id	sid	tid	token	lemma	pos
stem-5536	1	1	119	119	NUM
stem-5536	1	2	american	american	ADJ
stem-5536	1	3	journal	journal	PROPN
stem-5536	1	4	of	of	ADP
stem-5536	1	5	language	language	NOUN
stem-5536	1	6	,	,	PUNCT
stem-5536	1	7	literacy	literacy	NOUN
stem-5536	1	8	and	and	CCONJ
stem-5536	1	9	learning	learn	VERB
stem-5536	1	10	in	in	ADP
stem-5536	1	11	stem	stem	NOUN
stem-5536	1	12	education	education	NOUN
stem-5536	1	13	www	www	PROPN
stem-5536	1	14	.	.	PROPN
stem-5536	2	1	grnjournal.us	grnjournal.us	PROPN
stem-5536	2	2	american	american	PROPN
stem-5536	2	3	journal	journal	PROPN
stem-5536	2	4	of	of	ADP
stem-5536	2	5	language	language	NOUN
stem-5536	2	6	,	,	PUNCT
stem-5536	2	7	literacy	literacy	NOUN
stem-5536	2	8	and	and	CCONJ
stem-5536	2	9	learning	learn	VERB
stem-5536	2	10	in	in	ADP
stem-5536	2	11	stem	stem	NOUN
stem-5536	2	12	education	education	NOUN
stem-5536	2	13	volume	volume	NOUN
stem-5536	2	14	02	02	NUM
stem-5536	2	15	,	,	PUNCT
stem-5536	2	16	issue	issue	NOUN
stem-5536	2	17	07	07	NUM
stem-5536	2	18	,	,	PUNCT
stem-5536	2	19	2024	2024	NUM
stem-5536	2	20	issn	issn	X
stem-5536	2	21	(	(	PUNCT
stem-5536	2	22	e	e	NOUN
stem-5536	2	23	):	):	PUNCT
stem-5536	2	24	2993	2993	NUM
stem-5536	2	25	-	-	SYM
stem-5536	2	26	2769	2769	NUM
stem-5536	2	27	on	on	ADP
stem-5536	2	28	the	the	DET
stem-5536	2	29	basics	basic	NOUN
stem-5536	2	30	of	of	ADP
stem-5536	2	31	education	education	NOUN
stem-5536	2	32	of	of	ADP
stem-5536	2	33	mathematical	mathematical	ADJ
stem-5536	2	34	thinking	thinking	NOUN
stem-5536	2	35	in	in	ADP
stem-5536	2	36	the	the	DET
stem-5536	2	37	modern	modern	ADJ
stem-5536	2	38	course	course	NOUN
stem-5536	2	39	of	of	ADP
stem-5536	2	40	geometry	geometry	NOUN
stem-5536	2	41	in	in	ADP
stem-5536	2	42	a	a	DET
stem-5536	2	43	comprehensive	comprehensive	ADJ
stem-5536	2	44	school	school	NOUN
stem-5536	2	45	m.	m.	NOUN
stem-5536	2	46	m.	m.	NOUN
stem-5536	2	47	esonov	esonov	PROPN
stem-5536	2	48	senior	senior	ADJ
stem-5536	2	49	lecturer	lecturer	NOUN
stem-5536	2	50	,	,	PUNCT
stem-5536	2	51	kokand	kokand	NOUN
stem-5536	2	52	state	state	PROPN
stem-5536	2	53	pedagogical	pedagogical	PROPN
stem-5536	2	54	institute	institute	PROPN
stem-5536	2	55	kokand	kokand	PROPN
stem-5536	2	56	,	,	PUNCT
stem-5536	2	57	uzbekistan	uzbekistan	PROPN
stem-5536	2	58	abstract	abstract	NOUN
stem-5536	2	59	:	:	PUNCT
stem-5536	2	60	the	the	DET
stem-5536	2	61	article	article	NOUN
stem-5536	2	62	focuses	focus	VERB
stem-5536	2	63	on	on	ADP
stem-5536	2	64	the	the	DET
stem-5536	2	65	development	development	NOUN
stem-5536	2	66	of	of	ADP
stem-5536	2	67	mathematical	mathematical	ADJ
stem-5536	2	68	thinking	thinking	NOUN
stem-5536	2	69	in	in	ADP
stem-5536	2	70	students	student	NOUN
stem-5536	2	71	and	and	CCONJ
stem-5536	2	72	students	student	NOUN
stem-5536	2	73	of	of	ADP
stem-5536	2	74	the	the	DET
stem-5536	2	75	pedagogical	pedagogical	ADJ
stem-5536	2	76	university	university	NOUN
stem-5536	2	77	,	,	PUNCT
stem-5536	2	78	based	base	VERB
stem-5536	2	79	on	on	ADP
stem-5536	2	80	the	the	DET
stem-5536	2	81	solution	solution	NOUN
stem-5536	2	82	of	of	ADP
stem-5536	2	83	a	a	DET
stem-5536	2	84	system	system	NOUN
stem-5536	2	85	of	of	ADP
stem-5536	2	86	various	various	ADJ
stem-5536	2	87	geometric	geometric	ADJ
stem-5536	2	88	problems	problem	NOUN
stem-5536	2	89	.	.	PUNCT
stem-5536	3	1	the	the	DET
stem-5536	3	2	ability	ability	NOUN
stem-5536	3	3	to	to	PART
stem-5536	3	4	create	create	VERB
stem-5536	3	5	(	(	PUNCT
stem-5536	3	6	restore	restore	ADJ
stem-5536	3	7	)	)	PUNCT
stem-5536	3	8	geometric	geometric	ADJ
stem-5536	3	9	images	image	NOUN
stem-5536	3	10	used	use	VERB
stem-5536	3	11	in	in	ADP
stem-5536	3	12	design	design	NOUN
stem-5536	3	13	is	be	AUX
stem-5536	3	14	one	one	NUM
stem-5536	3	15	of	of	ADP
stem-5536	3	16	the	the	DET
stem-5536	3	17	features	feature	NOUN
stem-5536	3	18	of	of	ADP
stem-5536	3	19	functional	functional	ADJ
stem-5536	3	20	and	and	CCONJ
stem-5536	3	21	mathematical	mathematical	ADJ
stem-5536	3	22	thinking	thinking	NOUN
stem-5536	3	23	,	,	PUNCT
stem-5536	3	24	synthesizing	synthesize	VERB
stem-5536	3	25	solutions	solution	NOUN
stem-5536	3	26	of	of	ADP
stem-5536	3	27	complex	complex	ADJ
stem-5536	3	28	geometric	geometric	ADJ
stem-5536	3	29	problems	problem	NOUN
stem-5536	3	30	that	that	PRON
stem-5536	3	31	require	require	VERB
stem-5536	3	32	advanced	advanced	ADJ
stem-5536	3	33	stereographic	stereographic	ADJ
stem-5536	3	34	imagination	imagination	NOUN
stem-5536	3	35	from	from	ADP
stem-5536	3	36	the	the	DET
stem-5536	3	37	simplest	simple	ADJ
stem-5536	3	38	mental	mental	ADJ
stem-5536	3	39	imagery	imagery	NOUN
stem-5536	3	40	and	and	CCONJ
stem-5536	3	41	operations	operation	NOUN
stem-5536	3	42	.	.	PUNCT
stem-5536	4	1	it	it	PRON
stem-5536	4	2	also	also	ADV
stem-5536	4	3	discusses	discuss	VERB
stem-5536	4	4	a	a	DET
stem-5536	4	5	contemporary	contemporary	ADJ
stem-5536	4	6	methodological	methodological	ADJ
stem-5536	4	7	issue	issue	NOUN
stem-5536	4	8	,	,	PUNCT
stem-5536	4	9	namely	namely	ADV
stem-5536	4	10	,	,	PUNCT
stem-5536	4	11	the	the	DET
stem-5536	4	12	problem	problem	NOUN
stem-5536	4	13	of	of	ADP
stem-5536	4	14	the	the	DET
stem-5536	4	15	advanced	advanced	ADJ
stem-5536	4	16	development	development	NOUN
stem-5536	4	17	of	of	ADP
stem-5536	4	18	visual	visual	ADJ
stem-5536	4	19	thinking	thinking	NOUN
stem-5536	4	20	.	.	PUNCT
stem-5536	5	1	in	in	ADP
stem-5536	5	2	the	the	DET
stem-5536	5	3	current	current	ADJ
stem-5536	5	4	state	state	NOUN
stem-5536	5	5	of	of	ADP
stem-5536	5	6	mathematical	mathematical	ADJ
stem-5536	5	7	education	education	NOUN
stem-5536	5	8	,	,	PUNCT
stem-5536	5	9	this	this	DET
stem-5536	5	10	issue	issue	NOUN
stem-5536	5	11	has	have	VERB
stem-5536	5	12	many	many	ADJ
stem-5536	5	13	shades	shade	NOUN
stem-5536	5	14	in	in	ADP
stem-5536	5	15	pedagogical	pedagogical	ADJ
stem-5536	5	16	practice	practice	NOUN
stem-5536	5	17	one	one	NUM
stem-5536	5	18	of	of	ADP
stem-5536	5	19	them	they	PRON
stem-5536	5	20	is	be	AUX
stem-5536	5	21	the	the	DET
stem-5536	5	22	upbringing	upbringing	NOUN
stem-5536	5	23	of	of	ADP
stem-5536	5	24	figurative	figurative	ADJ
stem-5536	5	25	thinking	thinking	NOUN
stem-5536	5	26	and	and	CCONJ
stem-5536	5	27	operational	operational	ADJ
stem-5536	5	28	efficiency	efficiency	NOUN
stem-5536	5	29	.	.	PUNCT
stem-5536	6	1	visual	visual	ADJ
stem-5536	6	2	thinking	thinking	NOUN
stem-5536	6	3	is	be	AUX
stem-5536	6	4	used	use	VERB
stem-5536	6	5	from	from	ADP
stem-5536	6	6	kindergarten	kindergarten	NOUN
stem-5536	6	7	to	to	ADP
stem-5536	6	8	mathematics	mathematics	NOUN
stem-5536	6	9	students	student	NOUN
stem-5536	6	10	of	of	ADP
stem-5536	6	11	pedagogical	pedagogical	ADJ
stem-5536	6	12	and	and	CCONJ
stem-5536	6	13	technical	technical	ADJ
stem-5536	6	14	universities	university	NOUN
stem-5536	6	15	.	.	PUNCT
stem-5536	7	1	another	another	DET
stem-5536	7	2	issue	issue	NOUN
stem-5536	7	3	posed	pose	VERB
stem-5536	7	4	at	at	ADP
stem-5536	7	5	the	the	DET
stem-5536	7	6	beginning	beginning	NOUN
stem-5536	7	7	of	of	ADP
stem-5536	7	8	the	the	DET
stem-5536	7	9	last	last	ADJ
stem-5536	7	10	century	century	NOUN
stem-5536	7	11	by	by	ADP
stem-5536	7	12	the	the	DET
stem-5536	7	13	american	american	ADJ
stem-5536	7	14	teacher	teacher	NOUN
stem-5536	7	15	,	,	PUNCT
stem-5536	7	16	psychologist	psychologist	NOUN
stem-5536	7	17	j.	j.	PROPN
stem-5536	7	18	dewey	dewey	PROPN
stem-5536	7	19	the	the	DET
stem-5536	7	20	possibility	possibility	NOUN
stem-5536	7	21	of	of	ADP
stem-5536	7	22	educating	educate	VERB
stem-5536	7	23	thinking	thinking	NOUN
stem-5536	7	24	and	and	CCONJ
stem-5536	7	25	its	its	PRON
stem-5536	7	26	method	method	NOUN
stem-5536	7	27	currently	currently	ADV
stem-5536	7	28	has	have	VERB
stem-5536	7	29	verification	verification	NOUN
stem-5536	7	30	in	in	ADP
stem-5536	7	31	the	the	DET
stem-5536	7	32	world	world	NOUN
stem-5536	7	33	pedagogical	pedagogical	ADJ
stem-5536	7	34	experience	experience	NOUN
stem-5536	7	35	.	.	PUNCT
stem-5536	8	1	works	work	NOUN
stem-5536	8	2	of	of	ADP
stem-5536	8	3	psychologists	psychologist	NOUN
stem-5536	8	4	,	,	PUNCT
stem-5536	8	5	philosophers	philosopher	NOUN
stem-5536	8	6	,	,	PUNCT
stem-5536	8	7	lecturers	lecturer	NOUN
stem-5536	8	8	:	:	PUNCT
stem-5536	8	9	pavlova	pavlova	PROPN
stem-5536	8	10	i.p	i.p	PROPN
stem-5536	8	11	.	.	PROPN
stem-5536	8	12	,	,	PUNCT
stem-5536	8	13	bertrand	bertrand	PROPN
stem-5536	8	14	russell	russell	PROPN
stem-5536	8	15	,	,	PUNCT
stem-5536	8	16	bekhterev	bekhterev	PROPN
stem-5536	8	17	v.m	v.m	PROPN
stem-5536	8	18	.	.	PROPN
stem-5536	8	19	,	,	PUNCT
stem-5536	8	20	vygodsky	vygodsky	PROPN
stem-5536	8	21	l.s	l.s	PROPN
stem-5536	8	22	.	.	PROPN
stem-5536	8	23	,	,	PUNCT
stem-5536	8	24	ilyin	ilyin	PROPN
stem-5536	8	25	e.p	e.p	PROPN
stem-5536	8	26	.	.	PROPN
stem-5536	8	27	,	,	PUNCT
stem-5536	8	28	leontiev	leontiev	PROPN
stem-5536	8	29	a.n	a.n	PROPN
stem-5536	8	30	.	.	PROPN
stem-5536	8	31	,	,	PUNCT
stem-5536	8	32	rubinstein	rubinstein	PROPN
stem-5536	8	33	s.l	s.l	PROPN
stem-5536	8	34	.	.	PROPN
stem-5536	8	35	,	,	PUNCT
stem-5536	8	36	luier	luier	PROPN
stem-5536	8	37	a.r	a.r	PROPN
stem-5536	8	38	.	.	PROPN
stem-5536	8	39	,	,	PUNCT
stem-5536	8	40	davydova	davydova	PROPN
stem-5536	8	41	v.v	v.v	PROPN
stem-5536	8	42	.	.	PROPN
stem-5536	8	43	,	,	PUNCT
stem-5536	8	44	korchak	korchak	PROPN
stem-5536	8	45	y.	y.	PROPN
stem-5536	8	46	,	,	PUNCT
stem-5536	8	47	galperina	galperina	PROPN
stem-5536	8	48	p.ya	p.ya	PROPN
stem-5536	8	49	.	.	PROPN
stem-5536	8	50	,	,	PUNCT
stem-5536	8	51	gessen	gessen	VERB
stem-5536	8	52	s.i	s.i	PROPN
stem-5536	8	53	.	.	PROPN
stem-5536	8	54	,	,	PUNCT
stem-5536	8	55	shatalova	shatalova	PROPN
stem-5536	8	56	v.f	v.f	PROPN
stem-5536	8	57	.	.	PROPN
stem-5536	8	58	,	,	PUNCT
stem-5536	8	59	elkoina	elkoina	PROPN
stem-5536	8	60	d.b	d.b	PROPN
stem-5536	8	61	.	.	PROPN
stem-5536	9	1	and	and	CCONJ
stem-5536	9	2	many	many	ADJ
stem-5536	9	3	others	other	NOUN
stem-5536	9	4	elucidated	elucidate	VERB
stem-5536	9	5	,	,	PUNCT
stem-5536	9	6	to	to	ADP
stem-5536	9	7	one	one	NUM
stem-5536	9	8	degree	degree	NOUN
stem-5536	9	9	or	or	CCONJ
stem-5536	9	10	another	another	PRON
stem-5536	9	11	,	,	PUNCT
stem-5536	9	12	the	the	DET
stem-5536	9	13	indicated	indicate	VERB
stem-5536	9	14	issue	issue	NOUN
stem-5536	9	15	,	,	PUNCT
stem-5536	9	16	especially	especially	ADV
stem-5536	9	17	interesting	interesting	ADJ
stem-5536	9	18	in	in	ADP
stem-5536	9	19	terms	term	NOUN
stem-5536	9	20	of	of	ADP
stem-5536	9	21	applications	application	NOUN
stem-5536	9	22	to	to	ADP
stem-5536	9	23	the	the	DET
stem-5536	9	24	development	development	NOUN
stem-5536	9	25	or	or	CCONJ
stem-5536	9	26	discovery	discovery	NOUN
stem-5536	9	27	or	or	CCONJ
stem-5536	9	28	education	education	NOUN
stem-5536	9	29	of	of	ADP
stem-5536	9	30	mathematical	mathematical	ADJ
stem-5536	9	31	abilities	ability	NOUN
stem-5536	9	32	.	.	PUNCT
stem-5536	10	1	this	this	DET
stem-5536	10	2	article	article	NOUN
stem-5536	10	3	describes	describe	VERB
stem-5536	10	4	the	the	DET
stem-5536	10	5	method	method	NOUN
stem-5536	10	6	of	of	ADP
stem-5536	10	7	“	"	PUNCT
stem-5536	10	8	endto	endto	NOUN
stem-5536	10	9	-	-	PUNCT
stem-5536	10	10	end	end	NOUN
stem-5536	10	11	”	"	PUNCT
stem-5536	10	12	teaching	teaching	NOUN
stem-5536	10	13	of	of	ADP
stem-5536	10	14	mathematicians	mathematician	NOUN
stem-5536	10	15	in	in	ADP
stem-5536	10	16	a	a	DET
stem-5536	10	17	pedagogical	pedagogical	ADJ
stem-5536	10	18	university	university	NOUN
stem-5536	10	19	based	base	VERB
stem-5536	10	20	on	on	ADP
stem-5536	10	21	issues	issue	NOUN
stem-5536	10	22	in	in	ADP
stem-5536	10	23	geometry	geometry	NOUN
stem-5536	10	24	.	.	PUNCT
stem-5536	11	1	key	key	ADJ
stem-5536	11	2	words	word	NOUN
stem-5536	11	3	:	:	PUNCT
