iajs-825	33	63	i	i	PRON
iajs-825	33	64	(	(	PUNCT
iajs-825	33	65	n	n	CCONJ
iajs-825	33	66	–	–	PUNCT
iajs-825	33	67	secants	secant	NOUN
iajs-825	33	68	)	)	PUNCT
iajs-825	33	69	of	of	ADP
iajs-825	33	70	a	a	DET
iajs-825	33	71	through	through	ADP
iajs-825	33	72	n	n	CCONJ
iajs-825	33	73	,	,	PUNCT
iajs-825	33	74	one	one	PRON
iajs-825	33	75	can	can	AUX
iajs-825	33	76	denote	denote	VERB
iajs-825	33	77	the	the	DET
iajs-825	33	78	number	number	NOUN
iajs-825	33	79	of	of	ADP
iajs-825	33	80	points	point	NOUN
iajs-825	33	81	n	n	PROPN
iajs-825	33	82	of	of	ADP
iajs-825	33	83	index	index	NOUN
iajs-825	33	84	i	i	PRON
iajs-825	33	85	by	by	ADP
iajs-825	33	86	ci	ci	PROPN
iajs-825	33	87	.	.	PROPN
iajs-825	33	88	definition	definition	NOUN
iajs-825	33	89	4	4	NUM
iajs-825	33	90	:	:	PUNCT
iajs-825	33	91	(	(	PUNCT
iajs-825	33	92	k	k	X
iajs-825	33	93	,	,	PUNCT
iajs-825	33	94	n)-arc	n)-arc	AUX
iajs-825	33	95	a	a	PRON
iajs-825	33	96	is	be	AUX
iajs-825	33	97	complete	complete	ADJ
iajs-825	33	98	if	if	SCONJ
iajs-825	33	99	it	it	PRON
iajs-825	33	100	is	be	AUX
iajs-825	33	101	not	not	PART
iajs-825	33	102	contained	contain	VERB
iajs-825	33	103	in	in	ADP
iajs-825	33	104	any	any	DET
iajs-825	33	105	(	(	PUNCT
iajs-825	33	106	k	k	X
iajs-825	33	107	+	+	NOUN
iajs-825	33	108	1,n)-arc	1,n)-arc	NUM
iajs-825	33	109	.	.	PUNCT
iajs-825	34	1	from	from	ADP
iajs-825	34	2	definitions	definition	NOUN
iajs-825	34	3	3	3	NUM
iajs-825	34	4	and	and	CCONJ
iajs-825	34	5	4	4	NUM
iajs-825	34	6	,	,	PUNCT
iajs-825	34	7	it	it	PRON
iajs-825	34	8	is	be	AUX
iajs-825	34	9	concluded	conclude	VERB
iajs-825	34	10	that	that	SCONJ
iajs-825	34	11	the	the	DET
iajs-825	34	12	(	(	PUNCT
iajs-825	34	13	k	k	NOUN
iajs-825	34	14	,	,	PUNCT
iajs-825	34	15	n)-arc	n)-arc	X
iajs-825	34	16	is	be	AUX
iajs-825	34	17	complete	complete	ADJ
iajs-825	34	18	iff	iff	PROPN
iajs-825	34	19	c0	c0	PROPN
iajs-825	34	20	=	=	PROPN
iajs-825	34	21	0	0	X
iajs-825	34	22	.	.	PUNCT
iajs-825	35	1	thus	thus	ADV
iajs-825	35	2	the	the	DET
iajs-825	35	3	(	(	PUNCT
iajs-825	35	4	k	k	NOUN
iajs-825	35	5	,	,	PUNCT
iajs-825	35	6	n)-arc	n)-arc	X
iajs-825	35	7	is	be	AUX
iajs-825	35	8	complete	complete	ADJ
iajs-825	35	9	iff	iff	NOUN
iajs-825	35	10	every	every	DET
iajs-825	35	11	point	point	NOUN
iajs-825	35	12	of	of	ADP
iajs-825	35	13	pg(3,q	pg(3,q	NOUN
iajs-825	35	14	)	)	PUNCT
iajs-825	35	15	lies	lie	VERB
iajs-825	35	16	on	on	ADP
iajs-825	35	17	some	some	DET
iajs-825	35	18	n	n	NOUN
iajs-825	35	19	-	-	PUNCT
iajs-825	35	20	secant	secant	NOUN
iajs-825	35	21	of	of	ADP
iajs-825	35	22	the	the	DET
iajs-825	35	23	(	(	PUNCT
iajs-825	35	24	k	k	NOUN
iajs-825	35	25	,	,	PUNCT
iajs-825	35	26	n)-arc	n)-arc	X
iajs-825	35	27	.	.	PUNCT
iajs-825	36	1	definition	definition	NOUN
iajs-825	36	2	5	5	NUM
iajs-825	36	3	:	:	PUNCT
iajs-825	36	4	[	[	X
iajs-825	36	5	1,3	1,3	NUM
iajs-825	36	6	]	]	X
iajs-825	36	7	let	let	VERB
iajs-825	36	8	t	t	PROPN
iajs-825	36	9	i	i	PRON
iajs-825	36	10	be	be	AUX
iajs-825	36	11	the	the	DET
iajs-825	36	12	total	total	ADJ
iajs-825	36	13	number	number	NOUN
iajs-825	36	14	of	of	ADP
iajs-825	36	15	the	the	DET
iajs-825	36	16	i	i	NOUN
iajs-825	36	17	–	–	PUNCT
iajs-825	36	18	secants	secant	NOUN
iajs-825	36	19	of	of	ADP
iajs-825	36	20	a	a	DET
iajs-825	36	21	(	(	PUNCT
iajs-825	36	22	k	k	NOUN
iajs-825	36	23	,	,	PUNCT
iajs-825	36	24	n	n	CCONJ
iajs-825	36	25	)	)	PUNCT
iajs-825	36	26	–	–	PUNCT
iajs-825	36	27	arc	arc	NOUN
iajs-825	36	28	a	a	PRON
iajs-825	36	29	,	,	PUNCT
iajs-825	36	30	then	then	ADV
iajs-825	36	31	the	the	DET
iajs-825	36	32	type	type	NOUN
iajs-825	36	33	of	of	ADP
iajs-825	36	34	a	a	DET
iajs-825	36	35	denoted	denote	VERB
iajs-825	36	36	by	by	ADP
iajs-825	36	37	(	(	PUNCT
iajs-825	36	38	tn	tn	PROPN
iajs-825	36	39	,	,	PUNCT
iajs-825	36	40	tn	tn	PROPN
iajs-825	36	41	–	–	PUNCT
iajs-825	36	42	1	1	NUM
iajs-825	36	43	,	,	PUNCT
iajs-825	36	44			PROPN
iajs-825	36	45	,	,	PUNCT
iajs-825	36	46	t0	t0	PROPN
iajs-825	36	47	)	)	PUNCT
iajs-825	36	48	.	.	PUNCT
iajs-825	37	1	definition	definition	NOUN
iajs-825	37	2	6	6	NUM
iajs-825	37	3	:	:	PUNCT
iajs-825	38	1	[	[	X
iajs-825	38	2	1	1	NUM
iajs-825	38	3	]	]	X
iajs-825	38	4	let	let	NOUN
iajs-825	38	5	(	(	PUNCT
iajs-825	38	6	k1,n	k1,n	PROPN
iajs-825	38	7	)	)	PUNCT
iajs-825	38	8	–	–	PUNCT
iajs-825	38	9	arc	arc	NOUN
iajs-825	38	10	a	a	DET
iajs-825	38	11	is	be	AUX
iajs-825	38	12	of	of	ADP
iajs-825	38	13	type	type	NOUN
iajs-825	38	14	(	(	PUNCT
iajs-825	38	15	tn	tn	PROPN
iajs-825	38	16	,	,	PUNCT
iajs-825	38	17	tn	tn	PROPN
iajs-825	38	18	–	–	PUNCT
iajs-825	38	19	1,	1,	NUM
iajs-825	38	20	,	,	PUNCT
iajs-825	38	21	t0	t0	PROPN
iajs-825	38	22	)	)	PUNCT
iajs-825	38	23	and	and	CCONJ
iajs-825	38	24	(	(	PUNCT
iajs-825	38	25	k2,n	k2,n	PROPN
iajs-825	38	26	)	)	PUNCT
iajs-825	38	27	–	–	PUNCT
iajs-825	38	28	arc	arc	NOUN
iajs-825	38	29	b	b	NOUN
iajs-825	38	30	is	be	AUX
iajs-825	38	31	of	of	ADP
iajs-825	38	32	type	type	NOUN
iajs-825	38	33	(	(	PUNCT
iajs-825	38	34	sn	sn	PROPN
iajs-825	38	35	,	,	PUNCT
iajs-825	38	36	sn	sn	PROPN
iajs-825	38	37	–	–	PUNCT
iajs-825	38	38	1,,s0	1,,s0	NUM
iajs-825	38	39	)	)	PUNCT
iajs-825	38	40	,	,	PUNCT
iajs-825	38	41	then	then	ADV
iajs-825	38	42	a	a	PRON
iajs-825	38	43	and	and	CCONJ
iajs-825	38	44	b	b	NOUN
iajs-825	38	45	have	have	VERB
iajs-825	38	46	the	the	DET
iajs-825	38	47	same	same	ADJ
iajs-825	38	48	type	type	NOUN
iajs-825	39	1	iff	iff	PROPN
iajs-825	39	2	t	t	PROPN
iajs-825	39	3	i	i	NOUN
iajs-825	39	4	=	=	PUNCT
iajs-825	39	5	si	si	X
iajs-825	39	6	,	,	PUNCT
iajs-825	39	7	for	for	ADP
iajs-825	39	8	all	all	DET
iajs-825	39	9	i	i	PRON
iajs-825	39	10	,	,	PUNCT
iajs-825	39	11	in	in	ADP
iajs-825	39	12	this	this	DET
iajs-825	39	13	case	case	NOUN
iajs-825	39	14	they	they	PRON
iajs-825	39	15	are	be	AUX
iajs-825	39	16	projectively	projectively	ADV
iajs-825	39	17	equivalent	equivalent	ADJ
iajs-825	39	18	.	.	PUNCT
iajs-825	40	1	theorem	theorem	VERB
iajs-825	40	2	9	9	NUM
iajs-825	40	3	:	:	PUNCT
iajs-825	40	4	let	let	VERB
iajs-825	40	5	t(p	t(p	NOUN
iajs-825	40	6	)	)	PUNCT
iajs-825	40	7	represents	represent	VERB
iajs-825	40	8	the	the	DET
iajs-825	40	9	number	number	NOUN
iajs-825	40	10	of	of	ADP
iajs-825	40	11	1	1	NUM
iajs-825	40	12	-	-	PUNCT
iajs-825	40	13	secants	secant	NOUN
iajs-825	40	14	(	(	PUNCT
iajs-825	40	15	planes	plane	NOUN
iajs-825	40	16	)	)	PUNCT
iajs-825	40	17	through	through	ADP
iajs-825	40	18	a	a	DET
iajs-825	40	19	point	point	NOUN
iajs-825	40	20	p	p	NOUN
iajs-825	40	21	of	of	ADP
iajs-825	40	22	a	a	DET
iajs-825	40	23	(	(	PUNCT
iajs-825	40	24	k	k	NOUN
iajs-825	40	25	,	,	PUNCT
iajs-825	40	26	n	n	CCONJ
iajs-825	40	27	)	)	PUNCT
iajs-825	40	28	–	–	PUNCT
iajs-825	40	29	arc	arc	NOUN
iajs-825	40	30	a	a	NOUN
iajs-825	40	31	and	and	CCONJ
iajs-825	40	32	let	let	VERB
iajs-825	40	33	t	t	PROPN
iajs-825	40	34	i	i	PRON
iajs-825	40	35	represent	represent	VERB
iajs-825	40	36	the	the	DET
iajs-825	40	37	numbers	number	NOUN
iajs-825	40	38	of	of	ADP
iajs-825	40	39	i	i	PRON
iajs-825	40	40	–	–	PUNCT
iajs-825	40	41	secants	secant	NOUN
iajs-825	40	42	(	(	PUNCT
iajs-825	40	43	p	p	NOUN
iajs-825	40	44	lanes	lane	NOUN
iajs-825	40	45	)	)	PUNCT
iajs-825	40	46	for	for	ADP
iajs-825	40	47	the	the	DET
iajs-825	40	48	arc	arc	NOUN
iajs-825	40	49	a	a	PRON
iajs-825	40	50	in	in	ADP
iajs-825	40	51	pg(3,q	pg(3,q	NOUN
iajs-825	40	52	)	)	PUNCT
iajs-825	40	53	,	,	PUNCT
iajs-825	40	54	then	then	ADV
iajs-825	40	55	:	:	PUNCT
iajs-825	40	56	1	1	X
iajs-825	40	57	.	.	X
iajs-825	40	58	t	t	NOUN
iajs-825	40	59	=	=	SYM
iajs-825	40	60	t(p	t(p	PROPN
iajs-825	40	61	)	)	PUNCT
iajs-825	40	62	=	=	PUNCT
iajs-825	41	1	q	q	PROPN
iajs-825	41	2	2	2	NUM
iajs-825	42	1	+	+	CCONJ
iajs-825	42	2	q	q	NOUN
iajs-825	42	3	+	+	NUM
iajs-825	42	4	2	2	NUM
iajs-825	42	5	–	–	PUNCT
iajs-825	42	6	k	k	X
iajs-825	42	7	–	–	PUNCT
iajs-825	42	8	(	(	PUNCT
iajs-825	42	9	1	1	X
iajs-825	42	10	)	)	PUNCT
iajs-825	42	11	(	(	PUNCT
iajs-825	42	12	2	2	NUM
iajs-825	42	13	)	)	SYM
iajs-825	42	14	2	2	NUM
iajs-825	42	15			NOUN
iajs-825	42	16	k	k	NOUN
iajs-825	42	17	k	k	X
iajs-825	42	18	–	–	PUNCT
iajs-825	42	19			X
iajs-825	42	20	–	–	PUNCT
iajs-825	42	21	(	(	PUNCT
iajs-825	42	22	1	1	X
iajs-825	42	23	)	)	PUNCT
iajs-825	42	24	(	(	PUNCT
iajs-825	42	25	2	2	X
iajs-825	42	26	)	)	PUNCT
iajs-825	42	27	(	(	PUNCT
iajs-825	42	28	(	(	PUNCT
iajs-825	42	29	1	1	NUM
iajs-825	42	30	)	)	PUNCT
iajs-825	42	31	)	)	PUNCT
iajs-825	43	1	(	(	PUNCT
iajs-825	43	2	1	1	NUM
iajs-825	43	3	)	)	PUNCT
iajs-825	43	4	!	!	PUNCT
iajs-825	44	1			PROPN
iajs-825	44	2			PROPN
iajs-825	44	3			PROPN
iajs-825	44	4			PROPN
iajs-825	44	5			PROPN
iajs-825	44	6	k	k	NUM
iajs-825	44	7	k	k	PROPN
iajs-825	44	8	k	k	PROPN
iajs-825	44	9	n	n	CCONJ
iajs-825	44	10	n	n	ADV
iajs-825	44	11	2	2	NUM
iajs-825	44	12	.	.	PUNCT
iajs-825	45	1	t1	t1	NOUN
iajs-825	45	2	=	=	PUNCT
iajs-825	46	1	k	k	PROPN
iajs-825	46	2	t	t	PROPN
iajs-825	46	3	3	3	X
iajs-825	46	4	.	.	PUNCT
iajs-825	47	1	t2	t2	NOUN
iajs-825	47	2	=	=	SYM
iajs-825	47	3	(	(	PUNCT
iajs-825	47	4	1	1	NUM
iajs-825	47	5	)	)	SYM
iajs-825	47	6	2	2	NUM
iajs-825	47	7	k	k	NOUN
iajs-825	47	8	k	k	NOUN
iajs-825	47	9	4	4	X
iajs-825	47	10	.	.	PUNCT
iajs-825	47	11	t3	t3	PROPN
iajs-825	47	12	=	=	PUNCT
iajs-825	47	13	(	(	PUNCT
iajs-825	47	14	1	1	NUM
iajs-825	47	15	)	)	PUNCT
iajs-825	47	16	(	(	PUNCT
iajs-825	47	17	2	2	NUM
iajs-825	47	18	)	)	PUNCT
iajs-825	47	19	3	3	NUM
iajs-825	47	20	!	!	X
iajs-825	47	21			NOUN
iajs-825	47	22	k	k	PROPN
iajs-825	47	23	k	k	PROPN
iajs-825	47	24	k	k	PROPN
iajs-825	47	25	ibn	ibn	PROPN
iajs-825	47	26	alhaitham	alhaitham	PROPN
iajs-825	47	27	j.	j.	PROPN
iajs-825	47	28	for	for	ADP
iajs-825	47	29	pure	pure	ADJ
iajs-825	47	30	&	&	CCONJ
iajs-825	47	31	appl	appl	PROPN
iajs-825	47	32	.	.	PUNCT
iajs-825	48	1	sci	sci	PROPN
iajs-825	48	2	.	.	PUNCT