stem-5536	11	4	education	education	NOUN
stem-5536	11	5	,	,	PUNCT
stem-5536	11	6	development	development	NOUN
stem-5536	11	7	,	,	PUNCT
stem-5536	11	8	mathematical	mathematical	ADJ
stem-5536	11	9	thinking	thinking	NOUN
stem-5536	11	10	,	,	PUNCT
stem-5536	11	11	verbal	verbal	ADJ
stem-5536	11	12	-	-	ADJ
stem-5536	11	13	figurative	figurative	ADJ
stem-5536	11	14	thinking	thinking	NOUN
stem-5536	11	15	,	,	PUNCT
stem-5536	11	16	figurativeverbal	figurativeverbal	ADJ
stem-5536	11	17	thinking	thinking	NOUN
stem-5536	11	18	,	,	PUNCT
stem-5536	11	19	figurative	figurative	ADJ
stem-5536	11	20	logical	logical	ADJ
stem-5536	11	21	thinking	thinking	NOUN
stem-5536	11	22	,	,	PUNCT
stem-5536	11	23	abstract	abstract	ADJ
stem-5536	11	24	-	-	PUNCT
stem-5536	11	25	figurative	figurative	ADJ
stem-5536	11	26	thinking	thinking	NOUN
stem-5536	11	27	,	,	PUNCT
stem-5536	11	28	abstractlogical	abstractlogical	ADJ
stem-5536	11	29	thinking	thinking	NOUN
stem-5536	11	30	,	,	PUNCT
stem-5536	11	31	stereographic	stereographic	ADJ
stem-5536	11	32	thinking	thinking	NOUN
stem-5536	11	33	,	,	PUNCT
stem-5536	11	34	concrete	concrete	ADJ
stem-5536	11	35	thinking	thinking	NOUN
stem-5536	11	36	.	.	PUNCT
stem-5536	12	1	introduction	introduction	NOUN
stem-5536	12	2	it	it	PRON
stem-5536	12	3	is	be	AUX
stem-5536	12	4	well	well	ADV
stem-5536	12	5	known	know	VERB
stem-5536	12	6	that	that	SCONJ
stem-5536	12	7	the	the	DET
stem-5536	12	8	upbringing	upbringing	NOUN
stem-5536	12	9	and	and	CCONJ
stem-5536	12	10	development	development	NOUN
stem-5536	12	11	of	of	ADP
stem-5536	12	12	a	a	DET
stem-5536	12	13	person	person	NOUN
stem-5536	12	14	begins	begin	VERB
stem-5536	12	15	in	in	ADP
stem-5536	12	16	the	the	DET
stem-5536	12	17	family	family	NOUN
stem-5536	12	18	.	.	PUNCT
stem-5536	13	1	the	the	DET
stem-5536	13	2	child	child	NOUN
stem-5536	13	3	understands	understand	VERB
stem-5536	13	4	the	the	DET
stem-5536	13	5	habits	habit	NOUN
stem-5536	13	6	and	and	CCONJ
stem-5536	13	7	attitudes	attitude	NOUN
stem-5536	13	8	of	of	ADP
stem-5536	13	9	adults	adult	NOUN
stem-5536	13	10	from	from	ADP
stem-5536	13	11	an	an	DET
stem-5536	13	12	early	early	ADJ
stem-5536	13	13	age	age	NOUN
stem-5536	13	14	.	.	PUNCT
stem-5536	14	1	in	in	ADP
stem-5536	14	2	addition	addition	NOUN
stem-5536	14	3	,	,	PUNCT
stem-5536	14	4	its	its	PRON
stem-5536	14	5	bright	bright	ADJ
stem-5536	14	6	colors	color	NOUN
stem-5536	14	7	are	be	AUX
stem-5536	14	8	attractive	attractive	ADJ
stem-5536	14	9	.	.	PUNCT
stem-5536	15	1	grasp	grasp	VERB
stem-5536	15	2	everything	everything	PRON
stem-5536	15	3	you	you	PRON
stem-5536	15	4	catch	catch	VERB
stem-5536	15	5	reflexively	reflexively	ADV
stem-5536	15	6	,	,	PUNCT
stem-5536	15	7	as	as	ADV
stem-5536	15	8	well	well	ADV
stem-5536	15	9	as	as	ADP
stem-5536	15	10	react	react	VERB
stem-5536	15	11	to	to	ADP
stem-5536	15	12	different	different	ADJ
stem-5536	15	13	sounds	sound	NOUN
stem-5536	15	14	and	and	CCONJ
stem-5536	15	15	noises	noise	NOUN
stem-5536	15	16	.	.	PUNCT
stem-5536	16	1	all	all	PRON
stem-5536	16	2	of	of	ADP
stem-5536	16	3	these	these	DET
stem-5536	16	4	infant	infant	NOUN
stem-5536	16	5	-	-	PUNCT
stem-5536	16	6	specific	specific	ADJ
stem-5536	16	7	behaviors	behavior	NOUN
stem-5536	16	8	are	be	AUX
stem-5536	16	9	indicative	indicative	ADJ
stem-5536	16	10	of	of	ADP
stem-5536	16	11	a	a	DET
stem-5536	16	12	child	child	NOUN
stem-5536	16	13	’s	’s	PART
stem-5536	16	14	healthy	healthy	ADJ
stem-5536	16	15	reactions	reaction	NOUN
stem-5536	16	16	[	[	X
stem-5536	16	17	1	1	NUM
stem-5536	16	18	]	]	PUNCT
stem-5536	16	19	.	.	PUNCT
stem-5536	17	1	from	from	ADP
stem-5536	17	2	preschool	preschool	ADJ
stem-5536	17	3	age	age	NOUN
stem-5536	17	4	,	,	PUNCT
stem-5536	17	5	the	the	DET
stem-5536	17	6	child	child	NOUN
stem-5536	17	7	is	be	AUX
stem-5536	17	8	given	give	VERB
stem-5536	17	9	a	a	DET
stem-5536	17	10	poem	poem	NOUN
stem-5536	17	11	memorization	memorization	NOUN
stem-5536	17	12	,	,	PUNCT
stem-5536	17	13	classification	classification	NOUN
stem-5536	17	14	of	of	ADP
stem-5536	17	15	colors	color	NOUN
stem-5536	17	16	and	and	CCONJ
stem-5536	17	17	shapes	shape	NOUN
stem-5536	17	18	,	,	PUNCT
stem-5536	17	19	taking	take	VERB
stem-5536	17	20	into	into	ADP
stem-5536	17	21	account	account	NOUN
stem-5536	17	22	the	the	DET
stem-5536	17	23	age	age	NOUN
stem-5536	17	24	characteristics	characteristic	NOUN
stem-5536	17	25	of	of	ADP
stem-5536	17	26	the	the	DET
stem-5536	17	27	personality	personality	NOUN
stem-5536	17	28	.	.	PUNCT
stem-5536	18	1	determine	determine	VERB
stem-5536	18	2	the	the	DET
stem-5536	18	3	position	position	NOUN
stem-5536	18	4	of	of	ADP
stem-5536	18	5	objects	object	NOUN
stem-5536	18	6	in	in	ADP
stem-5536	18	7	space	space	NOUN
stem-5536	18	8	and	and	CCONJ
stem-5536	18	9	the	the	DET
stem-5536	18	10	figures	figure	NOUN
stem-5536	18	11	in	in	ADP
stem-5536	18	12	the	the	DET
stem-5536	18	13	plane	plane	NOUN
stem-5536	18	14	.	.	PUNCT
stem-5536	19	1	related	relate	VERB
stem-5536	19	2	to	to	ADP
stem-5536	19	3	the	the	DET
stem-5536	19	4	words	word	NOUN
stem-5536	19	5	“	"	PUNCT
stem-5536	19	6	up	up	ADP
stem-5536	19	7	”	"	PUNCT
stem-5536	19	8	,	,	PUNCT
stem-5536	19	9	“	"	PUNCT
stem-5536	19	10	down	down	ADP
stem-5536	19	11	”	"	PUNCT
stem-5536	19	12	,	,	PUNCT
stem-5536	19	13	“	"	PUNCT
stem-5536	19	14	right	right	ADJ
stem-5536	19	15	”	"	PUNCT
stem-5536	19	16	,	,	PUNCT
stem-5536	19	17	“	"	PUNCT
stem-5536	19	18	left	leave	VERB
stem-5536	19	19	”	"	PUNCT
stem-5536	19	20	,	,	PUNCT
stem-5536	19	21	“	"	PUNCT
stem-5536	19	22	forward	forward	ADV
stem-5536	19	23	”	"	PUNCT
stem-5536	19	24	,	,	PUNCT
stem-5536	19	25	“	"	PUNCT
stem-5536	19	26	back	back	ADV
stem-5536	19	27	”	"	PUNCT
stem-5536	19	28	,	,	PUNCT
stem-5536	19	29	“	"	PUNCT
stem-5536	19	30	behind	behind	ADP
stem-5536	19	31	”	"	PUNCT
stem-5536	19	32	,	,	PUNCT
stem-5536	19	33	“	"	PUNCT
stem-5536	19	34	in	in	ADP
stem-5536	19	35	front	front	NOUN
stem-5536	19	36	”	"	PUNCT
stem-5536	19	37	,	,	PUNCT
stem-5536	19	38	“	"	PUNCT
stem-5536	19	39	on	on	ADP
stem-5536	19	40	the	the	DET
stem-5536	19	41	side	side	NOUN
stem-5536	19	42	”	"	PUNCT
stem-5536	19	43	,	,	PUNCT
stem-5536	19	44	“	"	PUNCT
stem-5536	19	45	side	side	NOUN
stem-5536	19	46	”	"	PUNCT
stem-5536	19	47	perform	perform	VERB
stem-5536	19	48	a	a	DET
stem-5536	19	49	variety	variety	NOUN
stem-5536	19	50	of	of	ADP
stem-5536	19	51	actions	action	NOUN
stem-5536	19	52	.	.	PUNCT
stem-5536	20	1	120	120	NUM
stem-5536	20	2	american	american	ADJ
stem-5536	20	3	journal	journal	NOUN
stem-5536	20	4	of	of	ADP
stem-5536	20	5	language	language	NOUN
stem-5536	20	6	,	,	PUNCT
stem-5536	20	7	literacy	literacy	NOUN
stem-5536	20	8	and	and	CCONJ
stem-5536	20	9	learning	learn	VERB
stem-5536	20	10	in	in	ADP
stem-5536	20	11	stem	stem	NOUN
stem-5536	20	12	education	education	NOUN
stem-5536	20	13	www	www	PROPN
stem-5536	20	14	.	.	PUNCT
stem-5536	21	1	grnjournal.us	grnjournal.us	X
stem-5536	21	2	verbal	verbal	ADJ
stem-5536	21	3	and	and	CCONJ
stem-5536	21	4	logical	logical	ADJ
stem-5536	21	5	thinking	thinking	NOUN
stem-5536	21	6	also	also	ADV
stem-5536	21	7	develop	develop	VERB
stem-5536	21	8	through	through	ADP
stem-5536	21	9	these	these	DET
stem-5536	21	10	commands	command	NOUN
stem-5536	21	11	and	and	CCONJ
stem-5536	21	12	actions	action	NOUN
stem-5536	21	13	.	.	PUNCT
stem-5536	22	1	at	at	ADP
stem-5536	22	2	the	the	DET
stem-5536	22	3	preschool	preschool	ADJ
stem-5536	22	4	age	age	NOUN
stem-5536	22	5	,	,	PUNCT
stem-5536	22	6	elementary	elementary	ADJ
stem-5536	22	7	ideas	idea	NOUN
stem-5536	22	8	about	about	ADP
stem-5536	22	9	mathematical	mathematical	ADJ
stem-5536	22	10	figures	figure	NOUN
stem-5536	22	11	and	and	CCONJ
stem-5536	22	12	concepts	concept	NOUN
stem-5536	22	13	,	,	PUNCT
stem-5536	22	14	quantity	quantity	NOUN
stem-5536	22	15	,	,	PUNCT
stem-5536	22	16	size	size	NOUN
stem-5536	22	17	are	be	AUX
stem-5536	22	18	also	also	ADV
stem-5536	22	19	created	create	VERB
stem-5536	22	20	.	.	PUNCT
stem-5536	23	1	such	such	ADJ
stem-5536	23	2	as	as	ADP
stem-5536	23	3	“	"	PUNCT
stem-5536	23	4	more	more	ADJ
stem-5536	23	5	”	"	PUNCT
stem-5536	23	6	,	,	PUNCT
stem-5536	23	7	“	"	PUNCT
stem-5536	23	8	less	less	ADJ
stem-5536	23	9	”	"	PUNCT
stem-5536	23	10	,	,	PUNCT
stem-5536	23	11	“	"	PUNCT
stem-5536	23	12	equal	equal	ADJ
stem-5536	23	13	”	"	PUNCT
stem-5536	23	14	,	,	PUNCT
stem-5536	23	15	“	"	PUNCT
stem-5536	23	16	combine	combine	NOUN
stem-5536	23	17	”	"	PUNCT
stem-5536	23	18	(	(	PUNCT
stem-5536	23	19	comparison	comparison	NOUN
stem-5536	23	20	)	)	PUNCT
stem-5536	23	21	,	,	PUNCT
stem-5536	23	22	“	"	PUNCT
stem-5536	23	23	attach	attach	VERB
stem-5536	23	24	”	"	PUNCT
stem-5536	23	25	,	,	PUNCT
stem-5536	23	26	“	"	PUNCT
stem-5536	23	27	break	break	NOUN
stem-5536	23	28	into	into	ADP
stem-5536	23	29	parts	part	NOUN
stem-5536	23	30	”	"	PUNCT
stem-5536	23	31	(	(	PUNCT
stem-5536	23	32	cut	cut	NOUN
stem-5536	23	33	)	)	PUNCT
stem-5536	23	34	,	,	PUNCT
stem-5536	23	35	“	"	PUNCT
stem-5536	23	36	put	put	VERB
stem-5536	23	37	”	"	PUNCT
stem-5536	23	38	,	,	PUNCT
stem-5536	23	39	“	"	PUNCT
stem-5536	23	40	compare	compare	NOUN
stem-5536	23	41	”	"	PUNCT
stem-5536	23	42	.	.	PUNCT
stem-5536	24	1	as	as	ADP
stem-5536	24	2	experience	experience	NOUN
stem-5536	24	3	shows	show	NOUN
stem-5536	24	4	,	,	PUNCT
stem-5536	24	5	from	from	ADP
stem-5536	24	6	4	4	NUM
stem-5536	24	7	-	-	SYM
stem-5536	24	8	5	5	NUM
stem-5536	24	9	years	year	NOUN
stem-5536	24	10	old	old	ADJ
stem-5536	24	11	to	to	ADP
stem-5536	24	12	7	7	NUM
stem-5536	24	13	-	-	SYM
stem-5536	24	14	8	8	NUM
stem-5536	24	15	years	year	NOUN
stem-5536	24	16	old	old	ADJ
stem-5536	24	17	children	child	NOUN
stem-5536	24	18	develop	develop	VERB
stem-5536	24	19	figurativeverbal	figurativeverbal	ADJ
stem-5536	24	20	thinking	thinking	NOUN
stem-5536	24	21	.	.	PUNCT
stem-5536	25	1	during	during	ADP
stem-5536	25	2	this	this	DET
stem-5536	25	3	period	period	NOUN
stem-5536	25	4	,	,	PUNCT
stem-5536	25	5	a	a	DET
stem-5536	25	6	well	well	ADV
stem-5536	25	7	-	-	PUNCT
stem-5536	25	8	developed	develop	VERB
stem-5536	25	9	child	child	NOUN
stem-5536	25	10	easily	easily	ADV
stem-5536	25	11	perceives	perceive	VERB
stem-5536	25	12	the	the	DET
stem-5536	25	13	necessary	necessary	ADJ
stem-5536	25	14	information	information	NOUN
stem-5536	25	15	around	around	ADP
stem-5536	25	16	him	he	PRON
stem-5536	26	1	[	[	X
stem-5536	26	2	2	2	NUM
stem-5536	26	3	,	,	PUNCT
stem-5536	26	4	3	3	NUM
stem-5536	26	5	]	]	PUNCT
stem-5536	26	6	.	.	PUNCT
stem-5536	27	1	in	in	ADP
stem-5536	27	2	elementary	elementary	ADJ
stem-5536	27	3	school	school	PROPN
stem-5536	27	4	math	math	NOUN
stem-5536	27	5	classes	class	NOUN
stem-5536	27	6	,	,	PUNCT
stem-5536	27	7	students	student	NOUN
stem-5536	27	8	begin	begin	VERB
stem-5536	27	9	to	to	PART
stem-5536	27	10	form	form	VERB
stem-5536	27	11	word	word	NOUN
stem-5536	27	12	problems	problem	NOUN
stem-5536	27	13	of	of	ADP
stem-5536	27	14	different	different	ADJ
stem-5536	27	15	content	content	NOUN
stem-5536	27	16	,	,	PUNCT
stem-5536	27	17	ways	way	NOUN
stem-5536	27	18	to	to	PART
stem-5536	27	19	understand	understand	VERB
stem-5536	27	20	the	the	DET
stem-5536	27	21	content	content	NOUN
stem-5536	27	22	of	of	ADP
stem-5536	27	23	the	the	DET
stem-5536	27	24	problem	problem	NOUN
stem-5536	27	25	using	use	VERB
stem-5536	27	26	official	official	ADJ
stem-5536	27	27	language	language	NOUN
stem-5536	27	28	.	.	PUNCT
stem-5536	28	1	the	the	DET
stem-5536	28	2	educational	educational	ADJ
stem-5536	28	3	connection	connection	NOUN
stem-5536	28	4	,	,	PUNCT
stem-5536	28	5	depending	depend	VERB
stem-5536	28	6	on	on	ADP
stem-5536	28	7	the	the	DET
stem-5536	28	8	teacher	teacher	NOUN
stem-5536	28	9	’s	’s	PART
stem-5536	28	10	qualifications	qualification	NOUN