iajs-825	48	3	vol.24	vol.24	NOUN
iajs-825	48	4	(	(	PUNCT
iajs-825	48	5	3	3	NUM
iajs-825	48	6	)	)	PUNCT
iajs-825	48	7	2011	2011	NUM
iajs-825	48	8	5	5	NUM
iajs-825	48	9	.	.	PUNCT
iajs-825	48	10	tn	tn	NOUN
iajs-825	49	1	=	=	PUNCT
iajs-825	49	2	(	(	PUNCT
iajs-825	49	3	1	1	NUM
iajs-825	49	4	)	)	PUNCT
iajs-825	49	5	(	(	PUNCT
iajs-825	49	6	1	1	X
iajs-825	49	7	)	)	PUNCT
iajs-825	49	8	!	!	PUNCT
iajs-825	50	1			PROPN
iajs-825	50	2			PROPN
iajs-825	50	3	k	k	VERB
iajs-825	50	4	k	k	PROPN
iajs-825	50	5	k	k	PROPN
iajs-825	50	6	n	n	PROPN
iajs-825	50	7	n	n	ADV
iajs-825	50	8	6	6	NUM
iajs-825	50	9	.	.	PUNCT
iajs-825	51	1	t0	t0	NOUN
iajs-825	51	2	=	=	PUNCT
iajs-825	51	3	q3	q3	PROPN
iajs-825	51	4	+	+	PROPN
iajs-825	51	5	q2	q2	NOUN
iajs-825	52	1	+	+	CCONJ
iajs-825	52	2	q	q	PUNCT
iajs-825	53	1	+	+	NUM
iajs-825	53	2	1	1	NUM
iajs-825	53	3	–	–	PUNCT
iajs-825	53	4	k	k	PROPN
iajs-825	53	5	t	t	PROPN
iajs-825	53	6	–	–	PUNCT
iajs-825	53	7	(	(	PUNCT
iajs-825	53	8	1	1	X
iajs-825	53	9	)	)	SYM
iajs-825	53	10	2	2	NUM
iajs-825	53	11	k	k	NOUN
iajs-825	53	12	k	k	X
iajs-825	53	13	–	–	PUNCT
iajs-825	53	14	(	(	PUNCT
iajs-825	53	15	1	1	X
iajs-825	53	16	)	)	PUNCT
iajs-825	53	17	(	(	PUNCT
iajs-825	53	18	2	2	NUM
iajs-825	53	19	)	)	PUNCT
iajs-825	53	20	3	3	NUM
iajs-825	53	21	!	!	X
iajs-825	53	22			NOUN
iajs-825	53	23	k	k	PROPN
iajs-825	53	24	k	k	PROPN
iajs-825	53	25	k	k	PROPN
iajs-825	53	26	–	–	PUNCT
iajs-825	53	27			X
iajs-825	53	28	–	–	PUNCT
iajs-825	53	29	(	(	PUNCT
iajs-825	53	30	1	1	NUM
iajs-825	53	31	)	)	PUNCT
iajs-825	53	32	(	(	PUNCT
iajs-825	53	33	2	2	NUM
iajs-825	53	34	)	)	PUNCT
iajs-825	53	35	(	(	PUNCT
iajs-825	53	36	1	1	NUM
iajs-825	53	37	)	)	PUNCT
iajs-825	53	38	!	!	PUNCT
iajs-825	54	1			PROPN
iajs-825	54	2			PROPN
iajs-825	54	3			PROPN
iajs-825	54	4	k	k	VERB
iajs-825	54	5	k	k	PROPN
iajs-825	54	6	k	k	PROPN
iajs-825	54	7	k	k	PROPN
iajs-825	54	8	n	n	CCONJ
iajs-825	54	9	n	n	PRON
iajs-825	54	10	proof	proof	NOUN
iajs-825	54	11	:	:	PUNCT
iajs-825	54	12	1	1	X
iajs-825	54	13	.	.	X
iajs-825	54	14	there	there	PRON
iajs-825	54	15	exist	exist	VERB
iajs-825	54	16	(	(	PUNCT
iajs-825	54	17	k	k	X
iajs-825	54	18	–	–	PUNCT
iajs-825	54	19	1	1	NUM
iajs-825	54	20	)	)	PUNCT
iajs-825	54	21	2	2	NUM
iajs-825	54	22	-	-	PUNCT
iajs-825	54	23	secants	secant	NOUN
iajs-825	54	24	to	to	ADP
iajs-825	54	25	a	a	PRON
iajs-825	54	26	through	through	ADP
iajs-825	54	27	p	p	NOUN
iajs-825	54	28	and	and	CCONJ
iajs-825	54	29	there	there	PRON
iajs-825	54	30	exist	exist	VERB
iajs-825	54	31	1	1	NUM
iajs-825	54	32	2	2	NUM
iajs-825	54	33			PROPN
iajs-825	54	34			NOUN
iajs-825	55	1			PROPN
iajs-825	55	2			PROPN
iajs-825	56	1			PROPN
iajs-825	56	2			PROPN
iajs-825	56	3	k	k	X
iajs-825	56	4	(	(	PUNCT
iajs-825	56	5	3	3	NUM
iajs-825	56	6	-	-	PUNCT
iajs-825	56	7	secants	secant	NOUN
iajs-825	56	8	)	)	PUNCT
iajs-825	56	9	to	to	ADP
iajs-825	56	10	a	a	PRON
iajs-825	56	11	through	through	ADP
iajs-825	56	12	p	p	NOUN
iajs-825	56	13	,	,	PUNCT
iajs-825	56	14	and	and	CCONJ
iajs-825	56	15	so	so	ADV
iajs-825	56	16	there	there	PRON
iajs-825	56	17	exist	exist	VERB
iajs-825	56	18	1	1	NUM
iajs-825	56	19	1	1	NUM
iajs-825	56	20			PROPN
iajs-825	56	21			NOUN
iajs-825	56	22			PROPN
iajs-825	56	23			NOUN
iajs-825	56	24			PROPN
iajs-825	56	25	k	k	PROPN
iajs-825	56	26	n	n	CCONJ
iajs-825	56	27	n	n	PRON
iajs-825	56	28	secants	secant	NOUN
iajs-825	56	29	to	to	ADP
iajs-825	56	30	a	a	PRON
iajs-825	56	31	through	through	ADP
iajs-825	56	32	p	p	NOUN
iajs-825	56	33	,	,	PUNCT
iajs-825	56	34	and	and	CCONJ
iajs-825	56	35	since	since	SCONJ
iajs-825	56	36	there	there	PRON
iajs-825	56	37	exist	exist	VERB
iajs-825	56	38	exactly	exactly	ADV
iajs-825	56	39	q2	q2	NOUN
iajs-825	56	40	+	+	CCONJ
iajs-825	56	41	q	q	PUNCT
iajs-825	57	1	+	+	NUM
iajs-825	57	2	1	1	NUM
iajs-825	57	3	p	p	NOUN
iajs-825	57	4	lanes	lane	NOUN
iajs-825	57	5	through	through	ADP
iajs-825	57	6	p	p	NOUN
iajs-825	57	7	,	,	PUNCT
iajs-825	57	8	then	then	ADV
iajs-825	57	9	the	the	DET
iajs-825	57	10	number	number	NOUN
iajs-825	57	11	of	of	ADP
iajs-825	57	12	the	the	DET
iajs-825	57	13	1	1	NUM
iajs-825	57	14	-	-	PUNCT
iajs-825	57	15	secants	secant	NOUN
iajs-825	57	16	through	through	ADP
iajs-825	57	17	p	p	X
iajs-825	57	18	:	:	PUNCT
iajs-825	57	19	t(p	t(p	NOUN
iajs-825	57	20	)	)	PUNCT
iajs-825	57	21	=	=	SYM
iajs-825	57	22	q2	q2	NOUN
iajs-825	57	23	+	+	CCONJ
iajs-825	57	24	q	q	PUNCT
iajs-825	58	1	+	+	NUM
iajs-825	58	2	1	1	NUM
iajs-825	58	3	–	–	PUNCT
iajs-825	58	4	(	(	PUNCT
iajs-825	58	5	k	k	X
iajs-825	58	6	–	–	PUNCT
iajs-825	58	7	1	1	NUM
iajs-825	58	8	)	)	PUNCT
iajs-825	58	9	–	–	PUNCT
iajs-825	58	10	1	1	NUM
iajs-825	58	11	2	2	NUM
iajs-825	58	12			PROPN
iajs-825	58	13			NOUN
iajs-825	58	14			PROPN
iajs-825	58	15			PROPN
iajs-825	59	1			PROPN
iajs-825	59	2			PROPN
iajs-825	59	3	k	k	X
iajs-825	59	4	–	–	PUNCT
iajs-825	59	5			X
iajs-825	59	6	–	–	PUNCT
iajs-825	59	7	1	1	NUM
iajs-825	59	8	1	1	NUM
iajs-825	59	9			PROPN
iajs-825	59	10			NOUN
iajs-825	59	11			PROPN
iajs-825	59	12			NOUN
iajs-825	59	13			PROPN
iajs-825	59	14	k	k	NOUN
iajs-825	59	15	n	n	CCONJ
iajs-825	59	16	=	=	PROPN
iajs-825	59	17	q2	q2	PROPN
iajs-825	59	18	+	+	CCONJ
iajs-825	59	19	q	q	PUNCT
iajs-825	60	1	+	+	NUM
iajs-825	60	2	2	2	NUM
iajs-825	60	3	–	–	PUNCT
iajs-825	60	4	k	k	X
iajs-825	60	5	–	–	PUNCT
iajs-825	60	6	(	(	PUNCT
iajs-825	60	7	1	1	X
iajs-825	60	8	)	)	PUNCT
iajs-825	60	9	(	(	PUNCT
iajs-825	60	10	2	2	NUM
iajs-825	60	11	)	)	SYM
iajs-825	60	12	2	2	NUM
iajs-825	60	13			NOUN
iajs-825	60	14	k	k	NOUN
iajs-825	60	15	k	k	X
iajs-825	60	16	–	–	PUNCT
iajs-825	60	17			X
iajs-825	60	18	–	–	PUNCT
iajs-825	60	19	(	(	PUNCT
iajs-825	60	20	1	1	X
iajs-825	60	21	)	)	PUNCT
iajs-825	60	22	(	(	PUNCT
iajs-825	60	23	2	2	X
iajs-825	60	24	)	)	PUNCT
iajs-825	60	25	(	(	PUNCT
iajs-825	60	26	1	1	X
iajs-825	60	27	)	)	PUNCT
iajs-825	60	28	(	(	PUNCT
iajs-825	60	29	1	1	NUM
iajs-825	60	30	)	)	PUNCT
iajs-825	60	31	!	!	PUNCT
iajs-825	61	1			PROPN
iajs-825	61	2			PROPN
iajs-825	61	3			PROPN
iajs-825	61	4			PUNCT
iajs-825	61	5			PROPN
iajs-825	61	6	k	k	NUM
iajs-825	61	7	k	k	PROPN
iajs-825	61	8	k	k	PROPN
iajs-825	61	9	n	n	CCONJ
iajs-825	61	10	n	n	NOUN
iajs-825	61	11	=	=	NOUN
iajs-825	61	12	t.	t.	NOUN
iajs-825	61	13	2	2	NUM
iajs-825	61	14	.	.	PUNCT
iajs-825	62	1	t1	t1	NOUN
iajs-825	62	2	=	=	NOUN
iajs-825	63	1	the	the	DET
iajs-825	63	2	number	number	NOUN
iajs-825	63	3	of	of	ADP
iajs-825	63	4	1	1	NUM
iajs-825	63	5	-	-	PUNCT
iajs-825	63	6	secants	secant	NOUN
iajs-825	63	7	to	to	ADP
iajs-825	63	8	a	a	PRON
iajs-825	63	9	,	,	PUNCT
iajs-825	63	10	since	since	SCONJ
iajs-825	63	11	each	each	DET
iajs-825	63	12	point	point	NOUN
iajs-825	63	13	of	of	ADP
iajs-825	63	14	a	a	DET
iajs-825	63	15	has	ha	NOUN
iajs-825	63	16	t	t	X
iajs-825	63	17	(	(	PUNCT
iajs-825	63	18	1	1	NUM
iajs-825	63	19	-	-	PUNCT
iajs-825	63	20	secants	secant	NOUN
iajs-825	63	21	)	)	PUNCT
iajs-825	63	22	and	and	CCONJ
iajs-825	63	23	the	the	DET
iajs-825	63	24	number	number	NOUN
iajs-825	63	25	of	of	ADP
iajs-825	63	26	the	the	DET
iajs-825	63	27	points	point	NOUN
iajs-825	63	28	is	be	AUX
iajs-825	63	29	k	k	NOUN
iajs-825	63	30	,	,	PUNCT
iajs-825	63	31	then	then	ADV
iajs-825	63	32	t1	t1	NOUN
iajs-825	63	33	=	=	PUNCT
iajs-825	64	1	k	k	PROPN
iajs-825	64	2	t.	t.	PROPN
iajs-825	64	3	3	3	X
iajs-825	64	4	.	.	PUNCT
iajs-825	64	5	t2	t2	NOUN
iajs-825	64	6	=	=	PUNCT
iajs-825	64	7	the	the	DET
iajs-825	64	8	number	number	NOUN
iajs-825	64	9	of	of	ADP
iajs-825	64	10	2	2	NUM
iajs-825	64	11	-	-	PUNCT
iajs-825	64	12	secants	secant	NOUN
iajs-825	64	13	to	to	ADP
iajs-825	64	14	a	a	PRON
iajs-825	64	15	,	,	PUNCT
iajs-825	64	16	which	which	PRON
iajs-825	64	17	is	be	AUX
iajs-825	64	18	the	the	DET
iajs-825	64	19	number	number	NOUN
iajs-825	64	20	of	of	ADP
iajs-825	64	21	planes	plane	NOUN
iajs-825	64	22	passing	pass	VERB
iajs-825	64	23	through	through	ADP
iajs-825	64	24	any	any	DET
iajs-825	64	25	two	two	NUM
iajs-825	64	26	points	point	NOUN
iajs-825	64	27	of	of	ADP
iajs-825	64	28	a.	a.	NOUN
iajs-825	64	29	hence	hence	ADV
iajs-825	64	30	t2	t2	NOUN
iajs-825	64	31	=	=	SYM
iajs-825	64	32	2	2	NUM
iajs-825	64	33			NOUN
iajs-825	64	34			NOUN
iajs-825	64	35			PROPN
iajs-825	64	36			PROPN
iajs-825	65	1			PROPN
iajs-825	65	2			NOUN
iajs-825	65	3	k	k	X
iajs-825	66	1	=	=	PUNCT
iajs-825	66	2	(	(	PUNCT
iajs-825	66	3	1	1	NUM
iajs-825	66	4	)	)	SYM
iajs-825	66	5	2	2	NUM
iajs-825	66	6	k	k	NOUN
iajs-825	66	7	k	k	X
iajs-825	66	8	.	.	PUNCT
iajs-825	67	1	4	4	X
iajs-825	67	2	.	.	X
iajs-825	67	3	t3	t3	PROPN
iajs-825	67	4	=	=	PUNCT
iajs-825	68	1	the	the	DET
iajs-825	68	2	number	number	NOUN
iajs-825	68	3	of	of	ADP
iajs-825	68	4	3	3	NUM
iajs-825	68	5	-	-	PUNCT
iajs-825	68	6	secants	secant	NOUN
iajs-825	68	7	of	of	ADP
iajs-825	68	8	a	a	PRON
iajs-825	68	9	,	,	PUNCT
iajs-825	68	10	which	which	PRON
iajs-825	68	11	is	be	AUX
iajs-825	68	12	the	the	DET
iajs-825	68	13	number	number	NOUN
iajs-825	68	14	of	of	ADP
iajs-825	68	15	planes	plane	NOUN
iajs-825	68	16	passing	pass	VERB
iajs-825	68	17	through	through	ADP
iajs-825	68	18	any	any	DET
iajs-825	68	19	three	three	NUM
iajs-825	68	20	points	point	NOUN
iajs-825	68	21	of	of	ADP
iajs-825	68	22	a.	a.	NOUN
iajs-825	68	23	hence	hence	ADV
iajs-825	68	24	t3	t3	PROPN
iajs-825	68	25	=	=	SYM
iajs-825	68	26	3	3	NUM
iajs-825	68	27			NOUN
iajs-825	68	28			PROPN
iajs-825	68	29			PROPN
iajs-825	68	30			PROPN
iajs-825	68	31			PROPN
iajs-825	68	32			NOUN
iajs-825	68	33	k	k	X
iajs-825	68	34	=	=	PUNCT
iajs-825	68	35	(	(	PUNCT
iajs-825	68	36	1	1	NUM
iajs-825	68	37	)	)	PUNCT
iajs-825	68	38	(	(	PUNCT
iajs-825	68	39	2	2	NUM
iajs-825	68	40	)	)	PUNCT
iajs-825	68	41	3	3	NUM
iajs-825	68	42	!	!	X
iajs-825	68	43			NOUN
iajs-825	68	44	k	k	PROPN
iajs-825	68	45	k	k	PROPN
iajs-825	68	46	k	k	PROPN
iajs-825	68	47	.	.	PUNCT
iajs-825	69	1	5	5	X
iajs-825	69	2	.	.	X
iajs-825	69	3	tn	tn	NOUN
iajs-825	70	1	=	=	PUNCT
iajs-825	70	2	the	the	DET
iajs-825	70	3	number	number	NOUN
iajs-825	70	4	of	of	ADP
iajs-825	70	5	n	n	PRON
iajs-825	70	6	–	–	PUNCT
iajs-825	70	7	secants	secant	NOUN
iajs-825	70	8	p	p	NOUN
iajs-825	70	9	lanes	lane	NOUN
iajs-825	70	10	to	to	ADP
iajs-825	70	11	a	a	PRON
iajs-825	70	12	,	,	PUNCT
iajs-825	70	13	tn	tn	NOUN
iajs-825	70	14	=	=	SYM
iajs-825	70	15			NOUN
iajs-825	70	16			PROPN
iajs-825	70	17			PROPN
iajs-825	70	18			PROPN
iajs-825	71	1			PROPN
iajs-825	71	2			PROPN
iajs-825	71	3	k	k	NOUN
iajs-825	71	4	n	n	NOUN
iajs-825	71	5	=	=	SYM
iajs-825	71	6	(	(	PUNCT
iajs-825	71	7	1	1	NUM
iajs-825	71	8	)	)	PUNCT
iajs-825	71	9	(	(	PUNCT
iajs-825	71	10	1	1	X
iajs-825	71	11	)	)	PUNCT
iajs-825	71	12	!	!	PUNCT
iajs-825	72	1			PROPN
iajs-825	72	2			PROPN
iajs-825	72	3	k	k	VERB
iajs-825	72	4	k	k	PROPN
iajs-825	72	5	k	k	PROPN
iajs-825	72	6	n	n	CCONJ
iajs-825	72	7	n	n	NOUN
iajs-825	72	8	.	.	PUNCT
iajs-825	73	1	6	6	X
iajs-825	73	2	.	.	X
iajs-825	73	3	q3	q3	NOUN
iajs-825	73	4	+	+	CCONJ
iajs-825	73	5	q2	q2	NOUN
iajs-825	73	6	+	+	CCONJ
iajs-825	73	7	q	q	PUNCT
iajs-825	74	1	+	+	NOUN
iajs-825	74	2	1	1	NUM
iajs-825	74	3	represents	represent	VERB
iajs-825	74	4	the	the	DET
iajs-825	74	5	number	number	NOUN
iajs-825	74	6	of	of	ADP
iajs-825	74	7	all	all	DET
iajs-825	74	8	planes	plane	NOUN
iajs-825	74	9	,	,	PUNCT
iajs-825	74	10	then	then	ADV
iajs-825	74	11	in	in	ADP
iajs-825	74	12	a	a	DET
iajs-825	74	13	(	(	PUNCT
iajs-825	74	14	k	k	NOUN
iajs-825	74	15	,	,	PUNCT
iajs-825	74	16	n	n	CCONJ
iajs-825	74	17	)	)	PUNCT
iajs-825	74	18	–	–	PUNCT
iajs-825	74	19	arc	arc	NOUN
iajs-825	74	20	of	of	ADP
iajs-825	74	21	pg(3,q	pg(3,q	NOUN
iajs-825	74	22	)	)	PUNCT
iajs-825	74	23	,	,	PUNCT
iajs-825	74	24	q3	q3	PROPN
iajs-825	74	25	+	+	CCONJ
iajs-825	74	26	q2	q2	NOUN
iajs-825	74	27	+	+	CCONJ
iajs-825	74	28	q	q	PUNCT
iajs-825	75	1	+	+	NUM
iajs-825	75	2	1	1	NUM
iajs-825	75	3	=	=	SYM
iajs-825	75	4	t0	t0	PROPN
iajs-825	75	5	+	+	CCONJ
iajs-825	75	6	t1	t1	NOUN
iajs-825	75	7	+	+	CCONJ
iajs-825	75	8	t2	t2	NOUN
iajs-825	75	9	+	+	CCONJ
iajs-825	75	10	t3	t3	PROPN
iajs-825	75	11	+	+	X
iajs-825	75	12			X
iajs-825	75	13	+	+	NUM
iajs-825	75	14	tn	tn	NOUN
iajs-825	75	15	t0	t0	NOUN
iajs-825	75	16	=	=	PUNCT
iajs-825	75	17	q3	q3	PROPN
iajs-825	75	18	+	+	PROPN
iajs-825	75	19	q2	q2	NOUN
iajs-825	75	20	+	+	CCONJ
iajs-825	75	21	q	q	PUNCT
iajs-825	76	1	+	+	NUM
iajs-825	76	2	1	1	NUM
iajs-825	76	3	–	–	PUNCT
iajs-825	76	4	t1	t1	NOUN
iajs-825	76	5	–	–	PUNCT
iajs-825	76	6	t2	t2	PROPN
iajs-825	76	7	–	–	PUNCT
iajs-825	76	8	t3	t3	NOUN
iajs-825	76	9	–	–	PUNCT
iajs-825	76	10			X
iajs-825	76	11	–	–	PUNCT
iajs-825	76	12	tn	tn	NOUN
iajs-825	76	13	so	so	ADV
iajs-825	76	14	t0	t0	PROPN
iajs-825	76	15	=	=	SYM
iajs-825	76	16	q3	q3	PROPN
iajs-825	76	17	+	+	CCONJ
iajs-825	76	18	q2+q+1	q2+q+1	PROPN
iajs-825	76	19	–	–	PUNCT
iajs-825	76	20	k	k	PROPN
iajs-825	76	21	t	t	PROPN
iajs-825	76	22	–	–	PUNCT
iajs-825	76	23	(	(	PUNCT
iajs-825	76	24	1	1	X
iajs-825	76	25	)	)	SYM
iajs-825	76	26	2	2	NUM
iajs-825	76	27	k	k	NOUN
iajs-825	76	28	k	k	X
iajs-825	76	29	–	–	PUNCT
iajs-825	76	30	(	(	PUNCT
iajs-825	76	31	1	1	X
iajs-825	76	32	)	)	PUNCT
iajs-825	76	33	(	(	PUNCT
iajs-825	76	34	2	2	NUM
iajs-825	76	35	)	)	PUNCT
iajs-825	76	36	3	3	NUM
iajs-825	76	37	!	!	X
iajs-825	76	38			NOUN
iajs-825	76	39	k	k	PROPN
iajs-825	76	40	k	k	PROPN
iajs-825	76	41	k	k	PROPN
iajs-825	76	42	–	–	PUNCT
iajs-825	76	43			X
iajs-825	76	44	–	–	PUNCT
iajs-825	76	45	(	(	PUNCT
iajs-825	76	46	1	1	NUM
iajs-825	76	47	)	)	PUNCT
iajs-825	76	48	(	(	PUNCT
iajs-825	76	49	2	2	NUM
iajs-825	76	50	)	)	PUNCT
iajs-825	76	51	(	(	PUNCT
iajs-825	76	52	1	1	NUM
iajs-825	76	53	)	)	PUNCT
iajs-825	76	54	!	!	PUNCT
iajs-825	77	1			PROPN
iajs-825	77	2			PROPN
iajs-825	77	3			PROPN
iajs-825	77	4	k	k	VERB
iajs-825	77	5	k	k	PROPN
iajs-825	77	6	k	k	PROPN
iajs-825	77	7	k	k	PROPN
iajs-825	77	8	n	n	CCONJ
iajs-825	77	9	n	n	PROPN
iajs-825	77	10	.	.	PUNCT
iajs-825	78	1	theorem	theorem	ADJ
iajs-825	78	2	10	10	NUM
iajs-825	78	3	:	:	PUNCT
iajs-825	78	4	let	let	VERB
iajs-825	78	5	ti	ti	NOUN
iajs-825	78	6	represents	represent	VERB
iajs-825	78	7	the	the	DET
iajs-825	78	8	total	total	ADJ
iajs-825	78	9	number	number	NOUN
iajs-825	78	10	of	of	ADP
iajs-825	78	11	the	the	DET
iajs-825	78	12	i	i	NOUN
iajs-825	78	13	–	–	PUNCT
iajs-825	78	14	secants	secant	NOUN
iajs-825	78	15	for	for	ADP
iajs-825	78	16	a	a	DET
iajs-825	78	17	(	(	PUNCT
iajs-825	78	18	k	k	NOUN
iajs-825	78	19	,	,	PUNCT
iajs-825	78	20	n	n	CCONJ
iajs-825	78	21	)	)	PUNCT
iajs-825	78	22	–	–	PUNCT
iajs-825	78	23	arc	arc	VERB
iajs-825	78	24	a	a	PRON
iajs-825	78	25	in	in	ADP
iajs-825	78	26	pg(3,q	pg(3,q	NOUN
iajs-825	78	27	)	)	PUNCT
iajs-825	78	28	,	,	PUNCT
iajs-825	78	29	then	then	ADV
iajs-825	78	30	the	the	DET
iajs-825	78	31	following	follow	VERB
iajs-825	78	32	equations	equation	NOUN
iajs-825	78	33	are	be	AUX
iajs-825	78	34	satisfied	satisfied	ADJ
iajs-825	78	35	:	:	PUNCT
iajs-825	79	1	1	1	X
iajs-825	79	2	.	.	X
iajs-825	79	3	0	0	NUM
iajs-825	79	4			X
iajs-825	80	1	n	n	CCONJ
iajs-825	80	2	i	i	PRON
iajs-825	80	3	t	t	VERB
iajs-825	81	1	i	i	PRON
iajs-825	81	2	=	=	PUNCT
iajs-825	81	3	q	q	PROPN
iajs-825	82	1	3	3	NUM
iajs-825	82	2	+	+	CCONJ
iajs-825	82	3	q	q	PROPN
iajs-825	82	4	2	2	NUM
iajs-825	82	5	+	+	NOUN
iajs-825	82	6	q	q	NOUN
iajs-825	83	1	+	+	NUM
iajs-825	83	2	1	1	NUM
iajs-825	83	3	2	2	NUM
iajs-825	83	4	.	.	X
iajs-825	84	1	1	1	NUM
iajs-825	84	2			NUM
iajs-825	85	1	n	n	NOUN
iajs-825	85	2	i	i	PRON
iajs-825	86	1	i	i	INTJ
iajs-825	86	2	!	!	PUNCT
iajs-825	87	1	t	t	PROPN
iajs-825	88	1	i	i	PRON
iajs-825	88	2	=	=	SYM
iajs-825	89	1	k	k	PROPN
iajs-825	89	2	t	t	PROPN
iajs-825	89	3	+	+	CCONJ
iajs-825	89	4	k	k	PROPN
iajs-825	89	5	(	(	PUNCT
iajs-825	89	6	k	k	X
iajs-825	89	7	–	–	PUNCT
iajs-825	89	8	1	1	NUM
iajs-825	89	9	)	)	PUNCT
iajs-825	90	1	+	+	CCONJ
iajs-825	90	2	k	k	X
iajs-825	90	3	(	(	PUNCT
iajs-825	90	4	k	k	X
iajs-825	90	5	–	–	PUNCT
iajs-825	90	6	1)(k	1)(k	NUM
iajs-825	90	7	–	–	PUNCT
iajs-825	90	8	2	2	NUM
iajs-825	90	9	)	)	PUNCT
iajs-825	90	10	+	+	NUM
iajs-825	90	11			X
iajs-825	91	1	+	+	CCONJ
iajs-825	91	2	k	k	X
iajs-825	91	3	(	(	PUNCT
iajs-825	91	4	k	k	X
iajs-825	91	5	–	–	PUNCT
iajs-825	91	6	1	1	NUM
iajs-825	91	7	)	)	PUNCT
iajs-825	91	8			PUNCT
iajs-825	91	9	(	(	PUNCT
iajs-825	91	10	k	k	X
iajs-825	91	11	–	–	PUNCT
iajs-825	91	12	n	n	CCONJ
iajs-825	91	13	)	)	PUNCT
iajs-825	91	14	ibn	ibn	NOUN
iajs-825	91	15	alhaitham	alhaitham	NOUN
iajs-825	91	16	j.	j.	PROPN
iajs-825	91	17	for	for	ADP
iajs-825	91	18	pure	pure	ADJ
iajs-825	91	19	&	&	CCONJ
iajs-825	91	20	appl	appl	PROPN
iajs-825	91	21	.	.	PUNCT
iajs-825	92	1	sci	sci	PROPN
iajs-825	92	2	.	.	PUNCT
iajs-825	92	3	vol.24	vol.24	NOUN
iajs-825	92	4	(	(	PUNCT
iajs-825	92	5	3	3	NUM
iajs-825	92	6	)	)	PUNCT
iajs-825	92	7	2011	2011	NUM
iajs-825	92	8	3	3	NUM
iajs-825	92	9	.	.	PUNCT
iajs-825	93	1	2	2	NUM
iajs-825	93	2			X
iajs-825	94	1	n	n	CCONJ
iajs-825	94	2	i	i	PRON
iajs-825	95	1	i	i	PRON
iajs-825	95	2	(	(	PUNCT
iajs-825	95	3	i	i	NOUN
iajs-825	95	4	–	–	PUNCT
iajs-825	95	5	1	1	NUM
iajs-825	95	6	)	)	PUNCT
iajs-825	95	7	t	t	NOUN
iajs-825	96	1	i	i	NOUN
iajs-825	96	2	=	=	SYM
iajs-825	96	3	k	k	X
iajs-825	96	4	(	(	PUNCT
iajs-825	96	5	k	k	X
iajs-825	96	6	–	–	PUNCT
iajs-825	96	7	1	1	NUM
iajs-825	96	8	)	)	PUNCT
iajs-825	97	1	+	+	CCONJ
iajs-825	97	2	k	k	X
iajs-825	97	3	(	(	PUNCT
iajs-825	97	4	k	k	X
iajs-825	97	5	–	–	PUNCT
iajs-825	97	6	1)(k	1)(k	NUM
iajs-825	97	7	–	–	PUNCT
iajs-825	97	8	2	2	NUM
iajs-825	97	9	)	)	PUNCT
iajs-825	97	10	+	+	CCONJ
iajs-825	97	11	1	1	NUM
iajs-825	97	12	2	2	NUM
iajs-825	97	13	k	k	X
iajs-825	97	14	(	(	PUNCT
iajs-825	97	15	k	k	X
iajs-825	97	16	–	–	PUNCT
iajs-825	97	17	1)(k	1)(k	NUM
iajs-825	97	18	–	–	SYM
iajs-825	97	19	2)(k	2)(k	NUM
iajs-825	97	20	–	–	PUNCT
iajs-825	97	21	3	3	NUM
iajs-825	97	22	)	)	PUNCT
iajs-825	97	23	+	+	NOUN
iajs-825	97	24			PUNCT
iajs-825	97	25	+	+	CCONJ
iajs-825	97	26	1	1	NUM
iajs-825	97	27	(	(	PUNCT
iajs-825	97	28	2)!n	2)!n	NUM
iajs-825	97	29	k	k	X
iajs-825	97	30	(	(	PUNCT
iajs-825	97	31	k	k	X
iajs-825	97	32	–	–	PUNCT
iajs-825	97	33	1	1	NUM
iajs-825	97	34	)	)	PUNCT
iajs-825	97	35			PUNCT
iajs-825	97	36	(	(	PUNCT
iajs-825	97	37	k	k	X
iajs-825	97	38	–	–	PUNCT
iajs-825	97	39	n	n	CCONJ
iajs-825	97	40	)	)	PUNCT
iajs-825	97	41	.	.	PUNCT
iajs-825	98	1	proof	proof	NOUN
iajs-825	98	2	:	:	PUNCT
iajs-825	98	3	1	1	X
iajs-825	98	4	.	.	X
iajs-825	98	5	0	0	NUM
iajs-825	98	6			X
iajs-825	99	1	n	n	CCONJ
iajs-825	99	2	i	i	PRON
iajs-825	99	3	t	t	PROPN
iajs-825	100	1	i	i	PRON
iajs-825	100	2	represents	represent	VERB
iajs-825	100	3	the	the	DET
iajs-825	100	4	sum	sum	NOUN
iajs-825	100	5	of	of	ADP
iajs-825	100	6	numbers	number	NOUN
iajs-825	100	7	of	of	ADP
iajs-825	100	8	all	all	DET
iajs-825	100	9	i	i	PRON
iajs-825	100	10	–	–	PUNCT
iajs-825	100	11	secants	secant	NOUN
iajs-825	100	12	to	to	ADP
iajs-825	100	13	a	a	PRON
iajs-825	100	14	,	,	PUNCT
iajs-825	100	15	which	which	PRON
iajs-825	100	16	is	be	AUX
iajs-825	100	17	the	the	DET
iajs-825	100	18	number	number	NOUN
iajs-825	100	19	of	of	ADP
iajs-825	100	20	all	all	DET
iajs-825	100	21	planes	plane	NOUN
iajs-825	100	22	in	in	ADP
iajs-825	100	23	the	the	DET
iajs-825	100	24	space	space	NOUN
iajs-825	100	25	.	.	PUNCT
iajs-825	101	1	hence	hence	ADV
iajs-825	101	2	0	0	VERB
iajs-825	101	3			X
iajs-825	102	1	n	n	NOUN
iajs-825	102	2	i	i	PRON
iajs-825	102	3	ti	ti	NOUN
iajs-825	102	4	=	=	NOUN
iajs-825	102	5	q3	q3	NOUN
iajs-825	102	6	+	+	PROPN
iajs-825	102	7	q2	q2	NOUN
iajs-825	102	8	+	+	CCONJ
iajs-825	102	9	q	q	NOUN
iajs-825	103	1	+	+	NUM
iajs-825	103	2	1	1	NUM
iajs-825	103	3	.	.	NOUN
iajs-825	103	4	2	2	NUM
iajs-825	103	5	.	.	X