stem-5536	28	11	,	,	PUNCT
stem-5536	28	12	should	should	AUX
stem-5536	28	13	require	require	VERB
stem-5536	28	14	the	the	DET
stem-5536	28	15	student	student	NOUN
stem-5536	28	16	to	to	PART
stem-5536	28	17	use	use	VERB
stem-5536	28	18	mathematical	mathematical	ADJ
stem-5536	28	19	discourse	discourse	NOUN
stem-5536	28	20	.	.	PUNCT
stem-5536	29	1	thus	thus	ADV
stem-5536	29	2	,	,	PUNCT
stem-5536	29	3	competent	competent	ADJ
stem-5536	29	4	mathematical	mathematical	ADJ
stem-5536	29	5	discourse	discourse	NOUN
stem-5536	29	6	develops	develop	VERB
stem-5536	29	7	.	.	PUNCT
stem-5536	30	1	preconditions	precondition	NOUN
stem-5536	30	2	are	be	AUX
stem-5536	30	3	created	create	VERB
stem-5536	30	4	for	for	ADP
stem-5536	30	5	the	the	DET
stem-5536	30	6	development	development	NOUN
stem-5536	30	7	of	of	ADP
stem-5536	30	8	verbal	verbal	ADJ
stem-5536	30	9	-	-	ADJ
stem-5536	30	10	figurative	figurative	ADJ
stem-5536	30	11	thinking	thinking	NOUN
stem-5536	30	12	.	.	PUNCT
stem-5536	31	1	over	over	ADP
stem-5536	31	2	time	time	NOUN
stem-5536	31	3	,	,	PUNCT
stem-5536	31	4	from	from	ADP
stem-5536	31	5	grades	grade	NOUN
stem-5536	31	6	5	5	NUM
stem-5536	31	7	-	-	SYM
stem-5536	31	8	6	6	NUM
stem-5536	31	9	,	,	PUNCT
stem-5536	31	10	students	student	NOUN
stem-5536	31	11	in	in	ADP
stem-5536	31	12	mathematics	mathematics	NOUN
stem-5536	31	13	lessons	lesson	NOUN
stem-5536	31	14	develop	develop	VERB
stem-5536	31	15	the	the	DET
stem-5536	31	16	need	need	NOUN
stem-5536	31	17	to	to	PART
stem-5536	31	18	translate	translate	VERB
stem-5536	31	19	texts	text	NOUN
stem-5536	31	20	into	into	ADP
stem-5536	31	21	images	image	NOUN
stem-5536	31	22	,	,	PUNCT
stem-5536	31	23	turning	turn	VERB
stem-5536	31	24	into	into	ADP
stem-5536	31	25	figurativelogical	figurativelogical	ADJ
stem-5536	31	26	,	,	PUNCT
stem-5536	31	27	and	and	CCONJ
stem-5536	31	28	then	then	ADV
stem-5536	31	29	verbal	verbal	ADJ
stem-5536	31	30	-	-	ADJ
stem-5536	31	31	logical	logical	ADJ
stem-5536	31	32	ideas	idea	NOUN
stem-5536	31	33	about	about	ADP
stem-5536	31	34	tasks	task	NOUN
stem-5536	31	35	[	[	X
stem-5536	31	36	4	4	NUM
stem-5536	31	37	]	]	PUNCT
stem-5536	31	38	.	.	PUNCT
stem-5536	32	1	this	this	PRON
stem-5536	32	2	means	mean	VERB
stem-5536	32	3	that	that	SCONJ
stem-5536	32	4	word	word	NOUN
stem-5536	32	5	problems	problem	NOUN
stem-5536	32	6	transform	transform	VERB
stem-5536	32	7	figurative	figurative	ADJ
stem-5536	32	8	pictures	picture	NOUN
stem-5536	32	9	and	and	CCONJ
stem-5536	32	10	thoughts	thought	NOUN
stem-5536	32	11	into	into	ADP
stem-5536	32	12	an	an	DET
stem-5536	32	13	abstract	abstract	ADJ
stem-5536	32	14	form	form	NOUN
stem-5536	32	15	,	,	PUNCT
stem-5536	32	16	represent	represent	VERB
stem-5536	32	17	the	the	DET
stem-5536	32	18	meaning	meaning	NOUN
stem-5536	32	19	(	(	PUNCT
stem-5536	32	20	what	what	PRON
stem-5536	32	21	is	be	AUX
stem-5536	32	22	required	require	VERB
stem-5536	32	23	to	to	PART
stem-5536	32	24	find	find	VERB
stem-5536	32	25	)	)	PUNCT
stem-5536	32	26	in	in	ADP
stem-5536	32	27	the	the	DET
stem-5536	32	28	problem	problem	NOUN
stem-5536	32	29	and	and	CCONJ
stem-5536	32	30	decompose	decompose	VERB
stem-5536	32	31	its	its	PRON
stem-5536	32	32	solution	solution	NOUN
stem-5536	32	33	into	into	ADP
stem-5536	32	34	elementary	elementary	ADJ
stem-5536	32	35	actions	action	NOUN
stem-5536	32	36	and	and	CCONJ
stem-5536	32	37	tasks	task	NOUN
stem-5536	32	38	.	.	PUNCT
stem-5536	33	1	starting	start	VERB
stem-5536	33	2	from	from	ADP
stem-5536	33	3	the	the	DET
stem-5536	33	4	7th	7th	ADJ
stem-5536	33	5	grade	grade	NOUN
stem-5536	33	6	,	,	PUNCT
stem-5536	33	7	when	when	SCONJ
stem-5536	33	8	they	they	PRON
stem-5536	33	9	begin	begin	VERB
stem-5536	33	10	to	to	PART
stem-5536	33	11	study	study	VERB
stem-5536	33	12	the	the	DET
stem-5536	33	13	discipline	discipline	NOUN
stem-5536	33	14	“	"	PUNCT
stem-5536	33	15	geometry	geometry	NOUN
stem-5536	33	16	”	"	PUNCT
stem-5536	33	17	,	,	PUNCT
stem-5536	33	18	they	they	PRON
stem-5536	33	19	purposefully	purposefully	ADV
stem-5536	33	20	develop	develop	VERB
stem-5536	33	21	the	the	DET
stem-5536	33	22	figurative	figurative	ADJ
stem-5536	33	23	-	-	PUNCT
stem-5536	33	24	logical	logical	ADJ
stem-5536	33	25	component	component	NOUN
stem-5536	33	26	of	of	ADP
stem-5536	33	27	mathematical	mathematical	ADJ
stem-5536	33	28	thinking	thinking	NOUN
stem-5536	33	29	.	.	PUNCT
stem-5536	34	1	the	the	DET
stem-5536	34	2	development	development	NOUN
stem-5536	34	3	of	of	ADP
stem-5536	34	4	figurative	figurative	ADJ
stem-5536	34	5	-	-	PUNCT
stem-5536	34	6	logical	logical	ADJ
stem-5536	34	7	thinking	thinking	NOUN
stem-5536	34	8	is	be	AUX
stem-5536	34	9	mentioned	mention	VERB
stem-5536	34	10	in	in	ADP
stem-5536	34	11	[	[	X
stem-5536	34	12	5	5	NUM
stem-5536	34	13	]	]	PUNCT
stem-5536	34	14	.	.	PUNCT
stem-5536	35	1	these	these	DET
stem-5536	35	2	methods	method	NOUN
stem-5536	35	3	of	of	ADP
stem-5536	35	4	organizing	organize	VERB
stem-5536	35	5	educational	educational	ADJ
stem-5536	35	6	texts	text	NOUN
stem-5536	35	7	contribute	contribute	VERB
stem-5536	35	8	to	to	ADP
stem-5536	35	9	the	the	DET
stem-5536	35	10	development	development	NOUN
stem-5536	35	11	of	of	ADP
stem-5536	35	12	mathematical	mathematical	ADJ
stem-5536	35	13	thinking	thinking	NOUN
stem-5536	35	14	.	.	PUNCT
stem-5536	36	1	geometric	geometric	ADJ
stem-5536	36	2	pictures	picture	NOUN
stem-5536	36	3	of	of	ADP
stem-5536	36	4	the	the	DET
stem-5536	36	5	world	world	NOUN
stem-5536	36	6	in	in	ADP
stem-5536	36	7	figurative	figurative	ADJ
stem-5536	36	8	-	-	ADJ
stem-5536	36	9	verbal	verbal	ADJ
stem-5536	36	10	and	and	CCONJ
stem-5536	36	11	verbal	verbal	ADJ
stem-5536	36	12	-	-	PUNCT
stem-5536	36	13	figurative	figurative	ADJ
stem-5536	36	14	forms	form	NOUN
stem-5536	36	15	are	be	AUX
stem-5536	36	16	transformed	transform	VERB
stem-5536	36	17	directly	directly	ADV
stem-5536	36	18	in	in	ADP
stem-5536	36	19	geometry	geometry	NOUN
stem-5536	36	20	lessons	lesson	NOUN
stem-5536	36	21	into	into	ADP
stem-5536	36	22	a	a	DET
stem-5536	36	23	figurative	figurative	ADJ
stem-5536	36	24	-	-	PUNCT
stem-5536	36	25	logical	logical	ADJ
stem-5536	36	26	form	form	NOUN
stem-5536	36	27	in	in	ADP
stem-5536	36	28	which	which	PRON
stem-5536	36	29	the	the	DET
stem-5536	36	30	text	text	NOUN
stem-5536	36	31	of	of	ADP
stem-5536	36	32	the	the	DET
stem-5536	36	33	problem	problem	NOUN
stem-5536	36	34	and	and	CCONJ
stem-5536	36	35	the	the	DET
stem-5536	36	36	text	text	NOUN
stem-5536	36	37	of	of	ADP
stem-5536	36	38	the	the	DET
stem-5536	36	39	student	student	NOUN
stem-5536	36	40	's	's	PART
stem-5536	36	41	reasoning	reasoning	NOUN
stem-5536	36	42	are	be	AUX
stem-5536	36	43	consistent	consistent	ADJ
stem-5536	36	44	with	with	ADP
stem-5536	36	45	the	the	DET
stem-5536	36	46	rules	rule	NOUN
stem-5536	36	47	of	of	ADP
stem-5536	36	48	the	the	DET
stem-5536	36	49	native	native	ADJ
stem-5536	36	50	language	language	NOUN
stem-5536	36	51	and	and	CCONJ
stem-5536	36	52	mathematical	mathematical	ADJ
stem-5536	36	53	logic	logic	NOUN
stem-5536	36	54	(	(	PUNCT
stem-5536	36	55	propaedeutics	propaedeutic	NOUN
stem-5536	36	56	of	of	ADP
stem-5536	36	57	the	the	DET
stem-5536	36	58	concepts	concept	NOUN
stem-5536	36	59	of	of	ADP
stem-5536	36	60	mathematical	mathematical	ADJ
stem-5536	36	61	logic	logic	NOUN
stem-5536	36	62	)	)	PUNCT
stem-5536	36	63	.	.	PUNCT
stem-5536	37	1	the	the	DET
stem-5536	37	2	main	main	ADJ
stem-5536	37	3	findings	finding	NOUN
stem-5536	37	4	and	and	CCONJ
stem-5536	37	5	results	result	VERB
stem-5536	37	6	it	it	PRON
stem-5536	37	7	should	should	AUX
stem-5536	37	8	be	be	AUX
stem-5536	37	9	noted	note	VERB
stem-5536	37	10	that	that	SCONJ
stem-5536	37	11	the	the	DET
stem-5536	37	12	age	age	NOUN
stem-5536	37	13	-	-	PUNCT
stem-5536	37	14	related	relate	VERB
stem-5536	37	15	features	feature	NOUN
stem-5536	37	16	of	of	ADP
stem-5536	37	17	upbringing	upbringing	NOUN
stem-5536	37	18	and	and	CCONJ
stem-5536	37	19	education	education	NOUN
stem-5536	37	20	lead	lead	NOUN
stem-5536	37	21	to	to	ADP
stem-5536	37	22	significant	significant	ADJ
stem-5536	37	23	changes	change	NOUN
stem-5536	37	24	in	in	ADP
stem-5536	37	25	the	the	DET
stem-5536	37	26	psychophysiological	psychophysiological	ADJ
stem-5536	37	27	state	state	NOUN
stem-5536	37	28	of	of	ADP
stem-5536	37	29	children	child	NOUN
stem-5536	37	30	under	under	ADP
stem-5536	37	31	9th	9th	ADJ
stem-5536	37	32	grade	grade	NOUN
stem-5536	37	33	.	.	PUNCT
stem-5536	38	1	in	in	ADP
stem-5536	38	2	high	high	ADJ
stem-5536	38	3	school	school	NOUN
stem-5536	38	4	and	and	CCONJ
stem-5536	38	5	early	early	ADJ
stem-5536	38	6	school	school	NOUN
stem-5536	38	7	years	year	NOUN
stem-5536	38	8	,	,	PUNCT
stem-5536	38	9	logical	logical	ADJ
stem-5536	38	10	-	-	PUNCT
stem-5536	38	11	abstract	abstract	ADJ
stem-5536	38	12	thinking	thinking	NOUN
stem-5536	38	13	develops	develop	VERB
stem-5536	38	14	.	.	PUNCT
stem-5536	39	1	there	there	PRON
stem-5536	39	2	are	be	VERB
stem-5536	39	3	professional	professional	ADJ
stem-5536	39	4	aspirations	aspiration	NOUN
stem-5536	39	5	and	and	CCONJ
stem-5536	39	6	development	development	NOUN
stem-5536	39	7	programs	program	NOUN
stem-5536	39	8	of	of	ADP
stem-5536	39	9	students	student	NOUN
stem-5536	39	10	[	[	X
stem-5536	39	11	6	6	NUM
stem-5536	39	12	,	,	PUNCT
stem-5536	39	13	7	7	NUM
stem-5536	39	14	,	,	PUNCT
stem-5536	39	15	8	8	NUM
stem-5536	39	16	]	]	PUNCT
stem-5536	39	17	.	.	PUNCT
stem-5536	40	1	a	a	DET
stem-5536	40	2	few	few	ADJ
stem-5536	40	3	words	word	NOUN
stem-5536	40	4	about	about	ADP
stem-5536	40	5	the	the	DET
stem-5536	40	6	geometric	geometric	ADJ
stem-5536	40	7	image	image	NOUN
stem-5536	40	8	and	and	CCONJ
stem-5536	40	9	the	the	DET
stem-5536	40	10	geometric	geometric	ADJ
stem-5536	40	11	location	location	NOUN
stem-5536	40	12	of	of	ADP
stem-5536	40	13	points	point	NOUN
stem-5536	40	14	and	and	CCONJ
stem-5536	40	15	their	their	PRON
stem-5536	40	16	methodological	methodological	ADJ
stem-5536	40	17	usefulness	usefulness	NOUN
stem-5536	40	18	it	it	PRON
stem-5536	40	19	is	be	AUX
stem-5536	40	20	well	well	ADV
stem-5536	40	21	known	know	VERB
stem-5536	40	22	that	that	SCONJ
stem-5536	40	23	professional	professional	ADJ
stem-5536	40	24	thinking	thinking	NOUN
stem-5536	40	25	,	,	PUNCT
stem-5536	40	26	especially	especially	ADV
stem-5536	40	27	engineering	engineering	NOUN
stem-5536	40	28	thinking	thinking	NOUN
stem-5536	40	29	,	,	PUNCT
stem-5536	40	30	is	be	AUX
stem-5536	40	31	associated	associate	VERB
stem-5536	40	32	with	with	ADP
stem-5536	40	33	the	the	DET
stem-5536	40	34	“	"	PUNCT
stem-5536	40	35	old	old	ADJ
stem-5536	40	36	”	"	PUNCT
stem-5536	40	37	type	type	NOUN
stem-5536	40	38	of	of	ADP
stem-5536	40	39	thinking	thinking	NOUN
stem-5536	40	40	,	,	PUNCT
stem-5536	40	41	i.e.	i.e.	X
stem-5536	40	42	,	,	PUNCT
stem-5536	40	43	stereographic	stereographic	ADJ
stem-5536	40	44	,	,	PUNCT
stem-5536	40	45	volumetric	volumetric	ADJ
stem-5536	40	46	thinking	thinking	NOUN
stem-5536	40	47	,	,	PUNCT
stem-5536	40	48	despite	despite	SCONJ
stem-5536	40	49	computerization	computerization	NOUN
stem-5536	40	50	and	and	CCONJ
stem-5536	40	51	the	the	DET
stem-5536	40	52	development	development	NOUN
stem-5536	40	53	of	of	ADP
stem-5536	40	54	artificial	artificial	ADJ
stem-5536	40	55	intelligence	intelligence	NOUN
stem-5536	40	56	.	.	PUNCT
stem-5536	41	1	indeed	indeed	ADV
stem-5536	41	2	,	,	PUNCT
stem-5536	41	3	before	before	ADP
stem-5536	41	4	constructing	construct	VERB
stem-5536	41	5	any	any	DET
stem-5536	41	6	machine	machine	NOUN
stem-5536	41	7	,	,	PUNCT
stem-5536	41	8	building	building	NOUN
stem-5536	41	9	or	or	CCONJ
stem-5536	41	10	structure	structure	NOUN
stem-5536	41	11	,	,	PUNCT
stem-5536	41	12	they	they	PRON
stem-5536	41	13	usually	usually	ADV