iajs-825	104	1	t1	t1	NOUN
iajs-825	104	2	=	=	PROPN
iajs-825	105	1	k	k	PROPN
iajs-825	105	2	t	t	PROPN
iajs-825	105	3	,	,	PUNCT
iajs-825	105	4	t	t	NOUN
iajs-825	105	5	=	=	SYM
iajs-825	105	6	q2	q2	PROPN
iajs-825	105	7	+	+	CCONJ
iajs-825	105	8	q	q	PUNCT
iajs-825	106	1	+	+	NUM
iajs-825	106	2	2	2	NUM
iajs-825	106	3	–	–	PUNCT
iajs-825	106	4	k	k	X
iajs-825	106	5	–	–	PUNCT
iajs-825	106	6	(	(	PUNCT
iajs-825	106	7	1	1	X
iajs-825	106	8	)	)	PUNCT
iajs-825	106	9	(	(	PUNCT
iajs-825	106	10	2	2	NUM
iajs-825	106	11	)	)	SYM
iajs-825	106	12	2	2	NUM
iajs-825	106	13			NOUN
iajs-825	106	14	k	k	NOUN
iajs-825	106	15	k	k	X
iajs-825	106	16	–	–	PUNCT
iajs-825	106	17			X
iajs-825	106	18	–	–	PUNCT
iajs-825	106	19	(	(	PUNCT
iajs-825	106	20	1	1	X
iajs-825	106	21	)	)	PUNCT
iajs-825	106	22	(	(	PUNCT
iajs-825	106	23	1	1	X
iajs-825	106	24	)	)	PUNCT
iajs-825	106	25	(	(	PUNCT
iajs-825	106	26	1	1	NUM
iajs-825	106	27	)	)	PUNCT
iajs-825	106	28	!	!	PUNCT
iajs-825	107	1			PROPN
iajs-825	107	2			PROPN
iajs-825	107	3			VERB
iajs-825	107	4			PROPN
iajs-825	107	5	k	k	NUM
iajs-825	107	6	k	k	PROPN
iajs-825	107	7	n	n	CCONJ
iajs-825	107	8	n	n	NOUN
iajs-825	107	9	,	,	PUNCT
iajs-825	107	10	t2	t2	NOUN
iajs-825	107	11	=	=	SYM
iajs-825	107	12	(	(	PUNCT
iajs-825	107	13	1	1	NUM
iajs-825	107	14	)	)	SYM
iajs-825	107	15	2	2	NUM
iajs-825	107	16	k	k	NOUN
iajs-825	107	17	k	k	PROPN
iajs-825	107	18	,	,	PUNCT
iajs-825	107	19	t3	t3	PROPN
iajs-825	107	20	=	=	PUNCT
iajs-825	107	21	(	(	PUNCT
iajs-825	107	22	1	1	NUM
iajs-825	107	23	)	)	PUNCT
iajs-825	107	24	(	(	PUNCT
iajs-825	107	25	2	2	NUM
iajs-825	107	26	)	)	PUNCT
iajs-825	107	27	3	3	NUM
iajs-825	107	28	!	!	X
iajs-825	108	1			NOUN
iajs-825	108	2	k	k	PROPN
iajs-825	108	3	k	k	PROPN
iajs-825	108	4	k	k	PROPN
iajs-825	108	5	,	,	PUNCT
iajs-825	108	6	t4	t4	PROPN
iajs-825	108	7	=	=	PUNCT
iajs-825	108	8	(	(	PUNCT
iajs-825	108	9	1	1	NUM
iajs-825	108	10	)	)	PUNCT
iajs-825	108	11	(	(	PUNCT
iajs-825	108	12	2	2	NUM
iajs-825	108	13	)	)	PUNCT
iajs-825	108	14	(	(	PUNCT
iajs-825	108	15	3	3	NUM
iajs-825	108	16	)	)	PUNCT
iajs-825	108	17	4	4	NUM
iajs-825	108	18	!	!	X
iajs-825	109	1			NOUN
iajs-825	109	2			PROPN
iajs-825	109	3	k	k	NOUN
iajs-825	109	4	k	k	PROPN
iajs-825	109	5	k	k	PROPN
iajs-825	109	6	k	k	PROPN
iajs-825	109	7	,	,	PUNCT
iajs-825	109	8			PROPN
iajs-825	109	9	,	,	PUNCT
iajs-825	109	10	tn	tn	PROPN
iajs-825	109	11	=	=	PUNCT
iajs-825	109	12	(	(	PUNCT
iajs-825	109	13	1	1	NUM
iajs-825	109	14	)	)	PUNCT
iajs-825	109	15	(	(	PUNCT
iajs-825	109	16	1	1	X
iajs-825	109	17	)	)	PUNCT
iajs-825	109	18	!	!	PUNCT
iajs-825	110	1			PROPN
iajs-825	110	2			PROPN
iajs-825	110	3	k	k	VERB
iajs-825	110	4	k	k	PROPN
iajs-825	110	5	k	k	PROPN
iajs-825	110	6	n	n	CCONJ
iajs-825	110	7	n	n	PROPN
iajs-825	110	8	1	1	NUM
iajs-825	110	9			X
iajs-825	111	1	n	n	NOUN
iajs-825	111	2	i	i	PRON
iajs-825	112	1	i	i	INTJ
iajs-825	112	2	!	!	PUNCT
iajs-825	113	1	t	t	PROPN
iajs-825	114	1	i	i	PRON
iajs-825	114	2	=	=	PROPN
iajs-825	115	1	t1	t1	NOUN
iajs-825	115	2	+	+	CCONJ
iajs-825	115	3	2	2	NUM
iajs-825	115	4	!	!	PUNCT
iajs-825	116	1	t2	t2	NOUN
iajs-825	116	2	+	+	CCONJ
iajs-825	117	1	3	3	NUM
iajs-825	117	2	!	!	PUNCT
iajs-825	118	1	t3	t3	PROPN
iajs-825	119	1	+	+	CCONJ
iajs-825	119	2			X
iajs-825	119	3	+	+	CCONJ
iajs-825	119	4	n	n	NOUN
iajs-825	119	5	!	!	PUNCT
iajs-825	120	1	tn	tn	X
iajs-825	121	1	=	=	SYM
iajs-825	121	2	k	k	PROPN
iajs-825	121	3	t	t	PROPN
iajs-825	121	4	+	+	CCONJ
iajs-825	121	5	k	k	PROPN
iajs-825	121	6	(	(	PUNCT
iajs-825	121	7	k	k	X
iajs-825	121	8	–	–	PUNCT
iajs-825	121	9	1	1	NUM
iajs-825	121	10	)	)	PUNCT
iajs-825	122	1	+	+	CCONJ
iajs-825	122	2	k	k	X
iajs-825	122	3	(	(	PUNCT
iajs-825	122	4	k	k	X
iajs-825	122	5	–	–	PUNCT
iajs-825	122	6	1)(k	1)(k	NUM
iajs-825	122	7	–	–	PUNCT
iajs-825	122	8	2	2	NUM
iajs-825	122	9	)	)	PUNCT
iajs-825	122	10	+	+	NUM
iajs-825	122	11			X
iajs-825	123	1	+	+	CCONJ
iajs-825	124	1	k	k	X
iajs-825	124	2	(	(	PUNCT
iajs-825	124	3	k	k	X
iajs-825	124	4	–	–	PUNCT
iajs-825	124	5	1	1	NUM
iajs-825	124	6	)	)	PUNCT
iajs-825	124	7			PUNCT
iajs-825	124	8	(	(	PUNCT
iajs-825	124	9	k	k	X
iajs-825	124	10	–	–	PUNCT
iajs-825	124	11	n	n	PROPN
iajs-825	124	12	+	+	CCONJ
iajs-825	124	13	1	1	NUM
iajs-825	124	14	)	)	PUNCT
iajs-825	124	15	3	3	NUM
iajs-825	124	16	.	.	X
iajs-825	125	1	2	2	NUM
iajs-825	125	2			X
iajs-825	126	1	n	n	CCONJ
iajs-825	126	2	i	i	PRON
iajs-825	127	1	i	i	PRON
iajs-825	127	2	(	(	PUNCT
iajs-825	127	3	i	i	NOUN
iajs-825	127	4	–	–	PUNCT
iajs-825	127	5	1	1	NUM
iajs-825	127	6	)	)	PUNCT
iajs-825	127	7	t	t	NOUN
iajs-825	128	1	i	i	NOUN
iajs-825	128	2	=	=	SYM
iajs-825	128	3	2	2	NUM
iajs-825	128	4	t2	t2	NOUN
iajs-825	128	5	+	+	CCONJ
iajs-825	128	6	6	6	NUM
iajs-825	128	7	t3	t3	NOUN
iajs-825	128	8	+	+	CCONJ
iajs-825	128	9	12	12	NUM
iajs-825	128	10	t4	t4	PROPN
iajs-825	128	11	+	+	X
iajs-825	128	12			X
iajs-825	128	13	+	+	CCONJ
iajs-825	128	14	n	n	CCONJ
iajs-825	128	15	(	(	PUNCT
iajs-825	128	16	n	n	CCONJ
iajs-825	128	17	–	–	PUNCT
iajs-825	128	18	1	1	NUM
iajs-825	128	19	)	)	PUNCT
iajs-825	128	20	tn	tn	NOUN
iajs-825	129	1	=	=	SYM
iajs-825	129	2	k	k	PROPN
iajs-825	129	3	(	(	PUNCT
iajs-825	129	4	k	k	X
iajs-825	129	5	–	–	PUNCT
iajs-825	129	6	1	1	NUM
iajs-825	129	7	)	)	PUNCT
iajs-825	130	1	+	+	CCONJ
iajs-825	130	2	k	k	X
iajs-825	130	3	(	(	PUNCT
iajs-825	130	4	k	k	X
iajs-825	130	5	–	–	PUNCT
iajs-825	130	6	1)(k	1)(k	NUM
iajs-825	130	7	–	–	PUNCT
iajs-825	130	8	2	2	NUM
iajs-825	130	9	)	)	PUNCT
iajs-825	130	10	+	+	CCONJ
iajs-825	130	11	1	1	NUM
iajs-825	130	12	2	2	NUM
iajs-825	130	13	k	k	X
iajs-825	130	14	(	(	PUNCT
iajs-825	130	15	k	k	X
iajs-825	130	16	–	–	PUNCT
iajs-825	130	17	1)(k	1)(k	NUM
iajs-825	130	18	–	–	SYM
iajs-825	130	19	2)(k	2)(k	NUM
iajs-825	130	20	–	–	PUNCT
iajs-825	130	21	3	3	NUM
iajs-825	130	22	)	)	PUNCT
iajs-825	130	23	+	+	NOUN
iajs-825	130	24			PUNCT
iajs-825	130	25	+	+	CCONJ
iajs-825	130	26	1	1	NUM
iajs-825	130	27	(	(	PUNCT
iajs-825	130	28	2)!n	2)!n	NUM
iajs-825	130	29	k	k	X
iajs-825	130	30	(	(	PUNCT
iajs-825	130	31	k	k	X
iajs-825	130	32	–	–	PUNCT
iajs-825	130	33	1	1	NUM
iajs-825	130	34	)	)	PUNCT
iajs-825	130	35			PUNCT
iajs-825	130	36	(	(	PUNCT
iajs-825	130	37	k	k	X
iajs-825	130	38	–	–	PUNCT
iajs-825	130	39	n	n	PROPN
iajs-825	130	40	+	+	CCONJ
iajs-825	130	41	1	1	NUM
iajs-825	130	42	)	)	PUNCT
iajs-825	130	43	theorem	theorem	NOUN
iajs-825	130	44	11	11	NUM
iajs-825	130	45	:	:	PUNCT
iajs-825	130	46	let	let	VERB
iajs-825	130	47	ri	ri	PROPN
iajs-825	130	48	=	=	PRON
iajs-825	130	49	ri(p	ri(p	NOUN
iajs-825	130	50	)	)	PUNCT
iajs-825	130	51	represents	represent	VERB
iajs-825	130	52	the	the	DET
iajs-825	130	53	number	number	NOUN
iajs-825	130	54	of	of	ADP
iajs-825	130	55	the	the	DET
iajs-825	130	56	i	i	NOUN
iajs-825	130	57	–	–	PUNCT
iajs-825	130	58	secants	secant	NOUN
iajs-825	130	59	(	(	PUNCT
iajs-825	130	60	planes	plane	NOUN
iajs-825	130	61	)	)	PUNCT
iajs-825	130	62	through	through	ADP
iajs-825	130	63	a	a	DET
iajs-825	130	64	point	point	NOUN
iajs-825	130	65	p	p	NOUN
iajs-825	130	66	of	of	ADP
iajs-825	130	67	a	a	DET
iajs-825	130	68	(	(	PUNCT
iajs-825	130	69	k	k	NOUN
iajs-825	130	70	,	,	PUNCT
iajs-825	130	71	n	n	CCONJ
iajs-825	130	72	)	)	PUNCT
iajs-825	130	73	–	–	PUNCT
iajs-825	130	74	arc	arc	NOUN
iajs-825	130	75	a	a	PRON
iajs-825	130	76	,	,	PUNCT
iajs-825	130	77	in	in	ADP
iajs-825	130	78	pg(3,q	pg(3,q	NOUN
iajs-825	130	79	)	)	PUNCT
iajs-825	130	80	then	then	ADV
iajs-825	130	81	the	the	DET
iajs-825	130	82	following	follow	VERB
iajs-825	130	83	equations	equation	NOUN
iajs-825	130	84	are	be	AUX
iajs-825	130	85	satisfied	satisfied	ADJ
iajs-825	130	86	:	:	PUNCT
iajs-825	130	87	1	1	NUM
iajs-825	130	88	.	.	X
iajs-825	130	89	1	1	NUM
iajs-825	130	90			X
iajs-825	130	91	n	n	NOUN
iajs-825	130	92	i	i	PRON
iajs-825	130	93	ri	ri	PROPN
iajs-825	130	94	=	=	SYM
iajs-825	130	95	q2	q2	PROPN
iajs-825	130	96	+	+	CCONJ
iajs-825	130	97	q	q	PUNCT
iajs-825	131	1	+	+	NUM
iajs-825	131	2	1	1	NUM
iajs-825	131	3	2	2	NUM
iajs-825	131	4	.	.	PUNCT
iajs-825	132	1	2	2	NUM
iajs-825	132	2			X
iajs-825	133	1	n	n	INTJ
iajs-825	133	2	i	i	PRON
iajs-825	133	3	(	(	PUNCT
iajs-825	133	4	i	i	NOUN
iajs-825	133	5	–	–	PUNCT
iajs-825	133	6	1	1	NUM
iajs-825	133	7	)	)	PUNCT
iajs-825	133	8	!	!	PUNCT
iajs-825	134	1	ri	ri	PROPN
iajs-825	135	1	=	=	PUNCT
iajs-825	135	2	(	(	PUNCT
iajs-825	135	3	k	k	X
iajs-825	135	4	–	–	PUNCT
iajs-825	135	5	1	1	NUM
iajs-825	135	6	)	)	PUNCT
iajs-825	135	7	+	+	CCONJ
iajs-825	135	8	(	(	PUNCT
iajs-825	135	9	k	k	X
iajs-825	135	10	–	–	PUNCT
iajs-825	135	11	1)(k	1)(k	NUM
iajs-825	135	12	–	–	PUNCT
iajs-825	135	13	2	2	NUM
iajs-825	135	14	)	)	PUNCT
iajs-825	135	15	+	+	NUM
iajs-825	135	16			X
iajs-825	135	17	+	+	CCONJ
iajs-825	135	18	(	(	PUNCT
iajs-825	135	19	k	k	X
iajs-825	135	20	–	–	PUNCT
iajs-825	135	21	1)(k	1)(k	NUM
iajs-825	135	22	–	–	SYM
iajs-825	135	23	2	2	NUM
iajs-825	135	24	)	)	PUNCT
iajs-825	135	25			NOUN
iajs-825	135	26	(	(	PUNCT
iajs-825	135	27	k	k	X
iajs-825	135	28	–	–	PUNCT
iajs-825	135	29	n	n	CCONJ
iajs-825	135	30	–	–	PUNCT
iajs-825	135	31	1	1	NUM
iajs-825	135	32	)	)	PUNCT
iajs-825	135	33	=	=	SYM
iajs-825	135	34	1	1	NUM
iajs-825	135	35	1	1	NUM
iajs-825	135	36			NOUN
iajs-825	135	37			NOUN
iajs-825	135	38			X
iajs-825	136	1	n	n	NOUN
iajs-825	136	2	i	i	PRON
iajs-825	136	3	(	(	PUNCT
iajs-825	136	4	k	k	PROPN
iajs-825	136	5	–	–	PUNCT
iajs-825	136	6	1	1	NUM
iajs-825	136	7	)	)	PUNCT
iajs-825	136	8			PUNCT
iajs-825	136	9	(	(	PUNCT
iajs-825	136	10	k	k	X
iajs-825	136	11	–	–	PUNCT
iajs-825	136	12	i	i	NOUN
iajs-825	136	13	)	)	PUNCT
iajs-825	136	14	proof	proof	NOUN
iajs-825	136	15	:	:	PUNCT
iajs-825	136	16	1	1	X
iajs-825	136	17	.	.	X
iajs-825	137	1	1	1	NUM
iajs-825	137	2			X
iajs-825	138	1	n	n	NOUN
iajs-825	138	2	i	i	PRON
iajs-825	138	3	ri	ri	PROPN
iajs-825	139	1	=	=	PROPN
iajs-825	139	2	r1	r1	PROPN
iajs-825	139	3	+	+	CCONJ
iajs-825	139	4	r2	r2	PROPN
iajs-825	139	5	+	+	CCONJ
iajs-825	139	6			X
iajs-825	139	7	+	+	CCONJ
iajs-825	139	8	rn	rn	PROPN
iajs-825	139	9	,	,	PUNCT
iajs-825	139	10	1	1	NUM
iajs-825	139	11			X
iajs-825	140	1	n	n	NOUN
iajs-825	140	2	i	i	PRON
iajs-825	140	3	ri	ri	PROPN
iajs-825	140	4	represents	represent	VERB
iajs-825	140	5	the	the	DET
iajs-825	140	6	sum	sum	NOUN
iajs-825	140	7	of	of	ADP
iajs-825	140	8	numbers	number	NOUN
iajs-825	140	9	of	of	ADP
iajs-825	140	10	all	all	DET
iajs-825	140	11	the	the	DET
iajs-825	140	12	i	i	NOUN
iajs-825	140	13	–	–	PUNCT
iajs-825	140	14	secants	secant	NOUN
iajs-825	140	15	through	through	ADP
iajs-825	140	16	a	a	DET
iajs-825	140	17	point	point	NOUN
iajs-825	140	18	p	p	NOUN
iajs-825	140	19	of	of	ADP
iajs-825	140	20	the	the	DET
iajs-825	140	21	arc	arc	NOUN
iajs-825	140	22	a	a	PRON
iajs-825	140	23	,	,	PUNCT
iajs-825	140	24	which	which	PRON
iajs-825	140	25	is	be	AUX
iajs-825	140	26	the	the	DET
iajs-825	140	27	number	number	NOUN
iajs-825	140	28	of	of	ADP
iajs-825	140	29	the	the	DET
iajs-825	140	30	planes	plane	NOUN
iajs-825	140	31	through	through	ADP
iajs-825	140	32	p.	p.	PROPN
iajs-825	140	33	thus	thus	ADV
iajs-825	140	34	,	,	PUNCT
iajs-825	141	1	1	1	NUM
iajs-825	141	2			X
iajs-825	141	3	n	n	NOUN
iajs-825	142	1	i	i	PRON
iajs-825	142	2	ri	ri	PROPN
iajs-825	143	1	=	=	PUNCT
iajs-825	143	2	q	q	PROPN
iajs-825	143	3	2	2	NUM
iajs-825	143	4	+	+	CCONJ
iajs-825	143	5	q	q	NOUN
iajs-825	144	1	+	+	NUM
iajs-825	144	2	1	1	X
iajs-825	144	3	.	.	X
iajs-825	144	4	ibn	ibn	PROPN
iajs-825	144	5	alhaitham	alhaitham	PROPN
iajs-825	144	6	j.	j.	PROPN
iajs-825	144	7	for	for	ADP
iajs-825	144	8	pure	pure	ADJ
iajs-825	144	9	&	&	CCONJ
iajs-825	144	10	appl	appl	PROPN
iajs-825	144	11	.	.	PUNCT
iajs-825	145	1	sci	sci	PROPN
iajs-825	145	2	.	.	PUNCT
iajs-825	145	3	vol.24	vol.24	NOUN
iajs-825	145	4	(	(	PUNCT
iajs-825	145	5	3	3	NUM
iajs-825	145	6	)	)	PUNCT
iajs-825	145	7	2011	2011	NUM
iajs-825	145	8	2	2	NUM
iajs-825	145	9	.	.	PUNCT
iajs-825	146	1	2	2	NUM
iajs-825	146	2			X
iajs-825	147	1	n	n	INTJ
iajs-825	147	2	i	i	PRON
iajs-825	147	3	(	(	PUNCT
iajs-825	147	4	i	i	NOUN
iajs-825	147	5	–	–	PUNCT
iajs-825	147	6	1	1	NUM
iajs-825	147	7	)	)	PUNCT
iajs-825	147	8	!	!	PUNCT
iajs-825	148	1	ri	ri	PROPN
iajs-825	149	1	=	=	PROPN
iajs-825	149	2	r2	r2	PROPN
iajs-825	149	3	+	+	CCONJ
iajs-825	149	4	2	2	X
iajs-825	149	5	!	!	X
iajs-825	149	6	r3	r3	NOUN
iajs-825	149	7	+	+	CCONJ
iajs-825	149	8	3	3	X
iajs-825	149	9	!	!	X
iajs-825	149	10	r4	r4	VERB
iajs-825	149	11	+	+	PRON
iajs-825	149	12			X
iajs-825	149	13	+	+	CCONJ
iajs-825	149	14	(	(	PUNCT
iajs-825	149	15	n	n	X
iajs-825	149	16	–	–	PUNCT
iajs-825	149	17	1	1	NUM
iajs-825	149	18	)	)	PUNCT
iajs-825	149	19	!	!	PUNCT
iajs-825	150	1	rn	rn	PROPN
iajs-825	150	2	from	from	ADP
iajs-825	150	3	proof	proof	NOUN
iajs-825	150	4	(	(	PUNCT
iajs-825	150	5	1	1	NUM
iajs-825	150	6	)	)	PUNCT
iajs-825	150	7	of	of	ADP
iajs-825	150	8	theorem	theorem	NOUN
iajs-825	150	9	9	9	NUM
iajs-825	150	10	,	,	PUNCT
iajs-825	150	11	there	there	PRON
iajs-825	150	12	exist	exist	VERB
iajs-825	150	13	(	(	PUNCT
iajs-825	150	14	k	k	X
iajs-825	150	15	–	–	PUNCT
iajs-825	150	16	1	1	NUM
iajs-825	150	17	)	)	PUNCT
iajs-825	150	18	2	2	NUM
iajs-825	150	19	-	-	PUNCT
iajs-825	150	20	secants	secant	NOUN
iajs-825	150	21	to	to	ADP
iajs-825	150	22	a	a	PRON
iajs-825	150	23	through	through	ADP
iajs-825	150	24	p	p	NOUN
iajs-825	150	25	,	,	PUNCT
iajs-825	150	26	and	and	CCONJ
iajs-825	150	27	there	there	PRON
iajs-825	150	28	exist	exist	VERB
iajs-825	150	29	1	1	NUM
iajs-825	150	30	2	2	NUM
iajs-825	150	31			PROPN
iajs-825	150	32			NOUN
iajs-825	151	1			PROPN
iajs-825	151	2			PROPN
iajs-825	152	1			PROPN
iajs-825	152	2			PROPN
iajs-825	152	3	k	k	ADJ
iajs-825	152	4	3	3	NUM
iajs-825	152	5	-	-	PUNCT
iajs-825	152	6	secants	secant	NOUN
iajs-825	152	7	to	to	ADP
iajs-825	152	8	a	a	PRON
iajs-825	152	9	through	through	ADP
iajs-825	152	10	p	p	NOUN
iajs-825	152	11	,	,	PUNCT
iajs-825	152	12	and	and	CCONJ
iajs-825	152	13	so	so	ADV
iajs-825	152	14	there	there	PRON
iajs-825	152	15	exist	exist	VERB
iajs-825	152	16	1	1	NUM
iajs-825	152	17	1	1	NUM
iajs-825	152	18			PROPN
iajs-825	152	19			NOUN
iajs-825	152	20			PROPN
iajs-825	152	21			NOUN
iajs-825	152	22			PROPN
iajs-825	152	23	k	k	PROPN
iajs-825	152	24	n	n	CCONJ
iajs-825	152	25	n	n	CCONJ
iajs-825	152	26	-	-	PUNCT
iajs-825	152	27	secants	secant	NOUN
iajs-825	152	28	to	to	ADP
iajs-825	152	29	a	a	PRON
iajs-825	152	30	through	through	ADP
iajs-825	152	31	p.	p.	NOUN
iajs-825	152	32	thus	thus	ADV
iajs-825	152	33	r2	r2	PROPN
iajs-825	152	34	=	=	SYM
iajs-825	152	35	k	k	PROPN
iajs-825	152	36	–	–	PUNCT
iajs-825	152	37	1	1	NUM
iajs-825	152	38	,	,	PUNCT
iajs-825	152	39	r3	r3	PROPN
iajs-825	152	40	=	=	SYM
iajs-825	152	41	1	1	NUM
iajs-825	152	42	2	2	NUM
iajs-825	152	43			PROPN
iajs-825	152	44			NOUN
iajs-825	152	45			PROPN
iajs-825	152	46			PROPN
iajs-825	153	1			PROPN
iajs-825	153	2			PROPN
iajs-825	153	3	k	k	NOUN
iajs-825	153	4	,	,	PUNCT
iajs-825	153	5	r4	r4	NOUN
iajs-825	153	6	=	=	NOUN
iajs-825	153	7	1	1	NUM
iajs-825	153	8	3	3	NUM
iajs-825	153	9			PROPN
iajs-825	153	10			NOUN
iajs-825	153	11			PROPN
iajs-825	153	12			PROPN
iajs-825	154	1			PROPN
iajs-825	154	2			PROPN
iajs-825	154	3	k	k	PROPN
iajs-825	154	4	,	,	PUNCT
iajs-825	154	5			PROPN
iajs-825	154	6	,	,	PUNCT
iajs-825	154	7	rn	rn	PROPN
iajs-825	154	8	=	=	NOUN
iajs-825	154	9	1	1	NUM
iajs-825	154	10	1	1	NUM
iajs-825	154	11			PROPN
iajs-825	154	12			NOUN
iajs-825	154	13			PROPN
iajs-825	154	14			NOUN
iajs-825	154	15			PROPN
iajs-825	154	16	k	k	PROPN
iajs-825	154	17	n	n	NUM
iajs-825	154	18	r3	r3	NOUN
iajs-825	154	19	=	=	SYM
iajs-825	154	20	(	(	PUNCT
iajs-825	154	21	1	1	NUM
iajs-825	154	22	)	)	PUNCT
iajs-825	154	23	!	!	PUNCT
iajs-825	155	1	2	2	X
iajs-825	155	2	!	!	X
iajs-825	155	3	(	(	PUNCT
iajs-825	155	4	3	3	NUM
iajs-825	155	5	)	)	PUNCT
iajs-825	155	6	!	!	PUNCT
iajs-825	156	1			NOUN
iajs-825	156	2			PROPN
iajs-825	156	3	k	k	PROPN
iajs-825	156	4	k	k	PROPN
iajs-825	156	5	,	,	PUNCT
iajs-825	156	6	r4	r4	PROPN
iajs-825	156	7	=	=	SYM
iajs-825	156	8	(	(	PUNCT
iajs-825	156	9	1	1	NUM
iajs-825	156	10	)	)	PUNCT
iajs-825	156	11	!	!	PUNCT
iajs-825	157	1	3	3	X
iajs-825	157	2	!	!	X
iajs-825	157	3	(	(	PUNCT
iajs-825	157	4	4	4	NUM
iajs-825	157	5	)	)	PUNCT
iajs-825	157	6	!	!	PUNCT
iajs-825	158	1			NOUN
iajs-825	158	2			PROPN
iajs-825	158	3	k	k	PROPN
iajs-825	158	4	k	k	PROPN
iajs-825	158	5	,	,	PUNCT
iajs-825	158	6			PROPN
iajs-825	158	7	,	,	PUNCT
iajs-825	158	8	rn	rn	PROPN
iajs-825	158	9	=	=	PUNCT
iajs-825	158	10	(	(	PUNCT
iajs-825	158	11	1	1	NUM
iajs-825	158	12	)	)	PUNCT
iajs-825	158	13	!	!	PUNCT
iajs-825	159	1	(	(	PUNCT
iajs-825	159	2	1	1	NUM
iajs-825	159	3	)	)	PUNCT
iajs-825	159	4	!	!	PUNCT
iajs-825	160	1	(	(	PUNCT
iajs-825	160	2	)	)	PUNCT
iajs-825	160	3	!	!	PUNCT
iajs-825	161	1			PROPN
iajs-825	161	2			PROPN
iajs-825	161	3			PROPN
iajs-825	161	4	k	k	PROPN
iajs-825	161	5	n	n	CCONJ
iajs-825	161	6	k	k	PROPN
iajs-825	161	7	n	n	CCONJ
iajs-825	161	8	r3	r3	PROPN
iajs-825	161	9	=	=	SYM
iajs-825	161	10	(	(	PUNCT
iajs-825	161	11	1	1	NUM
iajs-825	161	12	)	)	PUNCT
iajs-825	161	13	(	(	PUNCT
iajs-825	161	14	2	2	NUM
iajs-825	161	15	)	)	SYM
iajs-825	161	16	2	2	NUM
iajs-825	161	17			NOUN
iajs-825	161	18	k	k	NOUN
iajs-825	161	19	k	k	PROPN
iajs-825	161	20	,	,	PUNCT
iajs-825	161	21	r4	r4	PROPN
iajs-825	161	22	=	=	PUNCT
iajs-825	161	23	(	(	PUNCT
iajs-825	161	24	1	1	NUM
iajs-825	161	25	)	)	PUNCT
iajs-825	161	26	(	(	PUNCT
iajs-825	161	27	2	2	NUM
iajs-825	161	28	)	)	PUNCT
iajs-825	161	29	(	(	PUNCT
iajs-825	161	30	3	3	NUM
iajs-825	161	31	)	)	PUNCT
iajs-825	161	32	3	3	NUM
iajs-825	161	33	!	!	X
iajs-825	162	1			NOUN
iajs-825	162	2			PROPN
iajs-825	162	3	k	k	PROPN
iajs-825	162	4	k	k	PROPN
iajs-825	162	5	k	k	PROPN
iajs-825	162	6	,	,	PUNCT
iajs-825	162	7			PROPN
iajs-825	162	8	,	,	PUNCT
iajs-825	162	9	rn	rn	PROPN
iajs-825	162	10	=	=	PUNCT
iajs-825	162	11	(	(	PUNCT
iajs-825	162	12	1	1	NUM
iajs-825	162	13	)	)	PUNCT
iajs-825	162	14	(	(	PUNCT
iajs-825	162	15	(	(	PUNCT
iajs-825	162	16	1	1	NUM
iajs-825	162	17	)	)	PUNCT
iajs-825	162	18	)	)	PUNCT
iajs-825	162	19	(	(	PUNCT
iajs-825	162	20	1	1	NUM
iajs-825	162	21	)	)	PUNCT
iajs-825	162	22	!	!	PUNCT
iajs-825	163	1			PROPN
iajs-825	163	2			PROPN
iajs-825	163	3			PROPN
iajs-825	163	4			PROPN
iajs-825	163	5	k	k	NUM
iajs-825	163	6	k	k	PROPN
iajs-825	163	7	n	n	CCONJ
iajs-825	163	8	n	n	ADV
iajs-825	163	9	2	2	NUM
iajs-825	163	10	n	n	NOUN
iajs-825	163	11	i	i	PRON
iajs-825	163	12			VERB
iajs-825	163	13			X
iajs-825	163	14	(	(	PUNCT
iajs-825	163	15	i	i	NOUN
iajs-825	163	16	–	–	PUNCT
iajs-825	163	17	1	1	NUM
iajs-825	163	18	)	)	PUNCT
iajs-825	163	19	!	!	PUNCT
iajs-825	164	1	ri	ri	PROPN
iajs-825	165	1	=	=	PUNCT
iajs-825	165	2	k	k	PROPN
iajs-825	165	3	–	–	PUNCT
iajs-825	165	4	1	1	NUM
iajs-825	165	5	+	+	SYM
iajs-825	165	6	2	2	NUM
iajs-825	165	7	!	!	PUNCT
iajs-825	165	8	(	(	PUNCT
iajs-825	165	9	1	1	NUM
iajs-825	165	10	)	)	PUNCT
iajs-825	165	11	(	(	PUNCT
iajs-825	165	12	2	2	NUM
iajs-825	165	13	)	)	PUNCT
iajs-825	165	14	2	2	NUM
iajs-825	165	15	!	!	X
iajs-825	165	16			NOUN
iajs-825	165	17	k	k	PROPN
iajs-825	165	18	k	k	PROPN
iajs-825	166	1	+	+	PROPN
iajs-825	166	2	3	3	X
iajs-825	166	3	!	!	PUNCT
iajs-825	166	4	(	(	PUNCT
iajs-825	166	5	1	1	NUM
iajs-825	166	6	)	)	PUNCT
iajs-825	166	7	(	(	PUNCT
iajs-825	166	8	2	2	NUM
iajs-825	166	9	)	)	PUNCT
iajs-825	166	10	(	(	PUNCT
iajs-825	166	11	3	3	NUM
iajs-825	166	12	)	)	PUNCT
iajs-825	166	13	3	3	NUM
iajs-825	166	14	!	!	X
iajs-825	166	15			NOUN
iajs-825	166	16			PROPN
iajs-825	166	17	k	k	NOUN
iajs-825	166	18	k	k	PROPN
iajs-825	166	19	k	k	PROPN
iajs-825	166	20	+	+	PUNCT