stem-5536	41	14	draw	draw	VERB
stem-5536	41	15	their	their	PRON
stem-5536	41	16	images	image	NOUN
stem-5536	41	17	previously	previously	ADV
stem-5536	41	18	they	they	PRON
stem-5536	41	19	did	do	VERB
stem-5536	41	20	it	it	PRON
stem-5536	41	21	on	on	ADP
stem-5536	41	22	paper	paper	NOUN
stem-5536	41	23	,	,	PUNCT
stem-5536	41	24	now	now	ADV
stem-5536	41	25	they	they	PRON
stem-5536	41	26	make	make	VERB
stem-5536	41	27	drawings	drawing	NOUN
stem-5536	41	28	with	with	ADP
stem-5536	41	29	the	the	DET
stem-5536	41	30	help	help	NOUN
stem-5536	41	31	of	of	ADP
stem-5536	41	32	“	"	PUNCT
stem-5536	41	33	smart	smart	ADJ
stem-5536	41	34	”	"	PUNCT
stem-5536	41	35	computer	computer	NOUN
stem-5536	41	36	programs	program	NOUN
stem-5536	41	37	.	.	PUNCT
stem-5536	42	1	but	but	CCONJ
stem-5536	42	2	from	from	ADP
stem-5536	42	3	the	the	DET
stem-5536	42	4	conception	conception	NOUN
stem-5536	42	5	of	of	ADP
stem-5536	42	6	the	the	DET
stem-5536	42	7	object	object	NOUN
stem-5536	42	8	to	to	ADP
stem-5536	42	9	its	its	PRON
stem-5536	42	10	construction	construction	NOUN
stem-5536	42	11	,	,	PUNCT
stem-5536	42	12	a	a	DET
stem-5536	42	13	huge	huge	ADJ
stem-5536	42	14	intellectual	intellectual	ADJ
stem-5536	42	15	,	,	PUNCT
stem-5536	42	16	constructive	constructive	ADJ
stem-5536	42	17	work	work	NOUN
stem-5536	42	18	takes	take	VERB
stem-5536	42	19	place	place	NOUN
stem-5536	42	20	.	.	PUNCT
stem-5536	43	1	in	in	ADP
stem-5536	43	2	order	order	NOUN
stem-5536	43	3	to	to	PART
stem-5536	43	4	build	build	VERB
stem-5536	43	5	a	a	DET
stem-5536	43	6	car	car	NOUN
stem-5536	43	7	from	from	ADP
stem-5536	43	8	the	the	DET
stem-5536	43	9	image	image	NOUN
stem-5536	43	10	,	,	PUNCT
stem-5536	43	11	the	the	DET
stem-5536	43	12	image	image	NOUN
stem-5536	43	13	itself	itself	PRON
stem-5536	43	14	must	must	AUX
stem-5536	43	15	be	be	AUX
stem-5536	43	16	sufficiently	sufficiently	ADV
stem-5536	43	17	accurate	accurate	ADJ
stem-5536	43	18	and	and	CCONJ
stem-5536	43	19	meet	meet	VERB
stem-5536	43	20	certain	certain	ADJ
stem-5536	43	21	requirements	requirement	NOUN
stem-5536	43	22	.	.	PUNCT
stem-5536	44	1	in	in	ADP
stem-5536	44	2	the	the	DET
stem-5536	44	3	history	history	NOUN
stem-5536	44	4	of	of	ADP
stem-5536	44	5	science	science	NOUN
stem-5536	44	6	,	,	PUNCT
stem-5536	44	7	the	the	DET
stem-5536	44	8	need	need	NOUN
stem-5536	44	9	for	for	ADP
stem-5536	44	10	a	a	DET
stem-5536	44	11	theory	theory	NOUN
stem-5536	44	12	of	of	ADP
stem-5536	44	13	images	image	NOUN
stem-5536	44	14	became	become	VERB
stem-5536	44	15	clear	clear	ADJ
stem-5536	44	16	long	long	ADV
stem-5536	44	17	ago	ago	ADV
stem-5536	44	18	.	.	PUNCT
stem-5536	45	1	already	already	ADV
stem-5536	45	2	at	at	ADP
stem-5536	45	3	the	the	DET
stem-5536	45	4	beginning	beginning	NOUN
stem-5536	45	5	of	of	ADP
stem-5536	45	6	our	our	PRON
stem-5536	45	7	era	era	NOUN
stem-5536	45	8	,	,	PUNCT
stem-5536	45	9	the	the	DET
stem-5536	45	10	roman	roman	ADJ
stem-5536	45	11	historian	historian	NOUN
stem-5536	45	12	and	and	CCONJ
stem-5536	45	13	architect	architect	NOUN
stem-5536	45	14	vitruvius	vitruvius	PROPN
stem-5536	45	15	gives	give	VERB
stem-5536	45	16	some	some	DET
stem-5536	45	17	rules	rule	NOUN
stem-5536	45	18	for	for	ADP
stem-5536	45	19	constructing	construct	VERB
stem-5536	45	20	images	image	NOUN
stem-5536	45	21	.	.	PUNCT
stem-5536	46	1	among	among	ADP
stem-5536	46	2	the	the	DET
stem-5536	46	3	greatest	great	ADJ
stem-5536	46	4	thinkers	thinker	NOUN
stem-5536	46	5	of	of	ADP
stem-5536	46	6	mankind	mankind	NOUN
stem-5536	46	7	who	who	PRON
stem-5536	46	8	contributed	contribute	VERB
stem-5536	46	9	their	their	PRON
stem-5536	46	10	lempta	lempta	NOUN
stem-5536	46	11	to	to	ADP
stem-5536	46	12	the	the	DET
stem-5536	46	13	theory	theory	NOUN
stem-5536	46	14	of	of	ADP
stem-5536	46	15	images	image	NOUN
stem-5536	46	16	and	and	CCONJ
stem-5536	46	17	the	the	DET
stem-5536	46	18	development	development	NOUN
stem-5536	46	19	of	of	ADP
stem-5536	46	20	geometry	geometry	NOUN
stem-5536	46	21	as	as	ADP
stem-5536	46	22	a	a	DET
stem-5536	46	23	science	science	NOUN
stem-5536	46	24	were	be	AUX
stem-5536	46	25	:	:	PUNCT
stem-5536	46	26	leonardo	leonardo	PROPN
stem-5536	46	27	da	da	PROPN
stem-5536	46	28	vinci	vinci	PROPN
stem-5536	46	29	(	(	PUNCT
stem-5536	46	30	1452	1452	NUM
stem-5536	46	31	-	-	SYM
stem-5536	46	32	1519	1519	NUM
stem-5536	46	33	)	)	PUNCT
stem-5536	46	34	,	,	PUNCT
stem-5536	46	35	albrecht	albrecht	PROPN
stem-5536	46	36	durer	durer	PROPN
stem-5536	46	37	(	(	PUNCT
stem-5536	46	38	1471	1471	NUM
stem-5536	46	39	-	-	SYM
stem-5536	46	40	1528	1528	NUM
stem-5536	46	41	)	)	PUNCT
stem-5536	46	42	.	.	PUNCT
stem-5536	47	1	in	in	ADP
stem-5536	47	2	the	the	DET
stem-5536	47	3	history	history	NOUN
stem-5536	47	4	of	of	ADP
stem-5536	47	5	science	science	NOUN
stem-5536	47	6	,	,	PUNCT
stem-5536	47	7	a.	a.	PROPN
stem-5536	47	8	durer	durer	PROPN
stem-5536	47	9	’s	’s	PART
stem-5536	47	10	letter	letter	NOUN
stem-5536	47	11	is	be	AUX
stem-5536	47	12	famous	famous	ADJ
stem-5536	47	13	with	with	ADP
stem-5536	47	14	a	a	DET
stem-5536	47	15	request	request	NOUN
stem-5536	47	16	to	to	ADP
stem-5536	47	17	artists	artist	NOUN
stem-5536	47	18	and	and	CCONJ
stem-5536	47	19	with	with	ADP
stem-5536	47	20	a	a	DET
stem-5536	47	21	question	question	NOUN
stem-5536	47	22	about	about	ADP
stem-5536	47	23	their	their	PRON
stem-5536	47	24	description	description	NOUN
stem-5536	47	25	of	of	ADP
stem-5536	47	26	the	the	DET
stem-5536	47	27	process	process	NOUN
stem-5536	47	28	of	of	ADP
stem-5536	47	29	depicting	depict	VERB
stem-5536	47	30	objects	object	NOUN
stem-5536	47	31	“	"	PUNCT
stem-5536	47	32	i	i	PRON
stem-5536	47	33	ask	ask	VERB
stem-5536	47	34	everyone	everyone	PRON
stem-5536	47	35	who	who	PRON
stem-5536	47	36	has	have	VERB
stem-5536	47	37	knowledge	knowledge	NOUN
stem-5536	47	38	or	or	CCONJ
stem-5536	47	39	knowledge	knowledge	NOUN
stem-5536	47	40	to	to	PART
stem-5536	47	41	make	make	VERB
stem-5536	47	42	them	they	PRON
stem-5536	47	43	public	public	ADJ
stem-5536	47	44	...	...	PUNCT
stem-5536	47	45	”	"	PUNCT
stem-5536	47	46	.	.	PUNCT
stem-5536	48	1	answers	answer	NOUN
stem-5536	48	2	and	and	CCONJ
stem-5536	48	3	reflections	reflection	NOUN
stem-5536	48	4	formed	form	VERB
stem-5536	48	5	the	the	DET
stem-5536	48	6	basis	basis	NOUN
stem-5536	48	7	of	of	ADP
stem-5536	48	8	the	the	DET
stem-5536	48	9	books	book	NOUN
stem-5536	48	10	“	"	PUNCT
stem-5536	48	11	guide	guide	VERB
stem-5536	48	12	to	to	ADP
stem-5536	48	13	measurement	measurement	NOUN
stem-5536	48	14	”	"	PUNCT
stem-5536	48	15	(	(	PUNCT
stem-5536	48	16	about	about	ADP
stem-5536	48	17	construction	construction	NOUN
stem-5536	48	18	with	with	ADP
stem-5536	48	19	the	the	DET
stem-5536	48	20	help	help	NOUN
stem-5536	48	21	of	of	ADP
stem-5536	48	22	a	a	DET
stem-5536	48	23	compass	compass	NOUN
stem-5536	48	24	and	and	CCONJ
stem-5536	48	25	a	a	DET
stem-5536	48	26	ruler	ruler	NOUN
stem-5536	48	27	)	)	PUNCT
stem-5536	48	28	,	,	PUNCT
stem-5536	48	29	and	and	CCONJ
stem-5536	48	30	another	another	DET
stem-5536	48	31	book	book	NOUN
stem-5536	48	32	“	"	PUNCT
stem-5536	48	33	four	four	NUM
stem-5536	48	34	books	book	NOUN
stem-5536	48	35	on	on	ADP
stem-5536	48	36	proportions	proportion	NOUN
stem-5536	48	37	.	.	PUNCT
stem-5536	48	38	”	"	PUNCT
stem-5536	49	1	they	they	PRON
stem-5536	49	2	formulated	formulate	VERB
stem-5536	49	3	the	the	DET
stem-5536	49	4	most	most	ADV
stem-5536	49	5	famous	famous	ADJ
stem-5536	49	6	theorems	theorem	NOUN
stem-5536	49	7	of	of	ADP
stem-5536	49	8	projective	projective	PROPN
stem-5536	49	9	geometry	geometry	PROPN
stem-5536	49	10	a.	a.	PROPN
stem-5536	49	11	durer	durer	PROPN
stem-5536	49	12	’s	’s	PART
stem-5536	49	13	theory	theory	NOUN
stem-5536	49	14	of	of	ADP
stem-5536	49	15	perspective	perspective	NOUN
stem-5536	49	16	“	"	PUNCT
stem-5536	49	17	theory	theory	NOUN
stem-5536	49	18	is	be	AUX
stem-5536	49	19	by	by	ADP
stem-5536	49	20	no	no	DET
stem-5536	49	21	means	means	NOUN
stem-5536	49	22	a	a	DET
stem-5536	49	23	purely	purely	ADV
stem-5536	49	24	technical	technical	ADJ
stem-5536	49	25	discipline	discipline	NOUN
stem-5536	49	26	,	,	PUNCT
stem-5536	49	27	which	which	PRON
stem-5536	49	28	is	be	AUX
stem-5536	49	29	forever	forever	ADV
stem-5536	49	30	assigned	assign	VERB
stem-5536	49	31	a	a	DET
stem-5536	49	32	purely	purely	ADV
stem-5536	49	33	auxiliary	auxiliary	ADJ
stem-5536	49	34	role	role	NOUN
stem-5536	49	35	in	in	ADP
stem-5536	49	36	painting	painting	NOUN
stem-5536	49	37	and	and	CCONJ
stem-5536	49	38	architecture	architecture	NOUN
stem-5536	49	39	,	,	PUNCT
stem-5536	49	40	but	but	CCONJ
stem-5536	49	41	an	an	DET
stem-5536	49	42	important	important	ADJ
stem-5536	49	43	branch	branch	NOUN
stem-5536	49	44	of	of	ADP
stem-5536	49	45	mathematics	mathematic	NOUN
stem-5536	49	46	that	that	PRON
stem-5536	49	47	has	have	AUX
stem-5536	49	48	not	not	PART
stem-5536	49	49	lost	lose	VERB
stem-5536	49	50	the	the	DET
stem-5536	49	51	ability	ability	NOUN
stem-5536	49	52	to	to	PART
stem-5536	49	53	develop	develop	VERB
stem-5536	49	54	.	.	PUNCT
stem-5536	50	1	indeed	indeed	ADV
stem-5536	50	2	,	,	PUNCT
stem-5536	50	3	the	the	DET
stem-5536	50	4	theory	theory	NOUN
stem-5536	50	5	of	of	ADP
stem-5536	50	6	perspective	perspective	NOUN
stem-5536	50	7	eventually	eventually	ADV
stem-5536	50	8	developed	develop	VERB
stem-5536	50	9	into	into	ADP
stem-5536	50	10	projective	projective	ADJ
stem-5536	50	11	geometry	geometry	NOUN
stem-5536	50	12	,	,	PUNCT
stem-5536	50	13	cited	cite	VERB
stem-5536	50	14	in	in	ADP
stem-5536	50	15	[	[	PUNCT
stem-5536	50	16	9	9	NUM
stem-5536	50	17	]	]	PUNCT
stem-5536	50	18	“	"	PUNCT
stem-5536	50	19	further	further	ADJ
stem-5536	50	20	presentation	presentation	NOUN
stem-5536	50	21	of	of	ADP
stem-5536	50	22	the	the	DET
stem-5536	50	23	theory	theory	NOUN
stem-5536	50	24	of	of	ADP
stem-5536	50	25	perspective	perspective	NOUN
stem-5536	50	26	,	,	PUNCT
stem-5536	50	27	an	an	DET
stem-5536	50	28	outstanding	outstanding	ADJ
stem-5536	50	29	artist	artist	NOUN
stem-5536	50	30	of	of	ADP
stem-5536	50	31	the	the	DET
stem-5536	50	32	renaissance	renaissance	NOUN
stem-5536	50	33	,	,	PUNCT
stem-5536	50	34	led	lead	VERB
stem-5536	50	35	him	he	PRON
stem-5536	50	36	to	to	PART
stem-5536	50	37	affine	affine	VERB
stem-5536	50	38	geometry	geometry	NOUN
stem-5536	50	39	,	,	PUNCT
stem-5536	50	40	the	the	DET
stem-5536	50	41	121	121	NUM
stem-5536	50	42	american	american	ADJ
stem-5536	50	43	journal	journal	NOUN
stem-5536	50	44	of	of	ADP
stem-5536	50	45	language	language	NOUN
stem-5536	50	46	,	,	PUNCT
stem-5536	50	47	literacy	literacy	NOUN
stem-5536	50	48	and	and	CCONJ
stem-5536	50	49	learning	learn	VERB
stem-5536	50	50	in	in	ADP
stem-5536	50	51	stem	stem	NOUN
stem-5536	50	52	education	education	NOUN
stem-5536	50	53	www	www	PROPN
stem-5536	50	54	.	.	PUNCT
stem-5536	51	1	grnjournal.us	grnjournal.us	X
stem-5536	51	2	consideration	consideration	NOUN
stem-5536	51	3	of	of	ADP
stem-5536	51	4	the	the	DET
stem-5536	51	5	affine	affine	NOUN
stem-5536	51	6	properties	property	NOUN
stem-5536	51	7	of	of	ADP
stem-5536	51	8	figures	figure	NOUN
stem-5536	51	9	.	.	PUNCT
stem-5536	52	1	he	he	PRON
stem-5536	52	2	much	much	ADV
stem-5536	52	3	earlier	early	ADV
stem-5536	52	4	than	than	SCONJ
stem-5536	52	5	professional	professional	ADJ
stem-5536	52	6	mathematicians	mathematician	NOUN
stem-5536	52	7	approached	approach	VERB
stem-5536	52	8	the	the	DET
stem-5536	52	9	theorem	theorem	NOUN
stem-5536	52	10	,	,	PUNCT
stem-5536	52	11	which	which	PRON
stem-5536	52	12	was	be	AUX
stem-5536	52	13	formulated	formulate	VERB
stem-5536	52	14	by	by	ADP
stem-5536	52	15	girard	girard	PROPN
stem-5536	52	16	desargues	desargue	NOUN
stem-5536	52	17	in	in	ADP
stem-5536	52	18	his	his	PRON
stem-5536	52	19	essay	essay	NOUN
stem-5536	52	20	on	on	ADP
stem-5536	52	21	perspective	perspective	NOUN
stem-5536	52	22	(	(	PUNCT
stem-5536	52	23	1636	1636	NUM
stem-5536	52	24	)	)	PUNCT
stem-5536	52	25	,	,	PUNCT
stem-5536	52	26	who	who	PRON
stem-5536	52	27	also	also	ADV
stem-5536	52	28	gave	give	VERB
stem-5536	52	29	strictly	strictly	ADV
stem-5536	52	30	scientifically	scientifically	ADV
stem-5536	52	31	substantiated	substantiate	VERB
stem-5536	52	32	construction	construction	NOUN
stem-5536	52	33	rules	rule	NOUN
stem-5536	52	34	in	in	ADP
stem-5536	52	35	the	the	DET
stem-5536	52	36	theory	theory	NOUN
stem-5536	52	37	of	of	ADP
stem-5536	52	38	images	image	NOUN
stem-5536	52	39	.	.	PUNCT
stem-5536	53	1	further	far	ADV
stem-5536	53	2	,	,	PUNCT
stem-5536	53	3	we	we	PRON
stem-5536	53	4	note	note	VERB
stem-5536	53	5	that	that	SCONJ
stem-5536	53	6	the	the	DET
stem-5536	53	7	creation	creation	NOUN
stem-5536	53	8	of	of	ADP
stem-5536	53	9	gaspard	gaspard	PROPN
stem-5536	53	10	monge	monge	PROPN
stem-5536	53	11	(	(	PUNCT
stem-5536	53	12	1745	1745	NUM
stem-5536	53	13	1818	1818	NUM
stem-5536	53	14	)	)	PUNCT
stem-5536	53	15	of	of	ADP
stem-5536	53	16	the	the	DET
stem-5536	53	17	method	method	NOUN
stem-5536	53	18	of	of	ADP
stem-5536	53	19	orthogonal	orthogonal	ADJ
stem-5536	53	20	projections	projection	NOUN
stem-5536	53	21	,	,	PUNCT
stem-5536	53	22	which	which	PRON
stem-5536	53	23	,	,	PUNCT
stem-5536	53	24	without	without	ADP
stem-5536	53	25	significant	significant	ADJ
stem-5536	53	26	changes	change	NOUN
stem-5536	53	27	,	,	PUNCT
stem-5536	53	28	is	be	AUX
stem-5536	53	29	widely	widely	ADV
stem-5536	53	30	used	use	VERB
stem-5536	53	31	in	in	ADP
stem-5536	53	32	our	our	PRON
stem-5536	53	33	time	time	NOUN
stem-5536	53	34	.	.	PUNCT
stem-5536	54	1	the	the	DET
stem-5536	54	2	military	military	ADJ
stem-5536	54	3	fortifier	fortifier	NOUN
stem-5536	54	4	engineer	engineer	NOUN
stem-5536	54	5	g.	g.	PROPN
stem-5536	54	6	monge	monge	PROPN
stem-5536	54	7	immersed	immerse	VERB
stem-5536	54	8	,	,	PUNCT
stem-5536	54	9	following	follow	VERB
stem-5536	54	10	r.	r.	PROPN
stem-5536	54	11	descartes	descartes	PROPN
stem-5536	54	12	and	and	CCONJ
stem-5536	54	13	his	his	PRON
stem-5536	54	14	method	method	NOUN
stem-5536	54	15	,	,	PUNCT
stem-5536	54	16	three¬dimensional	three¬dimensional	ADJ
stem-5536	54	17	space	space	NOUN
stem-5536	54	18	into	into	ADP
stem-5536	54	19	two	two	NUM
stem-5536	54	20	-	-	PUNCT
stem-5536	54	21	dimensional	dimensional	ADJ
stem-5536	54	22	using	use	VERB
stem-5536	54	23	projections	projection	NOUN
stem-5536	54	24	.	.	PUNCT
stem-5536	55	1	drawing	draw	VERB
stem-5536	55	2	plays	play	VERB
stem-5536	55	3	an	an	DET
stem-5536	55	4	important	important	ADJ
stem-5536	55	5	role	role	NOUN
stem-5536	55	6	when	when	SCONJ
stem-5536	55	7	studying	study	VERB
stem-5536	55	8	geometry	geometry	NOUN
stem-5536	55	9	in	in	ADP
stem-5536	55	10	a	a	DET
stem-5536	55	11	plane	plane	NOUN
stem-5536	55	12	.	.	PUNCT
stem-5536	56	1	as	as	ADP
stem-5536	56	2	a	a	DET
stem-5536	56	3	rule	rule	NOUN
stem-5536	56	4	,	,	PUNCT
stem-5536	56	5	the	the	DET
stem-5536	56	6	patterns	pattern	NOUN
stem-5536	56	7	present	present	ADJ
stem-5536	56	8	in	in	ADP
stem-5536	56	9	a	a	DET
stem-5536	56	10	beautifully	beautifully	ADV
stem-5536	56	11	drawn	draw	VERB
stem-5536	56	12	picture	picture	NOUN
stem-5536	56	13	are	be	AUX
stem-5536	56	14	preserved	preserve	VERB
stem-5536	56	15	in	in	ADP
stem-5536	56	16	high	high	ADJ
stem-5536	56	17	resolution	resolution	NOUN
stem-5536	56	18	:	:	PUNCT
stem-5536	56	19	the	the	DET
stem-5536	56	20	middle	middle	NOUN
stem-5536	56	21	of	of	ADP
stem-5536	56	22	the	the	DET
stem-5536	56	23	segment	segment	NOUN
stem-5536	56	24	is	be	AUX
stem-5536	56	25	in	in	ADP
stem-5536	56	26	the	the	DET
stem-5536	56	27	middle	middle	NOUN
stem-5536	56	28	,	,	PUNCT
stem-5536	56	29	the	the	DET
stem-5536	56	30	right	right	ADJ
stem-5536	56	31	corner	corner	NOUN
stem-5536	56	32	is	be	AUX
stem-5536	56	33	like	like	ADP
stem-5536	56	34	a	a	DET
stem-5536	56	35	right	right	ADJ
stem-5536	56	36	angle	angle	NOUN
stem-5536	56	37	,	,	PUNCT
stem-5536	56	38	and	and	CCONJ
stem-5536	56	39	so	so	ADV
stem-5536	56	40	on	on	ADV
stem-5536	56	41	.	.	PUNCT
stem-5536	57	1	judging	judge	VERB
stem-5536	57	2	by	by	ADP
stem-5536	57	3	the	the	DET
stem-5536	57	4	correctly	correctly	ADV
stem-5536	57	5	drawn	draw	VERB
stem-5536	57	6	pictures	picture	NOUN
stem-5536	57	7	,	,	PUNCT
stem-5536	57	8	the	the	DET
stem-5536	57	9	presence	presence	NOUN
stem-5536	57	10	of	of	ADP
stem-5536	57	11	certain	certain	ADJ
stem-5536	57	12	patterns	pattern	NOUN
stem-5536	57	13	can	can	AUX
stem-5536	57	14	be	be	AUX
stem-5536	57	15	assumed	assume	VERB
stem-5536	57	16	with	with	ADP
stem-5536	57	17	sufficient	sufficient	ADJ
stem-5536	57	18	confidence	confidence	NOUN
stem-5536	57	19	.	.	PUNCT
stem-5536	58	1	in	in	ADP
stem-5536	58	2	solid	solid	ADJ
stem-5536	58	3	geometry	geometry	NOUN
stem-5536	58	4	,	,	PUNCT
stem-5536	58	5	the	the	DET
stem-5536	58	6	parallel	parallel	ADJ
stem-5536	58	7	design	design	NOUN
stem-5536	58	8	method	method	NOUN
stem-5536	58	9	is	be	AUX
stem-5536	58	10	used	use	VERB
stem-5536	58	11	in	in	ADP
stem-5536	58	12	the	the	DET
stem-5536	58	13	construction	construction	NOUN
stem-5536	58	14	of	of	ADP
stem-5536	58	15	drawings	drawing	NOUN
stem-5536	58	16	.	.	PUNCT
stem-5536	59	1	we	we	PRON
stem-5536	59	2	have	have	AUX
stem-5536	59	3	studied	study	VERB
stem-5536	59	4	this	this	DET
stem-5536	59	5	method	method	NOUN
stem-5536	59	6	and	and	CCONJ
stem-5536	59	7	its	its	PRON
stem-5536	59	8	features	feature	NOUN
stem-5536	59	9	.	.	PUNCT
stem-5536	60	1	while	while	SCONJ
stem-5536	60	2	studying	study	VERB
stem-5536	60	3	the	the	DET
stem-5536	60	4	method	method	NOUN
stem-5536	60	5	of	of	ADP
stem-5536	60	6	concurrent	concurrent	ADJ
stem-5536	60	7	design	design	NOUN
stem-5536	60	8	,	,	PUNCT
stem-5536	60	9	we	we	PRON
stem-5536	60	10	came	come	VERB
stem-5536	60	11	across	across	ADP
stem-5536	60	12	an	an	DET
stem-5536	60	13	amazing	amazing	ADJ
stem-5536	60	14	way	way	NOUN
stem-5536	60	15	to	to	PART
stem-5536	60	16	solve	solve	VERB
stem-5536	60	17	a	a	DET
stem-5536	60	18	problem	problem	NOUN
stem-5536	60	19	.	.	PUNCT
stem-5536	61	1	it	it	PRON
stem-5536	61	2	turns	turn	VERB
stem-5536	61	3	out	out	ADP
stem-5536	61	4	that	that	SCONJ
stem-5536	61	5	any	any	DET
stem-5536	61	6	triangle	triangle	NOUN
stem-5536	61	7	can	can	AUX
stem-5536	61	8	be	be	AUX
stem-5536	61	9	designed	design	VERB
stem-5536	61	10	in	in	ADP
stem-5536	61	11	such	such	DET
stem-5536	61	12	a	a	DET
stem-5536	61	13	way	way	NOUN
stem-5536	61	14	that	that	PRON
stem-5536	61	15	it	it	PRON
stem-5536	61	16	becomes	become	VERB
stem-5536	61	17	equilateral	equilateral	ADJ
stem-5536	61	18	,	,	PUNCT
stem-5536	61	19	while	while	SCONJ
stem-5536	61	20	maintaining	maintain	VERB
stem-5536	61	21	the	the	DET
stem-5536	61	22	ratio	ratio	NOUN
stem-5536	61	23	and	and	CCONJ
stem-5536	61	24	parallelism	parallelism	NOUN
stem-5536	61	25	of	of	ADP
stem-5536	61	26	the	the	DET
stem-5536	61	27	segments	segment	NOUN
stem-5536	61	28	,	,	PUNCT
stem-5536	61	29	which	which	PRON
stem-5536	61	30	will	will	AUX
stem-5536	61	31	greatly	greatly	ADV
stem-5536	61	32	simplify	simplify	VERB
stem-5536	61	33	the	the	DET
stem-5536	61	34	solution	solution	NOUN
stem-5536	61	35	of	of	ADP
stem-5536	61	36	the	the	DET
stem-5536	61	37	problem	problem	NOUN
stem-5536	61	38	.	.	PUNCT
stem-5536	62	1	however	however	ADV
stem-5536	62	2	,	,	PUNCT
stem-5536	62	3	the	the	DET
stem-5536	62	4	images	image	NOUN
stem-5536	62	5	of	of	ADP
stem-5536	62	6	spatial	spatial	ADJ
stem-5536	62	7	figures	figure	NOUN
stem-5536	62	8	in	in	ADP
stem-5536	62	9	an	an	DET
stem-5536	62	10	airplane	airplane	NOUN
stem-5536	62	11	are	be	AUX
stem-5536	62	12	built	build	VERB
stem-5536	62	13	according	accord	VERB
stem-5536	62	14	to	to	ADP
stem-5536	62	15	certain	certain	ADJ
stem-5536	62	16	rules	rule	NOUN
stem-5536	62	17	,	,	PUNCT
stem-5536	62	18	and	and	CCONJ
stem-5536	62	19	in	in	ADP
stem-5536	62	20	a	a	DET
stem-5536	62	21	school	school	NOUN
stem-5536	62	22	geometry	geometry	NOUN
stem-5536	62	23	course	course	NOUN
stem-5536	62	24	they	they	PRON
stem-5536	62	25	are	be	AUX
stem-5536	62	26	usually	usually	ADV
stem-5536	62	27	done	do	VERB
stem-5536	62	28	using	use	VERB
stem-5536	62	29	the	the	DET
stem-5536	62	30	parallel	parallel	ADJ
stem-5536	62	31	design	design	NOUN
stem-5536	62	32	method	method	NOUN
stem-5536	62	33	,	,	PUNCT
stem-5536	62	34	the	the	DET
stem-5536	62	35	essence	essence	NOUN
stem-5536	62	36	of	of	ADP
stem-5536	62	37	which	which	PRON
stem-5536	62	38	is	be	AUX
stem-5536	62	39	as	as	SCONJ
stem-5536	62	40	follows	follow	VERB
stem-5536	62	41	.	.	PUNCT
stem-5536	63	1	let	let	VERB
stem-5536	63	2	’s	’s	NOUN
stem-5536	63	3	give	give	VERB
stem-5536	63	4	an	an	DET
stem-5536	63	5	example	example	NOUN
stem-5536	63	6	:	:	PUNCT
stem-5536	63	7	an	an	DET
stem-5536	63	8	arbitrary	arbitrary	ADJ
stem-5536	63	9	plane	plane	NOUN
stem-5536	63	10	is	be	AUX
stem-5536	63	11	selected	select	VERB
stem-5536	63	12	in	in	ADP
stem-5536	63	13	space	space	NOUN
stem-5536	63	14	,	,	PUNCT
stem-5536	63	15	which	which	PRON
stem-5536	63	16	is	be	AUX
stem-5536	63	17	called	call	VERB
stem-5536	63	18	the	the	DET
stem-5536	63	19	projection	projection	NOUN
stem-5536	63	20	plane	plane	NOUN
stem-5536	63	21	or	or	CCONJ
stem-5536	63	22	the	the	DET
stem-5536	63	23	image	image	NOUN
stem-5536	63	24	plane	plane	NOUN
stem-5536	63	25	,	,	PUNCT
stem-5536	63	26	and	and	CCONJ
stem-5536	64	1	the	the	DET
stem-5536	64	2	straight	straight	ADJ
stem-5536	64	3	line	line	NOUN
stem-5536	64	4	l	l	NOUN
stem-5536	64	5	intersecting	intersect	VERB
stem-5536	64	6	this	this	DET
stem-5536	64	7	plane	plane	NOUN
stem-5536	64	8	(	(	PUNCT
stem-5536	64	9	fig	fig	NOUN
stem-5536	64	10	.	.	PUNCT
stem-5536	64	11	1	1	NUM
stem-5536	64	12	,	,	PUNCT
stem-5536	64	13	a	a	PRON
stem-5536	64	14	)	)	PUNCT
stem-5536	64	15	.	.	PUNCT
stem-5536	65	1	let	let	VERB
stem-5536	65	2	m	m	PRON
stem-5536	65	3	'	'	PUNCT
stem-5536	65	4	be	be	AUX
stem-5536	65	5	an	an	DET
stem-5536	65	6	arbitrary	arbitrary	ADJ
stem-5536	65	7	point	point	NOUN
stem-5536	65	8	of	of	ADP
stem-5536	65	9	the	the	DET
stem-5536	65	10	space	space	NOUN
stem-5536	65	11	.	.	PUNCT
stem-5536	66	1	through	through	ADP
stem-5536	66	2	this	this	DET
stem-5536	66	3	point	point	NOUN
stem-5536	66	4	we	we	PRON
stem-5536	66	5	draw	draw	VERB
stem-5536	66	6	a	a	DET
stem-5536	66	7	line	line	NOUN
stem-5536	66	8	p	p	NOUN
stem-5536	66	9	parallel	parallel	NOUN
stem-5536	66	10	to	to	ADP
stem-5536	66	11	l.	l.	NOUN
stem-5536	66	12	the	the	DET
stem-5536	66	13	point	point	NOUN
stem-5536	66	14	m	m	NOUN
stem-5536	66	15	of	of	ADP
stem-5536	66	16	intersection	intersection	NOUN
stem-5536	66	17	of	of	ADP
stem-5536	66	18	the	the	DET
stem-5536	66	19	straight	straight	ADJ
stem-5536	66	20	line	line	NOUN
stem-5536	66	21	p	p	NOUN
stem-5536	66	22	with	with	ADP
stem-5536	66	23	the	the	DET
stem-5536	66	24	plane	plane	NOUN
stem-5536	66	25	n	n	NOUN
stem-5536	66	26	is	be	AUX
stem-5536	66	27	called	call	VERB
stem-5536	66	28	the	the	DET
stem-5536	66	29	parallel	parallel	ADJ
stem-5536	66	30	projection	projection	NOUN
stem-5536	66	31	of	of	ADP
stem-5536	66	32	the	the	DET
stem-5536	66	33	point	point	NOUN
stem-5536	66	34	m	m	NOUN
stem-5536	66	35	'	'	PUNCT
stem-5536	66	36	onto	onto	ADP
stem-5536	66	37	the	the	DET
stem-5536	66	38	plane	plane	NOUN
stem-5536	66	39	n	n	NOUN
stem-5536	66	40	in	in	ADP
stem-5536	66	41	the	the	DET
stem-5536	66	42	direction	direction	NOUN
stem-5536	66	43	of	of	ADP
stem-5536	66	44	the	the	DET
stem-5536	66	45	straight	straight	ADJ
stem-5536	66	46	line	line	NOUN
stem-5536	66	47	l.	l.	PROPN