iajs-825	166	21			X
iajs-825	166	22	+	+	CCONJ
iajs-825	166	23	(	(	PUNCT
iajs-825	166	24	1	1	NUM
iajs-825	166	25	)	)	PUNCT
iajs-825	166	26	!	!	PUNCT
iajs-825	167	1	(	(	PUNCT
iajs-825	167	2	1	1	X
iajs-825	167	3	)	)	PUNCT
iajs-825	167	4	(	(	PUNCT
iajs-825	167	5	2	2	NUM
iajs-825	167	6	)	)	PUNCT
iajs-825	167	7	(	(	PUNCT
iajs-825	167	8	(	(	PUNCT
iajs-825	167	9	1	1	NUM
iajs-825	167	10	)	)	PUNCT
iajs-825	167	11	)	)	PUNCT
iajs-825	168	1	(	(	PUNCT
iajs-825	168	2	1	1	NUM
iajs-825	168	3	)	)	PUNCT
iajs-825	168	4	!	!	PUNCT
iajs-825	169	1			PROPN
iajs-825	169	2			PROPN
iajs-825	169	3			PROPN
iajs-825	169	4			PROPN
iajs-825	169	5			PROPN
iajs-825	169	6			PROPN
iajs-825	169	7	n	n	NUM
iajs-825	169	8	k	k	PROPN
iajs-825	169	9	k	k	PROPN
iajs-825	169	10	k	k	PROPN
iajs-825	169	11	n	n	CCONJ
iajs-825	169	12	n	n	NOUN
iajs-825	169	13	=	=	SYM
iajs-825	169	14	(	(	PUNCT
iajs-825	169	15	k	k	X
iajs-825	169	16	–	–	PUNCT
iajs-825	169	17	1	1	NUM
iajs-825	169	18	)	)	PUNCT
iajs-825	169	19	+	+	CCONJ
iajs-825	169	20	(	(	PUNCT
iajs-825	169	21	k	k	X
iajs-825	169	22	–	–	PUNCT
iajs-825	169	23	1)(k	1)(k	NUM
iajs-825	169	24	–	–	SYM
iajs-825	169	25	2	2	NUM
iajs-825	169	26	)	)	PUNCT
iajs-825	169	27	+	+	PROPN
iajs-825	169	28	(	(	PUNCT
iajs-825	169	29	k	k	X
iajs-825	169	30	–	–	PUNCT
iajs-825	169	31	1)(k	1)(k	NUM
iajs-825	169	32	–	–	SYM
iajs-825	169	33	2)(k	2)(k	NUM
iajs-825	169	34	–	–	PUNCT
iajs-825	169	35	3)+	3)+	NUM
iajs-825	169	36			X
iajs-825	169	37	+	+	CCONJ
iajs-825	169	38	(	(	PUNCT
iajs-825	169	39	k	k	X
iajs-825	169	40	–	–	PUNCT
iajs-825	169	41	1)(k	1)(k	NUM
iajs-825	169	42	–	–	SYM
iajs-825	169	43	2	2	NUM
iajs-825	169	44	)	)	PUNCT
iajs-825	169	45			NOUN
iajs-825	169	46	(	(	PUNCT
iajs-825	169	47	k	k	X
iajs-825	169	48	–	–	PUNCT
iajs-825	169	49	(	(	PUNCT
iajs-825	169	50	n–1	n–1	NOUN
iajs-825	169	51	)	)	PUNCT
iajs-825	169	52	)	)	PUNCT
iajs-825	170	1	=	=	SYM
iajs-825	170	2	1	1	NUM
iajs-825	170	3	1	1	NUM
iajs-825	170	4			NOUN
iajs-825	170	5			NOUN
iajs-825	170	6			X
iajs-825	171	1	n	n	NOUN
iajs-825	171	2	i	i	PRON
iajs-825	171	3	(	(	PUNCT
iajs-825	171	4	k	k	PROPN
iajs-825	171	5	–	–	PUNCT
iajs-825	171	6	1	1	NUM
iajs-825	171	7	)	)	PUNCT
iajs-825	171	8			PUNCT
iajs-825	171	9	(	(	PUNCT
iajs-825	171	10	k	k	X
iajs-825	171	11	–	–	PUNCT
iajs-825	171	12	i	i	NOUN
iajs-825	171	13	)	)	PUNCT
iajs-825	171	14	theorem	theorem	VERB
iajs-825	171	15	12	12	NUM
iajs-825	171	16	:	:	PUNCT
iajs-825	171	17	let	let	VERB
iajs-825	171	18	si	si	X
iajs-825	171	19	=	=	PUNCT
iajs-825	171	20	si(q	si(q	PROPN
iajs-825	171	21	)	)	PUNCT
iajs-825	172	1	represent	represent	VERB
iajs-825	172	2	the	the	DET
iajs-825	172	3	numbers	number	NOUN
iajs-825	172	4	of	of	ADP
iajs-825	172	5	the	the	DET
iajs-825	172	6	i	i	NOUN
iajs-825	172	7	–	–	PUNCT
iajs-825	172	8	secants	secant	NOUN
iajs-825	172	9	(	(	PUNCT
iajs-825	172	10	p	p	NOUN
iajs-825	172	11	lanes	lane	NOUN
iajs-825	172	12	)	)	PUNCT
iajs-825	172	13	of	of	ADP
iajs-825	172	14	a	a	DET
iajs-825	172	15	(	(	PUNCT
iajs-825	172	16	k	k	NOUN
iajs-825	172	17	,	,	PUNCT
iajs-825	172	18	n	n	CCONJ
iajs-825	172	19	)	)	PUNCT
iajs-825	172	20	–	–	PUNCT
iajs-825	172	21	arc	arc	VERB
iajs-825	172	22	a	a	PRON
iajs-825	172	23	through	through	ADP
iajs-825	172	24	a	a	DET
iajs-825	172	25	point	point	NOUN
iajs-825	172	26	q	q	NOUN
iajs-825	172	27	not	not	PART
iajs-825	172	28	in	in	ADP
iajs-825	172	29	a	a	PRON
iajs-825	172	30	,	,	PUNCT
iajs-825	172	31	then	then	ADV
iajs-825	172	32	the	the	DET
iajs-825	172	33	following	follow	VERB
iajs-825	172	34	equations	equation	NOUN
iajs-825	172	35	are	be	AUX
iajs-825	172	36	satisfied	satisfied	ADJ
iajs-825	172	37	:	:	PUNCT
iajs-825	173	1	1	1	X
iajs-825	173	2	.	.	X
iajs-825	173	3	0	0	NUM
iajs-825	173	4			X
iajs-825	174	1	n	n	NOUN
iajs-825	174	2	i	i	PRON
iajs-825	174	3	si	si	NOUN
iajs-825	174	4	=	=	PROPN
iajs-825	174	5	q2	q2	PROPN
iajs-825	174	6	+	+	CCONJ
iajs-825	174	7	q	q	PUNCT
iajs-825	175	1	+	+	NUM
iajs-825	175	2	1	1	NUM
iajs-825	175	3	2	2	NUM
iajs-825	175	4	.	.	X
iajs-825	176	1	1	1	NUM
iajs-825	176	2			X
iajs-825	177	1	n	n	CCONJ
iajs-825	177	2	i	i	PRON
iajs-825	178	1	i	i	INTJ
iajs-825	178	2	si	si	NOUN
iajs-825	178	3	=	=	SYM
iajs-825	178	4	k	k	PROPN
iajs-825	178	5	proof	proof	NOUN
iajs-825	178	6	:	:	PUNCT
iajs-825	178	7	1	1	X
iajs-825	178	8	.	.	X
iajs-825	179	1	0	0	NUM
iajs-825	179	2			X
iajs-825	180	1	n	n	CCONJ
iajs-825	180	2	i	i	PRON
iajs-825	180	3	si	si	X
iajs-825	180	4	represents	represent	VERB
iajs-825	180	5	the	the	DET
iajs-825	180	6	sum	sum	NOUN
iajs-825	180	7	of	of	ADP
iajs-825	180	8	the	the	DET
iajs-825	180	9	total	total	ADJ
iajs-825	180	10	numbers	number	NOUN
iajs-825	180	11	of	of	ADP
iajs-825	180	12	all	all	DET
iajs-825	180	13	i	i	PRON
iajs-825	180	14	–	–	PUNCT
iajs-825	180	15	secants	secant	NOUN
iajs-825	180	16	to	to	ADP
iajs-825	180	17	a	a	PRON
iajs-825	180	18	through	through	ADP
iajs-825	180	19	a	a	DET
iajs-825	180	20	point	point	NOUN
iajs-825	180	21	q	q	NOUN
iajs-825	180	22	not	not	PART
iajs-825	180	23	in	in	ADP
iajs-825	180	24	a	a	PRON
iajs-825	180	25	,	,	PUNCT
iajs-825	180	26	which	which	PRON
iajs-825	180	27	is	be	AUX
iajs-825	180	28	equal	equal	ADJ
iajs-825	180	29	to	to	ADP
iajs-825	180	30	the	the	DET
iajs-825	180	31	number	number	NOUN
iajs-825	180	32	of	of	ADP
iajs-825	180	33	all	all	DET
iajs-825	180	34	planes	plane	NOUN
iajs-825	180	35	through	through	ADP
iajs-825	180	36	q.	q.	PROPN
iajs-825	180	37	thus	thus	ADV
iajs-825	180	38	0	0	VERB
iajs-825	180	39			X
iajs-825	181	1	n	n	NOUN
iajs-825	182	1	i	i	PRON
iajs-825	182	2	si	si	NOUN
iajs-825	183	1	=	=	SYM
iajs-825	183	2	q	q	PROPN
iajs-825	183	3	2	2	NUM
iajs-825	183	4	+	+	CCONJ
iajs-825	183	5	q	q	NOUN
iajs-825	184	1	+	+	NUM
iajs-825	184	2	1	1	NUM
iajs-825	184	3	.	.	NOUN
iajs-825	184	4	2	2	NUM
iajs-825	184	5	.	.	X
iajs-825	184	6	1	1	NUM
iajs-825	184	7			X
iajs-825	185	1	n	n	CCONJ
iajs-825	185	2	i	i	PRON
iajs-825	186	1	i	i	INTJ
iajs-825	186	2	si	si	NOUN
iajs-825	186	3	=	=	SYM
iajs-825	186	4	s1	s1	PROPN
iajs-825	186	5	+	+	CCONJ
iajs-825	186	6	2	2	NUM
iajs-825	186	7	s2	s2	NOUN
iajs-825	186	8	+	+	CCONJ
iajs-825	186	9	3	3	NUM
iajs-825	186	10	s3	s3	NOUN
iajs-825	186	11	+	+	CCONJ
iajs-825	186	12			X
iajs-825	186	13	+	+	CCONJ
iajs-825	186	14	n	n	CCONJ
iajs-825	186	15	sn	sn	NOUN
iajs-825	186	16	s1	s1	NOUN
iajs-825	186	17	,	,	PUNCT
iajs-825	186	18	s2	s2	PROPN
iajs-825	186	19	,	,	PUNCT
iajs-825	186	20			PROPN
iajs-825	186	21	,	,	PUNCT
iajs-825	186	22	sn	sn	PROPN
iajs-825	186	23	represent	represent	VERB
iajs-825	186	24	the	the	DET
iajs-825	186	25	numbers	number	NOUN
iajs-825	186	26	of	of	ADP
iajs-825	186	27	the	the	DET
iajs-825	186	28	i	i	NOUN
iajs-825	186	29	–	–	PUNCT
iajs-825	186	30	secants	secant	NOUN
iajs-825	186	31	of	of	ADP
iajs-825	186	32	the	the	DET
iajs-825	186	33	arc	arc	NOUN
iajs-825	186	34	a	a	PRON
iajs-825	186	35	through	through	ADP
iajs-825	186	36	the	the	DET
iajs-825	186	37	point	point	NOUN
iajs-825	186	38	q	q	NOUN
iajs-825	186	39	not	not	PART
iajs-825	186	40	in	in	ADP
iajs-825	186	41	a.	a.	NOUN
iajs-825	186	42	s1	s1	PROPN
iajs-825	186	43	is	be	AUX
iajs-825	186	44	the	the	DET
iajs-825	186	45	number	number	NOUN
iajs-825	186	46	of	of	ADP
iajs-825	186	47	the	the	DET
iajs-825	186	48	1	1	NUM
iajs-825	186	49	-	-	PUNCT
iajs-825	186	50	secants	secant	NOUN
iajs-825	186	51	to	to	ADP
iajs-825	186	52	a	a	PRON
iajs-825	186	53	,	,	PUNCT
iajs-825	186	54	each	each	DET
iajs-825	186	55	one	one	NOUN
iajs-825	186	56	passes	pass	VERB
iajs-825	186	57	through	through	ADP
iajs-825	186	58	one	one	NUM
iajs-825	186	59	point	point	NOUN
iajs-825	186	60	of	of	ADP
iajs-825	186	61	a.	a.	NOUN
iajs-825	186	62	s2	s2	PROPN
iajs-825	186	63	is	be	AUX
iajs-825	186	64	the	the	DET
iajs-825	186	65	number	number	NOUN
iajs-825	186	66	of	of	ADP
iajs-825	186	67	the	the	DET
iajs-825	186	68	2	2	NUM
iajs-825	186	69	-	-	PUNCT
iajs-825	186	70	secants	secant	NOUN
iajs-825	186	71	to	to	ADP
iajs-825	186	72	a	a	PRON
iajs-825	186	73	,	,	PUNCT
iajs-825	186	74	each	each	DET
iajs-825	186	75	one	one	NOUN
iajs-825	186	76	passes	pass	VERB
iajs-825	186	77	through	through	ADP
iajs-825	186	78	two	two	NUM
iajs-825	186	79	points	point	NOUN
iajs-825	186	80	of	of	ADP
iajs-825	186	81	a.	a.	NOUN
iajs-825	186	82	s3	s3	PROPN
iajs-825	186	83	is	be	AUX
iajs-825	186	84	the	the	DET
iajs-825	186	85	number	number	NOUN
iajs-825	186	86	of	of	ADP
iajs-825	186	87	the	the	DET
iajs-825	186	88	3	3	NUM
iajs-825	186	89	-	-	PUNCT
iajs-825	186	90	secants	secant	NOUN
iajs-825	186	91	to	to	ADP
iajs-825	186	92	a	a	PRON
iajs-825	186	93	,	,	PUNCT
iajs-825	186	94	each	each	DET
iajs-825	186	95	one	one	NOUN
iajs-825	186	96	passes	pass	VERB
iajs-825	186	97	through	through	ADP
iajs-825	186	98	three	three	NUM
iajs-825	186	99	points	point	NOUN
iajs-825	186	100	of	of	ADP
iajs-825	186	101	a.	a.	NOUN
iajs-825	186	102	also	also	ADV
iajs-825	186	103	,	,	PUNCT
iajs-825	186	104	sn	sn	PROPN
iajs-825	186	105	is	be	AUX
iajs-825	186	106	the	the	DET
iajs-825	186	107	number	number	NOUN
iajs-825	186	108	of	of	ADP
iajs-825	186	109	the	the	DET
iajs-825	186	110	n	n	NOUN
iajs-825	186	111	–	–	PUNCT
iajs-825	186	112	secants	secant	NOUN
iajs-825	186	113	to	to	ADP
iajs-825	186	114	a	a	PRON
iajs-825	186	115	,	,	PUNCT
iajs-825	186	116	each	each	DET
iajs-825	186	117	one	one	NOUN
iajs-825	186	118	passes	pass	VERB
iajs-825	186	119	through	through	ADP
iajs-825	186	120	n	n	ADP
iajs-825	186	121	points	point	NOUN
iajs-825	186	122	of	of	ADP
iajs-825	186	123	a.	a.	NOUN
iajs-825	186	124	since	since	SCONJ
iajs-825	186	125	the	the	DET
iajs-825	186	126	number	number	NOUN
iajs-825	186	127	of	of	ADP
iajs-825	186	128	points	point	NOUN
iajs-825	186	129	of	of	ADP
iajs-825	186	130	the	the	DET
iajs-825	186	131	(	(	PUNCT
iajs-825	186	132	k	k	NOUN
iajs-825	186	133	,	,	PUNCT