stem-5536	67	1	if	if	SCONJ
stem-5536	67	2	m	m	NOUN
stem-5536	67	3	'	'	PUNCT
stem-5536	67	4	is	be	AUX
stem-5536	67	5	a	a	DET
stem-5536	67	6	point	point	NOUN
stem-5536	67	7	in	in	ADP
stem-5536	67	8	the	the	DET
stem-5536	67	9	plane	plane	NOUN
stem-5536	67	10	n	n	CCONJ
stem-5536	67	11	,	,	PUNCT
stem-5536	67	12	then	then	ADV
stem-5536	67	13	m	m	VERB
stem-5536	67	14	coincides	coincide	VERB
stem-5536	67	15	with	with	ADP
stem-5536	67	16	m	m	NOUN
stem-5536	67	17	'	'	PART
stem-5536	67	18	.	.	PUNCT
stem-5536	68	1	fig	fig	NOUN
stem-5536	68	2	.	.	PUNCT
stem-5536	69	1	1	1	NUM
stem-5536	69	2	line	line	NOUN
stem-5536	69	3	l	l	NOUN
stem-5536	69	4	and	and	CCONJ
stem-5536	69	5	all	all	DET
stem-5536	69	6	straight	straight	ADJ
stem-5536	69	7	spaces	space	NOUN
stem-5536	69	8	parallel	parallel	ADJ
stem-5536	69	9	to	to	ADP
stem-5536	69	10	it	it	PRON
stem-5536	69	11	are	be	AUX
stem-5536	69	12	called	call	VERB
stem-5536	69	13	projecting	project	VERB
stem-5536	69	14	lines	line	NOUN
stem-5536	69	15	;	;	PUNCT
stem-5536	69	16	they	they	PRON
stem-5536	69	17	determine	determine	VERB
stem-5536	69	18	the	the	DET
stem-5536	69	19	direction	direction	NOUN
stem-5536	69	20	of	of	ADP
stem-5536	69	21	the	the	DET
stem-5536	69	22	design	design	NOUN
stem-5536	69	23	.	.	PUNCT
stem-5536	70	1	any	any	DET
stem-5536	70	2	plane	plane	NOUN
stem-5536	70	3	of	of	ADP
stem-5536	70	4	space	space	NOUN
stem-5536	70	5	parallel	parallel	NOUN
stem-5536	70	6	to	to	ADP
stem-5536	70	7	the	the	DET
stem-5536	70	8	projecting	projecting	NOUN
stem-5536	70	9	line	line	NOUN
stem-5536	70	10	is	be	AUX
stem-5536	70	11	called	call	VERB
stem-5536	70	12	the	the	DET
stem-5536	70	13	projecting	project	VERB
stem-5536	70	14	plane	plane	NOUN
stem-5536	70	15	.	.	PUNCT
stem-5536	71	1	the	the	DET
stem-5536	71	2	figure	figure	NOUN
stem-5536	71	3	that	that	PRON
stem-5536	71	4	is	be	AUX
stem-5536	71	5	designed	design	VERB
stem-5536	71	6	or	or	CCONJ
stem-5536	71	7	depicted	depict	VERB
stem-5536	71	8	is	be	AUX
stem-5536	71	9	called	call	VERB
stem-5536	71	10	the	the	DET
stem-5536	71	11	original	original	NOUN
stem-5536	71	12	.	.	PUNCT
stem-5536	72	1	to	to	PART
stem-5536	72	2	build	build	VERB
stem-5536	72	3	a	a	DET
stem-5536	72	4	projection	projection	NOUN
stem-5536	72	5	of	of	ADP
stem-5536	72	6	a	a	DET
stem-5536	72	7	figure	figure	NOUN
stem-5536	72	8	,	,	PUNCT
stem-5536	72	9	it	it	PRON
stem-5536	72	10	is	be	AUX
stem-5536	72	11	enough	enough	ADJ
stem-5536	72	12	to	to	PART
stem-5536	72	13	build	build	VERB
stem-5536	72	14	projections	projection	NOUN
stem-5536	72	15	of	of	ADP
stem-5536	72	16	all	all	DET
stem-5536	72	17	points	point	NOUN
stem-5536	72	18	of	of	ADP
stem-5536	72	19	this	this	DET
stem-5536	72	20	figure	figure	NOUN
stem-5536	72	21	or	or	CCONJ
stem-5536	72	22	projections	projection	NOUN
stem-5536	72	23	of	of	ADP
stem-5536	72	24	points	point	NOUN
stem-5536	72	25	of	of	ADP
stem-5536	72	26	the	the	DET
stem-5536	72	27	figure	figure	NOUN
stem-5536	72	28	that	that	PRON
stem-5536	72	29	define	define	VERB
stem-5536	72	30	it	it	PRON
stem-5536	72	31	.	.	PUNCT
stem-5536	73	1	in	in	ADP
stem-5536	73	2	figure	figure	NOUN
stem-5536	73	3	1	1	NUM
stem-5536	73	4	,	,	PUNCT
stem-5536	73	5	b	b	NOUN
stem-5536	73	6	,	,	PUNCT
stem-5536	73	7	triangle	triangle	NOUN
stem-5536	73	8	abc	abc	PROPN
stem-5536	73	9	is	be	AUX
stem-5536	73	10	a	a	DET
stem-5536	73	11	parallel	parallel	ADJ
stem-5536	73	12	projection	projection	NOUN
stem-5536	73	13	of	of	ADP
stem-5536	73	14	triangle	triangle	NOUN
stem-5536	73	15	abc	abc	PROPN
stem-5536	73	16	onto	onto	ADP
stem-5536	73	17	the	the	DET
stem-5536	73	18	plane	plane	NOUN
stem-5536	73	19	n	n	NOUN
stem-5536	73	20	in	in	ADP
stem-5536	73	21	the	the	DET
stem-5536	73	22	direction	direction	NOUN
stem-5536	73	23	of	of	ADP
stem-5536	73	24	the	the	DET
stem-5536	73	25	straight	straight	ADJ
stem-5536	73	26	line	line	NOUN
stem-5536	73	27	l.	l.	PROPN
stem-5536	73	28	comment	comment	PROPN
stem-5536	73	29	,	,	PUNCT
stem-5536	73	30	along	along	ADP
stem-5536	73	31	with	with	ADP
stem-5536	73	32	parallel	parallel	ADJ
stem-5536	73	33	design	design	NOUN
stem-5536	73	34	,	,	PUNCT
stem-5536	73	35	the	the	DET
stem-5536	73	36	central	central	ADJ
stem-5536	73	37	design	design	NOUN
stem-5536	73	38	of	of	ADP
stem-5536	73	39	figures	figure	NOUN
stem-5536	73	40	on	on	ADP
stem-5536	73	41	a	a	DET
stem-5536	73	42	plane	plane	NOUN
stem-5536	73	43	is	be	AUX
stem-5536	73	44	also	also	ADV
stem-5536	73	45	considered	consider	VERB
stem-5536	73	46	.	.	PUNCT
stem-5536	74	1	in	in	ADP
stem-5536	74	2	this	this	DET
stem-5536	74	3	case	case	NOUN
stem-5536	74	4	,	,	PUNCT
stem-5536	74	5	the	the	DET
stem-5536	74	6	projecting	project	VERB
stem-5536	74	7	straight	straight	ADJ
stem-5536	74	8	lines	line	NOUN
stem-5536	74	9	pass	pass	VERB
stem-5536	74	10	through	through	ADP
stem-5536	74	11	one	one	NUM
stem-5536	74	12	point	point	NOUN
stem-5536	74	13	—	—	PUNCT
stem-5536	74	14	the	the	DET
stem-5536	74	15	projection	projection	NOUN
stem-5536	74	16	center	center	NOUN
stem-5536	74	17	,	,	PUNCT
stem-5536	74	18	arbitrarily	arbitrarily	ADV
stem-5536	74	19	chosen	choose	VERB
stem-5536	74	20	outside	outside	ADP
stem-5536	74	21	the	the	DET
stem-5536	74	22	projection	projection	NOUN
stem-5536	74	23	plane	plane	NOUN
stem-5536	74	24	(	(	PUNCT
stem-5536	74	25	fig	fig	NOUN
stem-5536	74	26	.	.	PUNCT
stem-5536	75	1	1	1	NUM
stem-5536	75	2	,	,	PUNCT
stem-5536	75	3	c	c	NOUN
stem-5536	75	4	)	)	PUNCT
stem-5536	75	5	.	.	PUNCT
stem-5536	76	1	parallel	parallel	ADJ
stem-5536	76	2	and	and	CCONJ
stem-5536	76	3	central	central	ADJ
stem-5536	76	4	projection	projection	NOUN
stem-5536	76	5	can	can	AUX
stem-5536	76	6	be	be	AUX
stem-5536	76	7	observed	observe	VERB
stem-5536	76	8	in	in	ADP
stem-5536	76	9	real	real	ADJ
stem-5536	76	10	space	space	NOUN
stem-5536	76	11	:	:	PUNCT
stem-5536	76	12	the	the	DET
stem-5536	76	13	shadow	shadow	NOUN
stem-5536	76	14	that	that	SCONJ
stem-5536	76	15	an	an	DET
stem-5536	76	16	object	object	NOUN
stem-5536	76	17	casts	cast	VERB
stem-5536	76	18	on	on	ADP
stem-5536	76	19	a	a	DET
stem-5536	76	20	122	122	NUM
stem-5536	76	21	american	american	ADJ
stem-5536	76	22	journal	journal	NOUN
stem-5536	76	23	of	of	ADP
stem-5536	76	24	language	language	NOUN
stem-5536	76	25	,	,	PUNCT
stem-5536	76	26	literacy	literacy	NOUN
stem-5536	76	27	and	and	CCONJ
stem-5536	76	28	learning	learn	VERB
stem-5536	76	29	in	in	ADP
stem-5536	76	30	stem	stem	NOUN
stem-5536	76	31	education	education	NOUN
stem-5536	76	32	www	www	PROPN
stem-5536	76	33	.	.	PUNCT
stem-5536	77	1	grnjournal.us	grnjournal.us	X
stem-5536	77	2	sunny	sunny	ADJ
stem-5536	77	3	day	day	NOUN
stem-5536	77	4	is	be	AUX
stem-5536	77	5	a	a	DET
stem-5536	77	6	parallel	parallel	ADJ
stem-5536	77	7	projection	projection	NOUN
stem-5536	77	8	of	of	ADP
stem-5536	77	9	this	this	DET
stem-5536	77	10	object	object	NOUN
stem-5536	77	11	,	,	PUNCT
stem-5536	77	12	since	since	SCONJ
stem-5536	77	13	the	the	DET
stem-5536	77	14	sun	sun	NOUN
stem-5536	77	15	's	's	PART
stem-5536	77	16	rays	ray	NOUN
stem-5536	77	17	can	can	AUX
stem-5536	77	18	be	be	AUX
stem-5536	77	19	considered	consider	VERB
stem-5536	77	20	approximately	approximately	ADV
stem-5536	77	21	parallel	parallel	ADJ
stem-5536	77	22	due	due	ADP
stem-5536	77	23	to	to	ADP
stem-5536	77	24	the	the	DET
stem-5536	77	25	large	large	ADJ
stem-5536	77	26	distance	distance	NOUN
stem-5536	77	27	of	of	ADP
stem-5536	77	28	the	the	DET
stem-5536	77	29	sun	sun	NOUN
stem-5536	77	30	from	from	ADP
stem-5536	77	31	the	the	DET
stem-5536	77	32	earth	earth	NOUN
stem-5536	77	33	.	.	PUNCT
stem-5536	78	1	and	and	CCONJ
stem-5536	78	2	the	the	DET
stem-5536	78	3	image	image	NOUN
stem-5536	78	4	on	on	ADP
stem-5536	78	5	the	the	DET
stem-5536	78	6	cinema	cinema	NOUN
stem-5536	78	7	screen	screen	NOUN
stem-5536	78	8	of	of	ADP
stem-5536	78	9	the	the	DET
stem-5536	78	10	figure	figure	NOUN
stem-5536	78	11	filmed	film	VERB
stem-5536	78	12	on	on	ADP
stem-5536	78	13	film	film	NOUN
stem-5536	78	14	is	be	AUX
stem-5536	78	15	the	the	DET
stem-5536	78	16	central	central	ADJ
stem-5536	78	17	projection	projection	NOUN
stem-5536	78	18	of	of	ADP
stem-5536	78	19	this	this	DET
stem-5536	78	20	figure	figure	NOUN
stem-5536	78	21	.	.	PUNCT
stem-5536	79	1	for	for	ADP
stem-5536	79	2	the	the	DET
stem-5536	79	3	theory	theory	NOUN
stem-5536	79	4	of	of	ADP
stem-5536	79	5	constructing	construct	VERB
stem-5536	79	6	images	image	NOUN
stem-5536	79	7	of	of	ADP
stem-5536	79	8	spatial	spatial	ADJ
stem-5536	79	9	figures	figure	NOUN
stem-5536	79	10	on	on	ADP
stem-5536	79	11	a	a	DET
stem-5536	79	12	plane	plane	NOUN
stem-5536	79	13	,	,	PUNCT
stem-5536	79	14	an	an	DET
stem-5536	79	15	equally	equally	ADV
stem-5536	79	16	important	important	ADJ
stem-5536	79	17	conclusion	conclusion	NOUN
stem-5536	79	18	follows	follow	VERB
stem-5536	79	19	:	:	PUNCT
stem-5536	79	20	if	if	SCONJ
stem-5536	79	21	the	the	DET
stem-5536	79	22	segment	segment	NOUN
stem-5536	79	23	a'c	a'c	PROPN
stem-5536	79	24	'	'	PUNCT
stem-5536	79	25	is	be	AUX
stem-5536	79	26	projected	project	VERB
stem-5536	79	27	in	in	ADP
stem-5536	79	28	parallel	parallel	NOUN
stem-5536	79	29	onto	onto	ADP
stem-5536	79	30	the	the	DET
stem-5536	79	31	segment	segment	NOUN
stem-5536	79	32	ac	ac	PROPN
stem-5536	79	33	and	and	CCONJ
stem-5536	79	34	the	the	DET
stem-5536	79	35	point	point	NOUN
stem-5536	79	36	b	b	NOUN
stem-5536	79	37	'	'	PUNCT
stem-5536	79	38	divides	divide	VERB
stem-5536	79	39	the	the	DET
stem-5536	79	40	segment	segment	NOUN
stem-5536	79	41	a'c	a'c	ADJ
stem-5536	79	42	with	with	ADP
stem-5536	79	43	respect	respect	NOUN
stem-5536	79	44	to	to	ADP
stem-5536	79	45	a'b'b'c	a'b'b'c	PROPN
stem-5536	79	46	=	=	SYM
stem-5536	79	47	m	m	PROPN
stem-5536	79	48	:	:	PUNCT
stem-5536	79	49	n	n	CCONJ
stem-5536	79	50	,	,	PUNCT
stem-5536	79	51	then	then	ADV
stem-5536	79	52	the	the	DET
stem-5536	79	53	point	point	NOUN
stem-5536	79	54	b	b	NOUN
stem-5536	79	55	—	—	PUNCT
stem-5536	79	56	the	the	DET
stem-5536	79	57	projection	projection	NOUN
stem-5536	79	58	of	of	ADP
stem-5536	79	59	the	the	DET
stem-5536	79	60	point	point	NOUN
stem-5536	79	61	b	b	NOUN
stem-5536	79	62	'	'	PUNCT
stem-5536	79	63	—	—	PUNCT
stem-5536	79	64	divides	divide	VERB
stem-5536	79	65	the	the	DET
stem-5536	79	66	segment	segment	NOUN
stem-5536	79	67	ac	ac	VERB
stem-5536	79	68	in	in	ADP
stem-5536	79	69	that	that	SCONJ
stem-5536	79	70	the	the	DET
stem-5536	79	71	same	same	ADJ
stem-5536	79	72	ratio	ratio	NOUN
stem-5536	79	73	m	m	PROPN
stem-5536	79	74	:	:	PUNCT
stem-5536	79	75	n	n	CCONJ
stem-5536	79	76	,	,	PUNCT
stem-5536	79	77	i.e.	i.e.	X
stem-5536	79	78	ab	ab	X
stem-5536	79	79	:	:	PUNCT
stem-5536	79	80	bc	bc	PROPN
stem-5536	79	81	=	=	PROPN
stem-5536	79	82	a'b	a'b	PROPN
stem-5536	79	83	'	'	PUNCT
stem-5536	79	84	:	:	PUNCT
stem-5536	79	85	bc	bc	PROPN
stem-5536	79	86	=	=	PROPN
stem-5536	79	87	m	m	PROPN
stem-5536	79	88	:	:	PUNCT
stem-5536	79	89	n.	n.	ADJ
stem-5536	79	90	in	in	ADP
stem-5536	79	91	particular	particular	ADJ
stem-5536	79	92	,	,	PUNCT
stem-5536	79	93	the	the	DET
stem-5536	79	94	midpoint	midpoint	NOUN
stem-5536	79	95	of	of	ADP
stem-5536	79	96	the	the	DET
stem-5536	79	97	segment	segment	NOUN
stem-5536	79	98	a'c	a'c	PROPN
stem-5536	79	99	'	'	PUNCT
stem-5536	79	100	is	be	AUX
stem-5536	79	101	projected	project	VERB
stem-5536	79	102	in	in	ADP
stem-5536	79	103	parallel	parallel	NOUN
stem-5536	79	104	to	to	ADP
stem-5536	79	105	the	the	DET
stem-5536	79	106	midpoint	midpoint	NOUN
stem-5536	79	107	of	of	ADP
stem-5536	79	108	the	the	DET
stem-5536	79	109	segment	segment	NOUN
stem-5536	79	110	ac	ac	PROPN
stem-5536	79	111	(	(	PUNCT
stem-5536	79	112	m	m	NOUN
stem-5536	79	113	:	:	PUNCT
stem-5536	79	114	n	n	PROPN
stem-5536	79	115	=	=	SYM
stem-5536	79	116	1:1	1:1	NUM