iajs-825	186	134	n	n	CCONJ
iajs-825	186	135	)	)	PUNCT
iajs-825	186	136	–	–	PUNCT
iajs-825	186	137	arc	arc	NOUN
iajs-825	186	138	a	a	PRON
iajs-825	186	139	is	be	AUX
iajs-825	186	140	k	k	NOUN
iajs-825	186	141	,	,	PUNCT
iajs-825	186	142	then	then	ADV
iajs-825	186	143	1	1	NUM
iajs-825	186	144			X
iajs-825	187	1	n	n	CCONJ
iajs-825	187	2	i	i	PRON
iajs-825	188	1	i	i	INTJ
iajs-825	188	2	si	si	PROPN
iajs-825	188	3	=	=	PUNCT
iajs-825	188	4	k.	k.	PROPN
iajs-825	188	5	ibn	ibn	PROPN
iajs-825	188	6	alhaitham	alhaitham	PROPN
iajs-825	188	7	j.	j.	PROPN
iajs-825	188	8	for	for	ADP
iajs-825	188	9	pure	pure	ADJ
iajs-825	188	10	&	&	CCONJ
iajs-825	188	11	appl	appl	PROPN
iajs-825	188	12	.	.	PUNCT
iajs-825	189	1	sci	sci	PROPN
iajs-825	189	2	.	.	PUNCT
iajs-825	189	3	vol.24	vol.24	NOUN
iajs-825	189	4	(	(	PUNCT
iajs-825	189	5	3	3	NUM
iajs-825	189	6	)	)	PUNCT
iajs-825	189	7	2011	2011	NUM
iajs-825	189	8	theorem	theorem	VERB
iajs-825	189	9	13	13	NUM
iajs-825	189	10	:	:	PUNCT
iajs-825	189	11	let	let	VERB
iajs-825	189	12	ci	ci	NOUN
iajs-825	189	13	be	be	AUX
iajs-825	189	14	the	the	DET
iajs-825	189	15	number	number	NOUN
iajs-825	189	16	of	of	ADP
iajs-825	189	17	points	point	NOUN
iajs-825	189	18	of	of	ADP
iajs-825	189	19	index	index	NOUN
iajs-825	189	20	i	i	PRON
iajs-825	189	21	in	in	ADP
iajs-825	189	22	s	s	NOUN
iajs-825	189	23	=	=	ADJ
iajs-825	189	24	pg(3,q	pg(3,q	NOUN
iajs-825	189	25	)	)	PUNCT
iajs-825	189	26	which	which	PRON
iajs-825	189	27	are	be	AUX
iajs-825	189	28	not	not	PART
iajs-825	189	29	on	on	ADP
iajs-825	189	30	a	a	DET
iajs-825	189	31	complete	complete	ADJ
iajs-825	189	32	(	(	PUNCT
iajs-825	189	33	k	k	NOUN
iajs-825	189	34	,	,	PUNCT
iajs-825	189	35	n	n	CCONJ
iajs-825	189	36	)	)	PUNCT
iajs-825	189	37	–	–	PUNCT
iajs-825	189	38	arc	arc	NOUN
iajs-825	189	39	a	a	PRON
iajs-825	189	40	,	,	PUNCT
iajs-825	189	41	then	then	ADV
iajs-825	189	42	the	the	DET
iajs-825	189	43	constants	constant	NOUN
iajs-825	189	44	ci	ci	PROPN
iajs-825	189	45	of	of	ADP
iajs-825	189	46	a	a	DET
iajs-825	189	47	satisfy	satisfy	NOUN
iajs-825	189	48	the	the	DET
iajs-825	189	49	following	follow	VERB
iajs-825	189	50	equations	equation	NOUN
iajs-825	189	51	:	:	PUNCT
iajs-825	189	52	(	(	PUNCT
iajs-825	189	53	i	i	NOUN
iajs-825	189	54	)	)	PUNCT
iajs-825	189	55			PROPN
iajs-825	189	56			PROPN
iajs-825	189	57			NOUN
iajs-825	189	58	ci	ci	NOUN
iajs-825	189	59	=	=	PUNCT
iajs-825	189	60	q3	q3	PROPN
iajs-825	189	61	+	+	PROPN
iajs-825	189	62	q2	q2	NOUN
iajs-825	189	63	+	+	CCONJ
iajs-825	189	64	q	q	PUNCT
iajs-825	190	1	+	+	NUM
iajs-825	190	2	1	1	NUM
iajs-825	190	3	–	–	PUNCT
iajs-825	190	4	k	k	PROPN
iajs-825	190	5	(	(	PUNCT
iajs-825	190	6	ii	ii	NOUN
iajs-825	190	7	)	)	PUNCT
iajs-825	190	8			PROPN
iajs-825	191	1			NOUN
iajs-825	191	2			NOUN
iajs-825	192	1	i	i	PRON
iajs-825	192	2	ci	ci	NOUN
iajs-825	193	1	=	=	PUNCT
iajs-825	194	1	(	(	PUNCT
iajs-825	194	2	1	1	NUM
iajs-825	194	3	)	)	PUNCT
iajs-825	194	4	(	(	PUNCT
iajs-825	194	5	1	1	X
iajs-825	194	6	)	)	PUNCT
iajs-825	194	7	!	!	PUNCT
iajs-825	195	1			PROPN
iajs-825	195	2			PROPN
iajs-825	195	3	k	k	VERB
iajs-825	195	4	k	k	PROPN
iajs-825	195	5	k	k	PROPN
iajs-825	195	6	n	n	CCONJ
iajs-825	195	7	n	n	PROPN
iajs-825	195	8	(	(	PUNCT
iajs-825	195	9	q2	q2	NOUN
iajs-825	195	10	+	+	CCONJ
iajs-825	195	11	q	q	PUNCT
iajs-825	196	1	+	+	NUM
iajs-825	196	2	1	1	NUM
iajs-825	196	3	–	–	PUNCT
iajs-825	196	4	n	n	CCONJ
iajs-825	196	5	)	)	PUNCT
iajs-825	196	6	where	where	SCONJ
iajs-825	196	7			NOUN
iajs-825	196	8	is	be	AUX
iajs-825	196	9	the	the	DET
iajs-825	196	10	smallest	small	ADJ
iajs-825	196	11	i	i	PRON
iajs-825	196	12	for	for	ADP
iajs-825	196	13	which	which	PRON
iajs-825	196	14	ci	ci	PROPN
iajs-825	196	15			PROPN
iajs-825	196	16	0	0	NUM
iajs-825	196	17	,	,	PUNCT
iajs-825	196	18			PROPN
iajs-825	196	19	be	be	AUX
iajs-825	196	20	the	the	DET
iajs-825	196	21	largest	large	ADJ
iajs-825	196	22	i	i	NOUN
iajs-825	196	23	for	for	ADP
iajs-825	196	24	which	which	PRON
iajs-825	196	25	ci	ci	PROPN
iajs-825	196	26			NOUN
iajs-825	196	27	0	0	NUM
iajs-825	196	28	.	.	PUNCT
iajs-825	197	1	proof	proof	NOUN
iajs-825	197	2	:	:	PUNCT
iajs-825	197	3	the	the	DET
iajs-825	197	4	equations	equation	NOUN
iajs-825	197	5	express	express	VERB
iajs-825	197	6	in	in	ADP
iajs-825	197	7	different	different	ADJ
iajs-825	197	8	ways	way	NOUN
iajs-825	197	9	the	the	DET
iajs-825	197	10	cardinality	cardinality	NOUN
iajs-825	197	11	of	of	ADP
iajs-825	197	12	the	the	DET
iajs-825	197	13	following	follow	VERB
iajs-825	197	14	sets	set	NOUN
iajs-825	197	15	(	(	PUNCT
iajs-825	197	16	i	i	NOUN
iajs-825	197	17	)	)	PUNCT
iajs-825	197	18	{	{	PUNCT
iajs-825	197	19	q	q	NOUN
iajs-825	197	20			NUM
iajs-825	197	21	q	q	PROPN
iajs-825	197	22			PROPN
iajs-825	197	23	s	s	PART
iajs-825	197	24	\	\	PROPN
iajs-825	197	25	a	a	PRON
iajs-825	197	26	}	}	PUNCT
iajs-825	197	27	(	(	PUNCT
iajs-825	197	28	ii	ii	NOUN
iajs-825	197	29	)	)	PUNCT
iajs-825	197	30	{	{	PUNCT
iajs-825	197	31	(	(	PUNCT
iajs-825	197	32	q,	q,	NOUN
iajs-825	197	33	)	)	PUNCT
iajs-825	197	34			NUM
iajs-825	197	35	q	q	PROPN
iajs-825	197	36			PROPN
iajs-825	197	37			PROPN
iajs-825	197	38	\	\	PROPN
iajs-825	197	39	a	a	DET
iajs-825	197	40	,	,	PUNCT
iajs-825	197	41			NOUN
iajs-825	197	42	an	an	DET
iajs-825	197	43	n	n	ADJ
iajs-825	197	44	–	–	PUNCT
iajs-825	197	45	secant	secant	NOUN
iajs-825	197	46	of	of	ADP
iajs-825	197	47	a	a	PRON
iajs-825	197	48	}	}	PUNCT
iajs-825	197	49	for	for	ADP
iajs-825	197	50	in	in	ADP
iajs-825	197	51	(	(	PUNCT
iajs-825	197	52	i	i	NOUN
iajs-825	197	53	)	)	PUNCT
iajs-825	197	54	,	,	PUNCT
iajs-825	197	55			PROPN
iajs-825	197	56			PROPN
iajs-825	197	57			NOUN
iajs-825	197	58	ci	ci	PROPN
iajs-825	197	59	represents	represent	VERB
iajs-825	197	60	all	all	DET
iajs-825	197	61	points	point	NOUN
iajs-825	197	62	in	in	ADP
iajs-825	197	63	the	the	DET
iajs-825	197	64	space	space	NOUN
iajs-825	197	65	which	which	PRON
iajs-825	197	66	are	be	AUX
iajs-825	197	67	not	not	PART
iajs-825	197	68	in	in	ADP
iajs-825	197	69	a	a	PRON
iajs-825	197	70	,	,	PUNCT
iajs-825	197	71	then	then	ADV
iajs-825	197	72			PROPN
iajs-825	197	73			NOUN
iajs-825	197	74			X
iajs-825	197	75	ci	ci	NOUN
iajs-825	197	76	=	=	PUNCT
iajs-825	197	77	q	q	PROPN
iajs-825	197	78	3	3	NUM
iajs-825	197	79	+	+	CCONJ
iajs-825	197	80	q	q	PROPN
iajs-825	197	81	2	2	NUM
iajs-825	197	82	+	+	NOUN
iajs-825	197	83	q	q	NOUN
iajs-825	198	1	+	+	NUM
iajs-825	198	2	1	1	NUM
iajs-825	198	3	–	–	PUNCT
iajs-825	198	4	k	k	NOUN
iajs-825	198	5	,	,	PUNCT
iajs-825	198	6	and	and	CCONJ
iajs-825	198	7	in	in	ADP
iajs-825	198	8	(	(	PUNCT
iajs-825	198	9	ii	ii	NOUN
iajs-825	198	10	)	)	PUNCT
iajs-825	198	11			PROPN
iajs-825	199	1			NOUN
iajs-825	199	2			NOUN
iajs-825	199	3	i	i	PRON
iajs-825	199	4	ci	ci	NOUN
iajs-825	199	5	represents	represent	VERB
iajs-825	199	6	all	all	DET
iajs-825	199	7	points	point	NOUN
iajs-825	199	8	in	in	ADP
iajs-825	199	9	the	the	DET
iajs-825	199	10	space	space	NOUN
iajs-825	199	11	not	not	PART
iajs-825	199	12	in	in	ADP
iajs-825	199	13	a	a	PRON
iajs-825	199	14	,	,	PUNCT
iajs-825	199	15	which	which	PRON
iajs-825	199	16	are	be	AUX
iajs-825	199	17	on	on	ADP
iajs-825	199	18	n	n	PRON
iajs-825	199	19	–	–	PUNCT
iajs-825	199	20	secants	secant	NOUN
iajs-825	199	21	of	of	ADP
iajs-825	199	22	a	a	PRON
iajs-825	199	23	,	,	PUNCT
iajs-825	199	24	that	that	ADV
iajs-825	199	25	is	is	ADV
iajs-825	199	26	,	,	PUNCT
iajs-825	199	27	each	each	DET
iajs-825	199	28	n	n	ADJ
iajs-825	199	29	–	–	PUNCT
iajs-825	199	30	secant	secant	NOUN
iajs-825	199	31	contains	contain	VERB
iajs-825	199	32	q	q	PROPN
iajs-825	199	33	2	2	NUM
iajs-825	199	34	+	+	CCONJ
iajs-825	199	35	q	q	NOUN
iajs-825	200	1	+	+	NUM
iajs-825	200	2	1	1	NUM
iajs-825	200	3	–	–	PUNCT
iajs-825	200	4	n	n	NUM
iajs-825	200	5	points	point	NOUN
iajs-825	200	6	,	,	PUNCT
iajs-825	200	7	and	and	CCONJ
iajs-825	200	8	the	the	DET
iajs-825	200	9	number	number	NOUN
iajs-825	200	10	of	of	ADP
iajs-825	200	11	the	the	DET
iajs-825	200	12	n	n	NOUN
iajs-825	200	13	–	–	PUNCT
iajs-825	200	14	secants	secant	NOUN
iajs-825	200	15	is	be	AUX
iajs-825	200	16			NOUN
iajs-825	200	17			PROPN
iajs-825	201	1			PROPN
iajs-825	201	2			PROPN
iajs-825	202	1			PROPN
iajs-825	202	2			PROPN
iajs-825	202	3	k	k	NOUN
iajs-825	202	4	n	n	NOUN
iajs-825	202	5	,	,	PUNCT
iajs-825	202	6	then	then	ADV
iajs-825	202	7			PROPN
iajs-825	202	8			NOUN
iajs-825	202	9			NOUN
iajs-825	203	1	i	i	PRON
iajs-825	203	2	ci	ci	NOUN
iajs-825	203	3	=	=	VERB
iajs-825	203	4			NOUN
iajs-825	203	5			PROPN
iajs-825	203	6			PROPN
iajs-825	203	7			PROPN
iajs-825	204	1			PROPN
iajs-825	204	2			PROPN
iajs-825	204	3	k	k	NOUN
iajs-825	204	4	n	n	NOUN
iajs-825	204	5	(	(	PUNCT
iajs-825	204	6	q	q	PROPN
iajs-825	204	7	2	2	NUM
iajs-825	204	8	+	+	NOUN
iajs-825	204	9	q	q	NOUN
iajs-825	205	1	+	+	NUM
iajs-825	205	2	1	1	NUM
iajs-825	205	3	–	–	PUNCT
iajs-825	205	4	n	n	CCONJ
iajs-825	205	5	)	)	PUNCT
iajs-825	205	6	=	=	SYM
iajs-825	205	7	(	(	PUNCT
iajs-825	205	8	1	1	NUM
iajs-825	205	9	)	)	PUNCT
iajs-825	205	10	(	(	PUNCT
iajs-825	205	11	1	1	X
iajs-825	205	12	)	)	PUNCT
iajs-825	205	13	!	!	PUNCT
iajs-825	206	1			PROPN
iajs-825	206	2			PROPN
iajs-825	206	3	k	k	VERB
iajs-825	206	4	k	k	PROPN
iajs-825	206	5	k	k	PROPN
iajs-825	206	6	n	n	CCONJ
iajs-825	206	7	n	n	PROPN
iajs-825	206	8	(	(	PUNCT
iajs-825	206	9	q	q	PROPN
iajs-825	206	10	2	2	NUM
iajs-825	206	11	+	+	NOUN
iajs-825	206	12	q	q	NOUN
iajs-825	206	13	+	+	NUM
iajs-825	206	14	1	1	NUM
iajs-825	206	15	–	–	PUNCT
iajs-825	206	16	n	n	CCONJ
iajs-825	206	17	)	)	PUNCT
iajs-825	206	18	.	.	PUNCT
iajs-825	207	1	theorem	theorem	VERB
iajs-825	207	2	14	14	NUM
iajs-825	207	3	:	:	PUNCT
iajs-825	207	4	if	if	SCONJ
iajs-825	207	5	p	p	NOUN
iajs-825	207	6	is	be	AUX
iajs-825	207	7	a	a	DET