stem-5536	79	117	)	)	PUNCT
stem-5536	79	118	(	(	PUNCT
stem-5536	79	119	fig	fig	NOUN
stem-5536	79	120	.	.	PUNCT
stem-5536	80	1	2	2	NUM
stem-5536	80	2	)	)	PUNCT
stem-5536	80	3	.	.	PUNCT
stem-5536	81	1	fig	fig	NOUN
stem-5536	81	2	.	.	PUNCT
stem-5536	82	1	2	2	NUM
stem-5536	82	2	let	let	VERB
stem-5536	82	3	m	m	PRON
stem-5536	82	4	be	be	AUX
stem-5536	82	5	an	an	DET
stem-5536	82	6	interior	interior	ADJ
stem-5536	82	7	point	point	NOUN
stem-5536	82	8	of	of	ADP
stem-5536	82	9	the	the	DET
stem-5536	82	10	segment	segment	NOUN
stem-5536	82	11	ab	ab	PROPN
stem-5536	82	12	.	.	PUNCT
stem-5536	83	1	definition	definition	NOUN
stem-5536	83	2	:	:	PUNCT
stem-5536	83	3	the	the	DET
stem-5536	83	4	number	number	NOUN
stem-5536	83	5	𝛌	𝛌	PROPN
stem-5536	83	6	,	,	PUNCT
stem-5536	83	7	equal	equal	ADJ
stem-5536	83	8	to	to	ADP
stem-5536	83	9	the	the	DET
stem-5536	83	10	ratio	ratio	NOUN
stem-5536	83	11	of	of	ADP
stem-5536	83	12	the	the	DET
stem-5536	83	13	lengths	length	NOUN
stem-5536	83	14	of	of	ADP
stem-5536	83	15	the	the	DET
stem-5536	83	16	segments	segment	NOUN
stem-5536	83	17	am	be	AUX
stem-5536	83	18	and	and	CCONJ
stem-5536	83	19	mb	mb	ADP
stem-5536	83	20	,	,	PUNCT
stem-5536	83	21	into	into	ADP
stem-5536	83	22	which	which	PRON
stem-5536	83	23	the	the	DET
stem-5536	83	24	point	point	NOUN
stem-5536	83	25	m	m	VERB
stem-5536	83	26	divides	divide	VERB
stem-5536	83	27	the	the	DET
stem-5536	83	28	segment	segment	NOUN
stem-5536	83	29	ab	ab	PROPN
stem-5536	83	30	,	,	PUNCT
stem-5536	83	31	is	be	AUX
stem-5536	83	32	called	call	VERB
stem-5536	83	33	the	the	DET
stem-5536	83	34	simple	simple	ADJ
stem-5536	83	35	ratio	ratio	NOUN
stem-5536	83	36	of	of	ADP
stem-5536	83	37	three	three	NUM
stem-5536	83	38	points	point	NOUN
stem-5536	83	39	a	a	DET
stem-5536	83	40	,	,	PUNCT
stem-5536	83	41	b	b	NOUN
stem-5536	83	42	and	and	CCONJ
stem-5536	83	43	m	m	AUX
stem-5536	83	44	lying	lie	VERB
stem-5536	83	45	on	on	ADP
stem-5536	83	46	one	one	NUM
stem-5536	83	47	straight	straight	ADJ
stem-5536	83	48	line	line	NOUN
stem-5536	83	49	,	,	PUNCT
stem-5536	83	50	and	and	CCONJ
stem-5536	83	51	is	be	AUX
stem-5536	83	52	denoted	denote	VERB
stem-5536	83	53	by	by	ADP
stem-5536	83	54	(	(	PUNCT
stem-5536	83	55	ab	ab	PROPN
stem-5536	83	56	;	;	PUNCT
stem-5536	83	57	m	m	PROPN
stem-5536	83	58	)	)	PUNCT
stem-5536	83	59	,	,	PUNCT
stem-5536	83	60	that	that	ADV
stem-5536	83	61	is	is	ADV
stem-5536	83	62	,	,	PUNCT
stem-5536	83	63	(	(	PUNCT
stem-5536	83	64	ab	ab	X
stem-5536	83	65	;	;	PUNCT
stem-5536	83	66	m	m	NOUN
stem-5536	83	67	)	)	PUNCT
stem-5536	84	1	=	=	SYM
stem-5536	84	2	𝛌	𝛌	PROPN
stem-5536	84	3	=	=	PUNCT
stem-5536	84	4	am	be	AUX
stem-5536	84	5	:	:	PUNCT
stem-5536	84	6	mb	mb	ADJ
stem-5536	84	7	fig	fig	NOUN
stem-5536	84	8	.	.	PUNCT
stem-5536	85	1	3	3	NUM
stem-5536	85	2	in	in	ADP
stem-5536	85	3	this	this	DET
stem-5536	85	4	case	case	NOUN
stem-5536	85	5	,	,	PUNCT
stem-5536	85	6	points	point	VERB
stem-5536	85	7	a	a	PRON
stem-5536	85	8	and	and	CCONJ
stem-5536	85	9	b	b	NOUN
stem-5536	85	10	are	be	AUX
stem-5536	85	11	called	call	VERB
stem-5536	85	12	basic	basic	ADJ
stem-5536	85	13	,	,	PUNCT
stem-5536	85	14	and	and	CCONJ
stem-5536	85	15	point	point	NOUN
stem-5536	85	16	m	m	VERB
stem-5536	85	17	is	be	AUX
stem-5536	85	18	called	call	VERB
stem-5536	85	19	a	a	DET
stem-5536	85	20	dividing	dividing	NOUN
stem-5536	85	21	point	point	NOUN
stem-5536	85	22	.	.	PUNCT
stem-5536	86	1	the	the	DET
stem-5536	86	2	ordering	ordering	NOUN
stem-5536	86	3	of	of	ADP
stem-5536	86	4	the	the	DET
stem-5536	86	5	points	point	NOUN
stem-5536	86	6	of	of	ADP
stem-5536	86	7	a	a	DET
stem-5536	86	8	simple	simple	ADJ
stem-5536	86	9	relation	relation	NOUN
stem-5536	86	10	is	be	AUX
stem-5536	86	11	necessary	necessary	ADJ
stem-5536	86	12	.	.	PUNCT
stem-5536	87	1	for	for	ADP
stem-5536	87	2	example	example	NOUN
stem-5536	87	3	,	,	PUNCT
stem-5536	87	4	if	if	SCONJ
stem-5536	87	5	aa1	aa1	PROPN
stem-5536	87	6	is	be	AUX
stem-5536	87	7	the	the	DET
stem-5536	87	8	median	median	NOUN
stem-5536	87	9	of	of	ADP
stem-5536	87	10	triangle	triangle	PROPN
stem-5536	87	11	abc	abc	PROPN
stem-5536	87	12	,	,	PUNCT
stem-5536	87	13	m	m	VERB
stem-5536	87	14	is	be	AUX
stem-5536	87	15	its	its	PRON
stem-5536	87	16	centroid	centroid	NOUN
stem-5536	87	17	(	(	PUNCT
stem-5536	87	18	the	the	DET
stem-5536	87	19	point	point	NOUN
stem-5536	87	20	of	of	ADP
stem-5536	87	21	intersection	intersection	NOUN
stem-5536	87	22	of	of	ADP
stem-5536	87	23	the	the	DET
stem-5536	87	24	medians	median	NOUN
stem-5536	87	25	of	of	ADP
stem-5536	87	26	the	the	DET
stem-5536	87	27	triangle	triangle	NOUN
stem-5536	87	28	)	)	PUNCT
stem-5536	87	29	,	,	PUNCT
stem-5536	87	30	then	then	ADV
stem-5536	87	31	(	(	PUNCT
stem-5536	87	32	aa1m)=am	aa1m)=am	NUM
stem-5536	87	33	:	:	PUNCT
stem-5536	87	34	ma1=2:1	ma1=2:1	PROPN
stem-5536	87	35	,	,	PUNCT
stem-5536	87	36	but	but	CCONJ
stem-5536	87	37	(	(	PUNCT
stem-5536	87	38	a1am)=a1m	a1am)=a1m	PROPN
stem-5536	87	39	:	:	PUNCT
stem-5536	87	40	ma=1:2	ma=1:2	X
stem-5536	87	41	(	(	PUNCT
stem-5536	87	42	fig.3	fig.3	PROPN
stem-5536	87	43	)	)	PUNCT
stem-5536	87	44	.	.	PUNCT
stem-5536	88	1	therefore	therefore	ADV
stem-5536	88	2	,	,	PUNCT
stem-5536	88	3	if	if	SCONJ
stem-5536	88	4	am≠ma1	am≠ma1	NUM
stem-5536	88	5	,	,	PUNCT
stem-5536	88	6	then	then	ADV
stem-5536	88	7	(	(	PUNCT
stem-5536	88	8	aa1;m)≠(a1	aa1;m)≠(a1	PROPN
stem-5536	88	9	a;m	a;m	NUM
stem-5536	88	10	)	)	PUNCT
stem-5536	88	11	.	.	PUNCT
stem-5536	89	1	considering	consider	VERB
stem-5536	89	2	the	the	DET
stem-5536	89	3	property	property	NOUN
stem-5536	89	4	of	of	ADP
stem-5536	89	5	parallel	parallel	ADJ
stem-5536	89	6	design	design	NOUN
stem-5536	89	7	,	,	PUNCT
stem-5536	89	8	we	we	PRON
stem-5536	89	9	can	can	AUX
stem-5536	89	10	conclude	conclude	VERB
stem-5536	89	11	:	:	PUNCT
stem-5536	89	12	the	the	DET
stem-5536	89	13	simple	simple	ADJ
stem-5536	89	14	ratio	ratio	NOUN
stem-5536	89	15	of	of	ADP
stem-5536	89	16	three	three	NUM
stem-5536	89	17	points	point	NOUN
stem-5536	89	18	lying	lie	VERB
stem-5536	89	19	on	on	ADP
stem-5536	89	20	one	one	NUM
stem-5536	89	21	straight	straight	ADJ
stem-5536	89	22	line	line	NOUN
stem-5536	89	23	is	be	AUX
stem-5536	89	24	preserved	preserve	VERB
stem-5536	89	25	in	in	ADP
stem-5536	89	26	parallel	parallel	ADJ
stem-5536	89	27	design	design	NOUN
stem-5536	89	28	.	.	PUNCT
stem-5536	90	1	in	in	ADP
stem-5536	90	2	this	this	DET
stem-5536	90	3	case	case	NOUN
stem-5536	90	4	,	,	PUNCT
stem-5536	90	5	it	it	PRON
stem-5536	90	6	is	be	AUX
stem-5536	90	7	also	also	ADV
stem-5536	90	8	said	say	VERB
stem-5536	90	9	that	that	SCONJ
stem-5536	90	10	a	a	DET
stem-5536	90	11	simple	simple	ADJ
stem-5536	90	12	ratio	ratio	NOUN
stem-5536	90	13	of	of	ADP
stem-5536	90	14	three	three	NUM
stem-5536	90	15	points	point	NOUN
stem-5536	90	16	lying	lie	VERB
stem-5536	90	17	on	on	ADP
stem-5536	90	18	one	one	NUM
stem-5536	90	19	straight	straight	ADJ
stem-5536	90	20	line	line	NOUN
stem-5536	90	21	is	be	AUX
stem-5536	90	22	an	an	DET
stem-5536	90	23	invariant	invariant	NOUN
stem-5536	90	24	of	of	ADP
stem-5536	90	25	parallel	parallel	ADJ
stem-5536	90	26	projection	projection	NOUN
stem-5536	90	27	the	the	DET
stem-5536	90	28	shape	shape	NOUN
stem-5536	90	29	properties	property	NOUN
stem-5536	90	30	that	that	PRON
stem-5536	90	31	are	be	AUX
stem-5536	90	32	preserved	preserve	VERB
stem-5536	90	33	across	across	ADP
stem-5536	90	34	the	the	DET
stem-5536	90	35	parallel	parallel	ADJ
stem-5536	90	36	design	design	NOUN
stem-5536	90	37	are	be	AUX
stem-5536	90	38	called	call	VERB
stem-5536	90	39	the	the	DET
stem-5536	90	40	shape	shape	NOUN
stem-5536	90	41	’s	’s	PART
stem-5536	90	42	affine	affine	NOUN
stem-5536	90	43	properties	property	NOUN
stem-5536	90	44	.	.	PUNCT
stem-5536	91	1	for	for	ADP
stem-5536	91	2	example	example	NOUN
stem-5536	91	3	,	,	PUNCT
stem-5536	91	4	the	the	DET
stem-5536	91	5	properties	property	NOUN
stem-5536	91	6	of	of	ADP
stem-5536	91	7	lines	line	NOUN
stem-5536	91	8	to	to	PART
stem-5536	91	9	be	be	AUX
stem-5536	91	10	parallel	parallel	ADJ
stem-5536	91	11	are	be	AUX
stem-5536	91	12	affine	affine	NOUN
stem-5536	91	13	properties	property	NOUN
stem-5536	91	14	of	of	ADP
stem-5536	91	15	these	these	DET
stem-5536	91	16	lines	line	NOUN
stem-5536	91	17	;	;	PUNCT
stem-5536	91	18	123	123	NUM
stem-5536	91	19	american	american	ADJ
stem-5536	91	20	journal	journal	NOUN
stem-5536	91	21	of	of	ADP
stem-5536	91	22	language	language	NOUN
stem-5536	91	23	,	,	PUNCT
stem-5536	91	24	literacy	literacy	NOUN
stem-5536	91	25	and	and	CCONJ
stem-5536	91	26	learning	learn	VERB
stem-5536	91	27	in	in	ADP
stem-5536	91	28	stem	stem	NOUN
stem-5536	91	29	education	education	NOUN
stem-5536	91	30	www	www	PROPN
stem-5536	91	31	.	.	PUNCT
stem-5536	92	1	grnjournal.us	grnjournal.us	X
stem-5536	92	2	invariance	invariance	NOUN
stem-5536	92	3	of	of	ADP
stem-5536	92	4	a	a	DET
stem-5536	92	5	simple	simple	ADJ
stem-5536	92	6	ratio	ratio	NOUN
stem-5536	92	7	of	of	ADP
stem-5536	92	8	three	three	NUM
stem-5536	92	9	points	point	NOUN
stem-5536	92	10	of	of	ADP
stem-5536	92	11	one	one	NUM
stem-5536	92	12	straight	straight	ADJ
stem-5536	92	13	line	line	NOUN
stem-5536	92	14	is	be	AUX
stem-5536	92	15	an	an	DET
stem-5536	92	16	affine	affine	ADJ
stem-5536	92	17	property	property	NOUN
stem-5536	92	18	of	of	ADP
stem-5536	92	19	such	such	ADJ
stem-5536	92	20	points	point	NOUN
stem-5536	92	21	.	.	PUNCT
stem-5536	93	1	conclusion	conclusion	NOUN
stem-5536	93	2	in	in	ADP
stem-5536	93	3	short	short	ADJ
stem-5536	93	4	,	,	PUNCT
stem-5536	93	5	the	the	DET
stem-5536	93	6	basis	basis	NOUN
stem-5536	93	7	of	of	ADP
stem-5536	93	8	visualizing	visualize	VERB
stem-5536	93	9	abstract	abstract	ADJ
stem-5536	93	10	knowledge	knowledge	NOUN
stem-5536	93	11	is	be	AUX
stem-5536	93	12	the	the	DET
stem-5536	93	13	student	student	NOUN
stem-5536	93	14	’s	’s	PART
stem-5536	93	15	ability	ability	NOUN
stem-5536	93	16	to	to	PART
stem-5536	93	17	“	"	PUNCT
stem-5536	93	18	work	work	VERB
stem-5536	93	19	”	"	PUNCT
stem-5536	93	20	with	with	ADP
stem-5536	93	21	the	the	DET
stem-5536	93	22	simplest	simple	ADJ
stem-5536	93	23	things	thing	NOUN
stem-5536	93	24	,	,	PUNCT
stem-5536	93	25	to	to	PART
stem-5536	93	26	construct	construct	VERB
stem-5536	93	27	them	they	PRON
stem-5536	93	28	,	,	PUNCT
stem-5536	93	29	to	to	PART
stem-5536	93	30	consider	consider	VERB
stem-5536	93	31	them	they	PRON
stem-5536	93	32	in	in	ADP
stem-5536	93	33	motion	motion	NOUN
stem-5536	93	34	,	,	PUNCT
stem-5536	93	35	in	in	ADP
stem-5536	93	36	projection	projection	NOUN
stem-5536	93	37	.	.	PUNCT
stem-5536	94	1	this	this	DET
stem-5536	94	2	skill	skill	NOUN
stem-5536	94	3	includes	include	VERB
stem-5536	94	4	the	the	DET
stem-5536	94	5	ability	ability	NOUN
stem-5536	94	6	to	to	PART
stem-5536	94	7	perform	perform	VERB
stem-5536	94	8	elementary	elementary	ADJ
stem-5536	94	9	lessons	lesson	NOUN
stem-5536	94	10	from	from	ADP
stem-5536	94	11	kindergarten	kindergarten	NOUN
stem-5536	94	12	,	,	PUNCT
stem-5536	94	13	the	the	DET
stem-5536	94	14	ability	ability	NOUN
stem-5536	94	15	to	to	PART
stem-5536	94	16	cut	cut	VERB
stem-5536	94	17	and	and	CCONJ
stem-5536	94	18	apply	apply	VERB
stem-5536	94	19	geometric	geometric	ADJ
stem-5536	94	20	shapes	shape	NOUN
stem-5536	94	21	to	to	ADP
stem-5536	94	22	each	each	DET
stem-5536	94	23	other	other	ADJ
stem-5536	94	24	,	,	PUNCT
stem-5536	94	25	to	to	PART
stem-5536	94	26	measure	measure	VERB
stem-5536	94	27	in	in	ADP
stem-5536	94	28	high	high	ADJ
stem-5536	94	29	school	school	NOUN
stem-5536	94	30	,	,	PUNCT
stem-5536	94	31	to	to	PART
stem-5536	94	32	get	get	AUX
stem-5536	94	33	acquainted	acquaint	VERB
stem-5536	94	34	with	with	ADP
stem-5536	94	35	the	the	DET
stem-5536	94	36	concept	concept	NOUN
stem-5536	94	37	of	of	ADP
stem-5536	94	38	measurability	measurability	NOUN
stem-5536	94	39	of	of	ADP
stem-5536	94	40	immeasurability	immeasurability	NOUN
stem-5536	94	41	"	"	PUNCT
stem-5536	94	42	manually	manually	ADV
stem-5536	94	43	"	"	PUNCT
stem-5536	94	44	,	,	PUNCT
stem-5536	94	45	to	to	PART
stem-5536	94	46	find	find	VERB
stem-5536	94	47	out	out	ADP
stem-5536	94	48	the	the	DET
stem-5536	94	49	origin	origin	NOUN
stem-5536	94	50	of	of	ADP
stem-5536	94	51	the	the	DET
stem-5536	94	52	multiplicity	multiplicity	NOUN
stem-5536	94	53	of	of	ADP
stem-5536	94	54	measurement	measurement	NOUN
stem-5536	94	55	methods	method	NOUN
stem-5536	94	56	and	and	CCONJ
stem-5536	94	57	a	a	DET
stem-5536	94	58	gradual	gradual	ADJ
stem-5536	94	59	transition	transition	NOUN
stem-5536	94	60	to	to	ADP
stem-5536	94	61	the	the	DET
stem-5536	94	62	limiting	limit	VERB
stem-5536	94	63	transition	transition	NOUN
stem-5536	94	64	to	to	ADP
stem-5536	94	65	the	the	DET
stem-5536	94	66	idea	idea	NOUN
stem-5536	94	67	of	of	ADP
stem-5536	94	68	rectifiability	rectifiability	NOUN
stem-5536	94	69	of	of	ADP
stem-5536	94	70	arcs	arc	NOUN
stem-5536	94	71	and	and	CCONJ
stem-5536	94	72	surfaces	surface	NOUN
stem-5536	94	73	in	in	ADP
stem-5536	94	74	the	the	DET
stem-5536	94	75	course	course	NOUN
stem-5536	94	76	of	of	ADP
stem-5536	94	77	geometry	geometry	NOUN
stem-5536	94	78	at	at	ADP
stem-5536	94	79	the	the	DET
stem-5536	94	80	university	university	NOUN
stem-5536	94	81	,	,	PUNCT
stem-5536	94	82	as	as	ADV
stem-5536	94	83	well	well	ADV
stem-5536	94	84	as	as	ADP
stem-5536	94	85	discover	discover	VERB
stem-5536	94	86	the	the	DET
stem-5536	94	87	possibilities	possibility	NOUN
stem-5536	94	88	of	of	ADP
stem-5536	94	89	design	design	NOUN
stem-5536	94	90	and	and	CCONJ
stem-5536	94	91	axonometric	axonometric	VERB
stem-5536	94	92	representations	representation	NOUN
stem-5536	94	93	of	of	ADP
stem-5536	94	94	geometric	geometric	ADJ
stem-5536	94	95	bodies	body	NOUN
stem-5536	94	96	.	.	PUNCT
stem-5536	95	1	in	in	ADP
stem-5536	95	2	terms	term	NOUN
stem-5536	95	3	of	of	ADP
stem-5536	95	4	having	have	VERB
stem-5536	95	5	the	the	DET
stem-5536	95	6	ability	ability	NOUN
stem-5536	95	7	to	to	PART
stem-5536	95	8	“	"	PUNCT
stem-5536	95	9	see	see	VERB
stem-5536	95	10	”	"	PUNCT
stem-5536	95	11	any	any	DET
stem-5536	95	12	abstract	abstract	ADJ
stem-5536	95	13	thing	thing	NOUN
stem-5536	95	14	with	with	ADP
stem-5536	95	15	their	their	PRON
stem-5536	95	16	own	own	ADJ
stem-5536	95	17	eyes	eye	NOUN
stem-5536	95	18	,	,	PUNCT
stem-5536	95	19	it	it	PRON
stem-5536	95	20	will	will	AUX
stem-5536	95	21	be	be	AUX
stem-5536	95	22	especially	especially	ADV
stem-5536	95	23	valuable	valuable	ADJ
stem-5536	95	24	for	for	ADP
stem-5536	95	25	future	future	ADJ
stem-5536	95	26	biologists	biologist	NOUN
stem-5536	95	27	,	,	PUNCT
stem-5536	95	28	chemists	chemist	NOUN
stem-5536	95	29	,	,	PUNCT
stem-5536	95	30	ecologists	ecologist	NOUN
stem-5536	95	31	,	,	PUNCT
stem-5536	95	32	especially	especially	ADV
stem-5536	95	33	if	if	SCONJ
stem-5536	95	34	the	the	DET
stem-5536	95	35	modern	modern	ADJ
stem-5536	95	36	capabilities	capability	NOUN
stem-5536	95	37	of	of	ADP
stem-5536	95	38	computer	computer	NOUN
stem-5536	95	39	technology	technology	NOUN
stem-5536	95	40	make	make	VERB
stem-5536	95	41	it	it	PRON
stem-5536	95	42	easy	easy	ADJ
stem-5536	95	43	to	to	PART
stem-5536	95	44	obtain	obtain	VERB
stem-5536	95	45	the	the	DET
stem-5536	95	46	impression	impression	NOUN
stem-5536	95	47	about	about	ADP
stem-5536	95	48	the	the	DET
stem-5536	95	49	object	object	NOUN
stem-5536	95	50	,	,	PUNCT
stem-5536	95	51	the	the	DET
stem-5536	95	52	stereographic	stereographic	ADJ
stem-5536	95	53	thinking	thinking	NOUN
stem-5536	95	54	of	of	ADP
stem-5536	95	55	the	the	DET
stem-5536	95	56	researcher	researcher	NOUN
stem-5536	95	57	is	be	AUX
stem-5536	95	58	the	the	DET
stem-5536	95	59	main	main	ADJ
stem-5536	95	60	manager	manager	NOUN
stem-5536	95	61	of	of	ADP
stem-5536	95	62	the	the	DET
stem-5536	95	63	reality	reality	NOUN
stem-5536	95	64	of	of	ADP
stem-5536	95	65	the	the	DET
stem-5536	95	66	research	research	NOUN
stem-5536	95	67	results	result	NOUN
stem-5536	95	68	.	.	PUNCT
stem-5536	96	1	the	the	DET
stem-5536	96	2	methodological	methodological	ADJ
stem-5536	96	3	effect	effect	NOUN
stem-5536	96	4	of	of	ADP
stem-5536	96	5	such	such	ADJ
stem-5536	96	6	training	training	NOUN
stem-5536	96	7	is	be	AUX
stem-5536	96	8	that	that	SCONJ
stem-5536	96	9	future	future	ADJ
stem-5536	96	10	mathematics	mathematic	NOUN
stem-5536	96	11	teachers	teacher	NOUN
stem-5536	96	12	will	will	AUX
stem-5536	96	13	have	have	VERB
stem-5536	96	14	the	the	DET
stem-5536	96	15	opportunity	opportunity	NOUN
stem-5536	96	16	to	to	PART
stem-5536	96	17	get	get	AUX
stem-5536	96	18	acquainted	acquaint	VERB
stem-5536	96	19	,	,	PUNCT
stem-5536	96	20	first	first	ADV
stem-5536	96	21	of	of	ADP
stem-5536	96	22	all	all	PRON
stem-5536	96	23	,	,	PUNCT
stem-5536	96	24	with	with	ADP
stem-5536	96	25	the	the	DET
stem-5536	96	26	origin	origin	NOUN
stem-5536	96	27	of	of	ADP
stem-5536	96	28	geometric	geometric	ADJ
stem-5536	96	29	construction	construction	NOUN
stem-5536	96	30	and	and	CCONJ
stem-5536	96	31	the	the	DET
stem-5536	96	32	theoretical	theoretical	ADJ
stem-5536	96	33	foundations	foundation	NOUN
stem-5536	96	34	of	of	ADP
stem-5536	96	35	the	the	DET
stem-5536	96	36	projection	projection	ADJ
stem-5536	96	37	part	part	NOUN
stem-5536	96	38	of	of	ADP
stem-5536	96	39	geometry	geometry	NOUN
stem-5536	96	40	,	,	PUNCT
stem-5536	96	41	as	as	SCONJ
stem-5536	96	42	the	the	DET
stem-5536	96	43	history	history	NOUN
stem-5536	96	44	of	of	ADP
stem-5536	96	45	geometry	geometry	NOUN
stem-5536	96	46	has	have	AUX
stem-5536	96	47	shown	show	VERB
stem-5536	96	48	necessary	necessary	ADJ
stem-5536	96	49	to	to	PART
stem-5536	96	50	visualize	visualize	VERB
stem-5536	96	51	objects	object	NOUN
stem-5536	96	52	.	.	PUNCT
stem-5536	97	1	references	reference	NOUN
stem-5536	97	2	1	1	NUM
stem-5536	97	3	.	.	PUNCT
stem-5536	97	4	bozhovich	bozhovich	PROPN
stem-5536	97	5	l.i	l.i	PROPN
stem-5536	97	6	.	.	PROPN
stem-5536	97	7	selected	select	VERB
stem-5536	97	8	psychological	psychological	ADJ
stem-5536	97	9	works	work	NOUN
stem-5536	97	10	.	.	PUNCT
stem-5536	98	1	moscow	moscow	PROPN
stem-5536	98	2	:	:	PUNCT
stem-5536	98	3	1995	1995	NUM
stem-5536	98	4	.	.	PUNCT
stem-5536	99	1	2	2	X
stem-5536	99	2	.	.	X
stem-5536	99	3	davydov	davydov	PROPN
stem-5536	99	4	v.v	v.v	PROPN
stem-5536	99	5	.	.	PROPN
stem-5536	99	6	personalities	personality	NOUN
stem-5536	99	7	need	need	VERB
stem-5536	99	8	to	to	PART
stem-5536	99	9	“	"	PUNCT
stem-5536	99	10	stand	stand	VERB
stem-5536	99	11	out	out	ADP
stem-5536	99	12	”	"	PUNCT
stem-5536	99	13	/	/	PUNCT
stem-5536	99	14	how	how	SCONJ
stem-5536	99	15	does	do	AUX
stem-5536	99	16	personality	personality	NOUN
stem-5536	99	17	begin	begin	VERB
stem-5536	99	18	.	.	PUNCT
stem-5536	100	1	moscow	moscow	PROPN
stem-5536	100	2	:	:	PUNCT
stem-5536	100	3	1979	1979	NUM
stem-5536	100	4	.	.	PUNCT
stem-5536	101	1	3	3	X
stem-5536	101	2	.	.	X
stem-5536	101	3	leontiev	leontiev	PROPN
stem-5536	101	4	a.n	a.n	PROPN
stem-5536	101	5	.	.	PROPN
stem-5536	101	6	activity	activity	NOUN
stem-5536	101	7	.	.	PUNCT
stem-5536	102	1	consciousness	consciousness	NOUN
stem-5536	102	2	.	.	PUNCT
stem-5536	103	1	personality	personality	NOUN
stem-5536	103	2	.	.	PUNCT
stem-5536	104	1	moscow	moscow	PROPN
stem-5536	104	2	:	:	PUNCT
stem-5536	104	3	1977	1977	NUM
stem-5536	104	4	.	.	PUNCT
stem-5536	105	1	4	4	X
stem-5536	105	2	.	.	X
stem-5536	105	3	leynes	leynes	PROPN
stem-5536	105	4	n.s	n.s	PROPN
stem-5536	105	5	.	.	PROPN
stem-5536	105	6	mental	mental	ADJ
stem-5536	105	7	abilities	ability	NOUN
stem-5536	105	8	and	and	CCONJ
stem-5536	105	9	age	age	NOUN
stem-5536	105	10	.	.	PUNCT
stem-5536	106	1	moscow	moscow	PROPN
stem-5536	106	2	:	:	PUNCT
stem-5536	106	3	1971	1971	NUM
stem-5536	106	4	.	.	PUNCT
stem-5536	107	1	5	5	NUM
stem-5536	107	2	.	.	X
stem-5536	107	3	esonov	esonov	PROPN
stem-5536	107	4	.	.	PUNCT
stem-5536	108	1	m.m	m.m	PROPN
stem-5536	108	2	.	.	PROPN
stem-5536	108	3	,	,	PUNCT
stem-5536	108	4	zharov	zharov	PROPN
stem-5536	108	5	.	.	PUNCT
stem-5536	109	1	vc	vc	PROPN
stem-5536	109	2	.	.	PUNCT
stem-5536	109	3	geometry	geometry	NOUN
stem-5536	109	4	as	as	ADP
stem-5536	109	5	a	a	DET
stem-5536	109	6	means	means	NOUN
stem-5536	109	7	of	of	ADP
stem-5536	109	8	visualizing	visualize	VERB
stem-5536	109	9	logic	logic	NOUN
stem-5536	109	10	and	and	CCONJ
stem-5536	109	11	operational	operational	ADJ
stem-5536	109	12	(	(	PUNCT
stem-5536	109	13	functional	functional	ADJ
stem-5536	109	14	)	)	PUNCT
stem-5536	109	15	thinking	thinking	NOUN
stem-5536	109	16	.	.	PUNCT
stem-5536	110	1	conference	conference	NOUN
stem-5536	110	2	materials	material	NOUN
stem-5536	110	3	international	international	ADJ
stem-5536	110	4	humanitarian	humanitarian	ADJ
stem-5536	110	5	scientific	scientific	ADJ
stem-5536	110	6	forum	forum	NOUN
stem-5536	110	7	“	"	PUNCT
stem-5536	110	8	humanitarian	humanitarian	ADJ
stem-5536	110	9	readings	reading	NOUN
stem-5536	110	10	rsuh-2019	rsuh-2019	ADJ
stem-5536	110	11	”	"	PUNCT
stem-5536	110	12	continuity	continuity	NOUN
stem-5536	110	13	and	and	CCONJ
stem-5536	110	14	gaps	gap	NOUN
stem-5536	110	15	:	:	PUNCT
stem-5536	110	16	social	social	ADJ
stem-5536	110	17	and	and	CCONJ
stem-5536	110	18	humanitarian	humanitarian	ADJ
stem-5536	110	19	dimensions	dimension	NOUN
stem-5536	110	20	,	,	PUNCT
stem-5536	110	21	2019	2019	NUM
stem-5536	110	22	6	6	NUM
stem-5536	110	23	.	.	PUNCT
stem-5536	110	24	feldshtein	feldshtein	PROPN
stem-5536	110	25	d.i	d.i	PROPN
stem-5536	110	26	.	.	PROPN
stem-5536	110	27	psychology	psychology	NOUN
stem-5536	110	28	of	of	ADP
stem-5536	110	29	the	the	DET
stem-5536	110	30	developing	develop	VERB
stem-5536	110	31	personality	personality	NOUN
stem-5536	110	32	in	in	ADP
stem-5536	110	33	ontogenesis	ontogenesis	NOUN
stem-5536	110	34	.	.	PUNCT
stem-5536	111	1	moscow	moscow	PROPN
stem-5536	111	2	:	:	PUNCT
stem-5536	111	3	1989	1989	NUM
stem-5536	111	4	.	.	PUNCT
stem-5536	112	1	7	7	X
stem-5536	112	2	.	.	X
stem-5536	112	3	elkonin	elkonin	PROPN
stem-5536	112	4	d.b	d.b	PROPN
stem-5536	112	5	.	.	PROPN
stem-5536	113	1	on	on	ADP
stem-5536	113	2	the	the	DET
stem-5536	113	3	problem	problem	NOUN
stem-5536	113	4	of	of	ADP
stem-5536	113	5	periodization	periodization	NOUN
stem-5536	113	6	of	of	ADP
stem-5536	113	7	mental	mental	ADJ
stem-5536	113	8	development	development	NOUN
stem-5536	113	9	in	in	ADP
stem-5536	113	10	childhood	childhood	NOUN
stem-5536	113	11	/	/	SYM
stem-5536	113	12	questions	question	NOUN
stem-5536	113	13	of	of	ADP
stem-5536	113	14	psychology	psychology	NOUN
stem-5536	113	15	.	.	PUNCT
stem-5536	114	1	1971	1971	NUM
stem-5536	114	2	.	.	PUNCT
stem-5536	115	1	no	no	INTJ
stem-5536	115	2	.	.	NOUN
stem-5536	116	1	4	4	NUM
stem-5536	116	2	.	.	NOUN
stem-5536	116	3	8	8	NUM
stem-5536	116	4	.	.	X
stem-5536	116	5	asmolov	asmolov	PROPN
stem-5536	116	6	a.g	a.g	PROPN
stem-5536	116	7	.	.	PROPN
stem-5536	116	8	psychology	psychology	NOUN
stem-5536	116	9	of	of	ADP
stem-5536	116	10	personality	personality	NOUN
stem-5536	116	11	.	.	PUNCT
stem-5536	117	1	moscow	moscow	PROPN
stem-5536	117	2	:	:	PUNCT
stem-5536	117	3	1990	1990	NUM
stem-5536	117	4	.	.	PUNCT
stem-5536	118	1	9	9	X
stem-5536	118	2	.	.	X
stem-5536	118	3	pidow	pidow	NOUN
stem-5536	118	4	d.	d.	PROPN
stem-5536	118	5	geometry	geometry	NOUN
stem-5536	118	6	and	and	CCONJ
stem-5536	118	7	art	art	NOUN
stem-5536	118	8	.	.	PUNCT
stem-5536	119	1	moscow	moscow	PROPN
stem-5536	119	2	:	:	PUNCT
stem-5536	119	3	mir	mir	PROPN
stem-5536	119	4	,	,	PUNCT
stem-5536	119	5	1979	1979	NUM
stem-5536	119	6	.-336	.-336	PROPN