iajs-825	207	8	point	point	NOUN
iajs-825	207	9	of	of	ADP
iajs-825	207	10	a	a	DET
iajs-825	207	11	(	(	PUNCT
iajs-825	207	12	k	k	NOUN
iajs-825	207	13	,	,	PUNCT
iajs-825	207	14	n)-arc	n)-arc	X
iajs-825	207	15	a	a	PRON
iajs-825	207	16	in	in	ADP
iajs-825	207	17	pg(3,q	pg(3,q	NOUN
iajs-825	207	18	)	)	PUNCT
iajs-825	207	19	,	,	PUNCT
iajs-825	207	20	which	which	PRON
iajs-825	207	21	lies	lie	VERB
iajs-825	207	22	on	on	ADP
iajs-825	207	23	an	an	DET
iajs-825	207	24	m	m	NOUN
iajs-825	207	25	-	-	NOUN
iajs-825	207	26	secant	secant	ADJ
iajs-825	207	27	(	(	PUNCT
iajs-825	207	28	plane	plane	NOUN
iajs-825	207	29	)	)	PUNCT
iajs-825	207	30	of	of	ADP
iajs-825	207	31	a	a	PRON
iajs-825	207	32	,	,	PUNCT
iajs-825	207	33	then	then	ADV
iajs-825	207	34	the	the	DET
iajs-825	207	35	planes	plane	NOUN
iajs-825	207	36	through	through	ADP
iajs-825	207	37	p	p	NOUN
iajs-825	207	38	contain	contain	VERB
iajs-825	207	39	at	at	ADP
iajs-825	207	40	most	most	ADV
iajs-825	207	41	(	(	PUNCT
iajs-825	207	42	n	n	CCONJ
iajs-825	207	43	–	–	PUNCT
iajs-825	207	44	1	1	NUM
iajs-825	207	45	)	)	PUNCT
iajs-825	207	46	q	q	NOUN
iajs-825	208	1	(	(	PUNCT
iajs-825	208	2	q	q	NOUN
iajs-825	208	3	+	+	NUM
iajs-825	208	4	1	1	NUM
iajs-825	208	5	)	)	PUNCT
iajs-825	209	1	+	+	NUM
iajs-825	209	2	m	m	NUM
iajs-825	209	3	points	point	NOUN
iajs-825	209	4	of	of	ADP
iajs-825	209	5	a.	a.	NOUN
iajs-825	209	6	proof	proof	NOUN
iajs-825	209	7	:	:	PUNCT
iajs-825	209	8	if	if	SCONJ
iajs-825	209	9	p	p	NOUN
iajs-825	209	10	in	in	ADP
iajs-825	209	11	a	a	DET
iajs-825	209	12	lies	lie	NOUN
iajs-825	209	13	on	on	ADP
iajs-825	209	14	an	an	DET
iajs-825	209	15	m	m	ADJ
iajs-825	209	16	–	–	PUNCT
iajs-825	209	17	secant	secant	ADJ
iajs-825	209	18	(	(	PUNCT
iajs-825	209	19	plane	plane	NOUN
iajs-825	209	20	)	)	PUNCT
iajs-825	209	21	,	,	PUNCT
iajs-825	209	22	then	then	ADV
iajs-825	209	23	every	every	DET
iajs-825	209	24	other	other	ADJ
iajs-825	209	25	plane	plane	NOUN
iajs-825	209	26	through	through	ADP
iajs-825	209	27	p	p	NOUN
iajs-825	209	28	contains	contain	VERB
iajs-825	209	29	at	at	ADP
iajs-825	209	30	most	most	ADV
iajs-825	209	31	n	n	NUM
iajs-825	209	32	–	–	PUNCT
iajs-825	209	33	1	1	NUM
iajs-825	209	34	points	point	NOUN
iajs-825	209	35	of	of	ADP
iajs-825	209	36	a	a	DET
iajs-825	209	37	distinct	distinct	NOUN
iajs-825	209	38	from	from	ADP
iajs-825	209	39	p.	p.	NOUN
iajs-825	209	40	hence	hence	ADV
iajs-825	209	41	the	the	DET
iajs-825	209	42	q	q	PROPN
iajs-825	209	43	2	2	NUM
iajs-825	209	44	+	+	NOUN
iajs-825	209	45	q	q	ADJ
iajs-825	210	1	+	+	CCONJ
iajs-825	210	2	1	1	NUM
iajs-825	210	3	planes	plane	NOUN
iajs-825	210	4	through	through	ADP
iajs-825	210	5	p	p	NOUN
iajs-825	210	6	contain	contain	VERB
iajs-825	210	7	at	at	ADP
iajs-825	210	8	most	most	ADV
iajs-825	210	9	(	(	PUNCT
iajs-825	210	10	n	n	CCONJ
iajs-825	210	11	–	–	PUNCT
iajs-825	210	12	1)(q	1)(q	NUM
iajs-825	210	13	2	2	NUM
iajs-825	210	14	+	+	CCONJ
iajs-825	210	15	q	q	X
iajs-825	210	16	)	)	PUNCT
iajs-825	211	1	+	+	NUM
iajs-825	211	2	m	m	NUM
iajs-825	211	3	points	point	NOUN
iajs-825	211	4	of	of	ADP
iajs-825	211	5	a.	a.	NOUN
iajs-825	211	6	references	reference	NOUN
iajs-825	211	7	1	1	NUM
iajs-825	211	8	.	.	PUNCT
iajs-825	212	1	al	al	PROPN
iajs-825	212	2	-	-	PUNCT
iajs-825	212	3	mukhtar	mukhtar	PROPN
iajs-825	212	4	,	,	PUNCT
iajs-825	212	5	a.sh	a.sh	PROPN
iajs-825	212	6	.	.	PROPN
iajs-825	212	7	,	,	PUNCT
iajs-825	212	8	(	(	PUNCT
iajs-825	212	9	2008	2008	NUM
iajs-825	212	10	)	)	PUNCT
iajs-825	212	11	complete	complete	ADJ
iajs-825	212	12	arcs	arc	NOUN
iajs-825	212	13	and	and	CCONJ
iajs-825	212	14	surfaces	surface	NOUN
iajs-825	212	15	in	in	ADP
iajs-825	212	16	three	three	NUM
iajs-825	212	17	dimensional	dimensional	ADJ
iajs-825	212	18	projective	projective	ADJ
iajs-825	212	19	space	space	NOUN
iajs-825	212	20	over	over	ADP
iajs-825	212	21	galois	galois	PROPN
iajs-825	212	22	field	field	NOUN
iajs-825	212	23	,	,	PUNCT
iajs-825	212	24	ph.d	ph.d	PROPN
iajs-825	212	25	.	.	PUNCT
iajs-825	213	1	thesis	thesis	NOUN
iajs-825	213	2	,	,	PUNCT
iajs-825	213	3	university	university	NOUN
iajs-825	213	4	of	of	ADP
iajs-825	213	5	technology	technology	NOUN
iajs-825	213	6	,	,	PUNCT
iajs-825	213	7	iraq	iraq	PROPN
iajs-825	213	8	.	.	PUNCT
iajs-825	214	1	2	2	X
iajs-825	214	2	.	.	X
iajs-825	214	3	kirdar	kirdar	PROPN
iajs-825	214	4	,	,	PUNCT
iajs-825	214	5	m.s	m.s	PROPN
iajs-825	214	6	.	.	PROPN
iajs-825	214	7	and	and	CCONJ
iajs-825	214	8	al	al	PROPN
iajs-825	214	9	-	-	PUNCT
iajs-825	214	10	mukhtar	mukhtar	PROPN
iajs-825	214	11	,	,	PUNCT
iajs-825	214	12	a.	a.	NOUN
iajs-825	214	13	sh	sh	PROPN
iajs-825	214	14	.	.	PROPN
iajs-825	214	15	,	,	PUNCT
iajs-825	214	16	(	(	PUNCT
iajs-825	214	17	2009	2009	NUM
iajs-825	214	18	)	)	PUNCT
iajs-825	214	19	,	,	PUNCT
iajs-825	214	20	engineering	engineering	NOUN
iajs-825	214	21	and	and	CCONJ
iajs-825	214	22	technology	technology	NOUN
iajs-825	214	23	journal	journal	NOUN
iajs-825	214	24	,	,	PUNCT
iajs-825	214	25	on	on	ADP
iajs-825	214	26	projective	projective	ADJ
iajs-825	214	27	3	3	NUM
iajs-825	214	28	-	-	PUNCT
iajs-825	214	29	space	space	NOUN
iajs-825	214	30	,	,	PUNCT
iajs-825	214	31	vol.27(8	vol.27(8	PROPN
iajs-825	214	32	):	):	PUNCT
iajs-825	214	33	3	3	NUM
iajs-825	214	34	.	.	X
iajs-825	214	35	hirschfeld	hirschfeld	PROPN
iajs-825	214	36	,	,	PUNCT
iajs-825	214	37	j.	j.	PROPN
iajs-825	214	38	w.	w.	PROPN
iajs-825	214	39	p.	p.	PROPN
iajs-825	214	40	,	,	PUNCT
iajs-825	214	41	(	(	PUNCT
iajs-825	214	42	1998	1998	NUM
iajs-825	214	43	)	)	PUNCT
iajs-825	214	44	,	,	PUNCT
iajs-825	214	45	projective	projective	PROPN
iajs-825	214	46	geometries	geometry	NOUN
iajs-825	214	47	over	over	ADP
iajs-825	214	48	finite	finite	ADJ
iajs-825	214	49	fields	field	NOUN
iajs-825	214	50	,	,	PUNCT
iajs-825	214	51	second	second	ADJ
iajs-825	214	52	edition	edition	NOUN
iajs-825	214	53	,	,	PUNCT
iajs-825	214	54	oxford	oxford	PROPN
iajs-825	214	55	university	university	PROPN
iajs-825	214	56	press	press	NOUN
iajs-825	214	57	.	.	PUNCT
iajs-825	215	1	2011	2011	NUM
iajs-825	215	2	)	)	PUNCT
iajs-825	215	3	3	3	NUM
iajs-825	215	4	(	(	PUNCT
iajs-825	215	5	24المجلد	24المجلد	NUM
iajs-825	215	6	قیة	قیة	PROPN
iajs-825	215	7	مجلة	مجلة	VERB
iajs-825	215	8	ابن	ابن	PROPN
iajs-825	215	9	الھیثم	الھیثم	PROPN
iajs-825	215	10	للعلوم	للعلوم	PROPN
iajs-825	215	11	الصرفة	الصرفة	PROPN
iajs-825	215	12	والتطبی	والتطبی	PROPN
iajs-825	215	13	ثالثي	ثالثي	PROPN
iajs-825	215	14	االبعاد	االبعاد	NOUN
iajs-825	215	15	فضاء	فضاء	VERB
iajs-825	215	16	اسقاطي	اسقاطي	NOUN
iajs-825	215	17	االقواس	االقواس	VERB
iajs-825	215	18	الكاملة	الكاملة	NOUN
iajs-825	215	19	في	في	SCONJ
iajs-825	215	20	حولبعض	حولبعض	PROPN
iajs-825	215	21	النتائج	النتائج	PROPN
iajs-825	215	22	حول	حول	PROPN
iajs-825	215	23	حقل	حقل	PROPN
iajs-825	215	24	كالوا	كالوا	PROPN
iajs-825	215	25	آمال	آمال	PROPN
iajs-825	215	26	شھاب	شھاب	VERB
iajs-825	215	27	المختار	المختار	PROPN
iajs-825	215	28	جامعة	جامعة	NOUN
iajs-825	215	29	بغداد،ابن	بغداد،ابن	PROPN
iajs-825	215	30	الھیثم	الھیثم	VERB
iajs-825	215	31	كلیة	كلیة	PRON
iajs-825	215	32	التربیة،قسم	التربیة،قسم	PROPN
iajs-825	215	33	الریاضیات	الریاضیات	VERB
iajs-825	215	34	2011آیار	2011آیار	NUM
iajs-825	215	35	11	11	NUM
iajs-825	215	36	:	:	PUNCT
iajs-825	215	37	استلم	استلم	PROPN
iajs-825	215	38	البحث	البحث	VERB
iajs-825	215	39	في	في	SCONJ
iajs-825	215	40	2011حزیران	2011حزیران	NUM
iajs-825	215	41	16	16	NUM
iajs-825	215	42	:	:	PUNCT
iajs-825	215	43	قبل	قبل	NOUN
iajs-825	215	44	البحث	البحث	VERB
iajs-825	215	45	في	في	ADP
iajs-825	215	46	الخالصة	الخالصة	PROPN
iajs-825	215	47	بحث	بحث	PROPN
iajs-825	215	48	من	من	PROPN
iajs-825	215	49	ھدفال	ھدفال	NOUN
iajs-825	215	50	،	،	PROPN
iajs-825	215	51	لبعض	لبعض	PROPN
iajs-825	215	52	قیم	قیم	PROPN
iajs-825	215	53	gf(q	gf(q	PUNCT
iajs-825	215	54	)	)	PUNCT
iajs-825	216	1	،	،	PROPN
iajs-825	216	2	q	q	X
iajs-825	216	3	=	=	SYM
iajs-825	216	4	pmحول	pmحول	VERB
iajs-825	216	5	حقل	حقل	PROPN
iajs-825	216	6	كالوا	كالوا	PROPN
iajs-825	216	7	تقدیم	تقدیم	VERB
iajs-825	216	8	تعریف	تعریف	PROPN
iajs-825	216	9	الفضاء	الفضاء	PROPN
iajs-825	216	10	الثالثي	الثالثي	PROPN
iajs-825	216	11	االسقاطيھو	االسقاطيھو	PROPN
iajs-825	216	12	ھذا	ھذا	VERB
iajs-825	216	13	ال	ال	ADP
iajs-825	216	14	p	p	PRON
iajs-825	217	1	وm	وm	INTJ
iajs-825	217	2	ان	ان	INTJ
iajs-825	217	3	اذp	اذp	PROPN
iajs-825	217	4	عدد	عدد	PROPN
iajs-825	217	5	أولي	أولي	PROPN
iajs-825	217	6	وm	وm	PROPN
iajs-825	217	7	عدد	عدد	PROPN
iajs-825	217	8	صحیح	صحیح	PROPN
iajs-825	217	9	.	.	PUNCT
iajs-825	218	1	طة	طة	PROPN
iajs-825	218	2	،	،	PROPN
iajs-825	218	3	واالقواس	واالقواس	PROPN
iajs-825	218	4	المتكافئة	المتكافئة	PROPN
iajs-825	218	5	،	،	PROPN
iajs-825	218	6	دلیل	دلیل	PROPN
iajs-825	218	7	النقn	النقn	PROPN
iajs-825	218	8	–	–	PUNCT
iajs-825	218	9	،	،	NOUN
iajs-825	218	10	االقواس	االقواس	PROPN
iajs-825	218	11	الكاملة	الكاملة	PROPN
iajs-825	218	12	،	،	X
iajs-825	218	13	القاطع	القاطع	PROPN
iajs-825	218	14	(	(	PUNCT
iajs-825	218	15	k	k	X
iajs-825	218	16	,	,	PUNCT
iajs-825	218	17	n	n	CCONJ
iajs-825	218	18	)	)	PUNCT
iajs-825	218	19	–	–	PUNCT
iajs-825	218	20	كذلك	كذلك	PROPN
iajs-825	218	21	أعطیت	أعطیت	PROPN
iajs-825	218	22	تعاریف	تعاریف	PROPN
iajs-825	218	23	االقواس	االقواس	NOUN
iajs-825	218	24	.اسقاطیا	.اسقاطیا	PUNCT
iajs-825	218	25	.على	.على	PUNCT
iajs-825	219	1	ذلك	ذلك	PROPN
iajs-825	219	2	برھنت	برھنت	VERB
iajs-825	219	3	بعض	بعض	NOUN
iajs-825	219	4	المبرھنات	المبرھنات	PROPN
iajs-825	219	5	حول	حول	AUX
iajs-825	219	6	ھذه	ھذه	VERB
iajs-825	219	7	المفاھیمفضال	المفاھیمفضال	NOUN
iajs-825	219	8	.االقواس	.االقواس	PUNCT
iajs-825	219	9	،	،	PROPN
iajs-825	219	10	الدلیل	الدلیل	PROPN
iajs-825	219	11	،	،	PROPN
iajs-825	220	1	المستوي	المستوي	PROPN
iajs-825	220	2	:	:	PUNCT
iajs-825	220	3	الكلمات	الكلمات	VERB
iajs-825	220	4	المفتاحیة	المفتاحیة	ADV