id	sid	tid	token	lemma	pos
grhe-5548	1	1	global	global	ADJ
grhe-5548	1	2	research	research	NOUN
grhe-5548	1	3	in	in	ADP
grhe-5548	1	4	higher	high	ADJ
grhe-5548	1	5	education	education	NOUN
grhe-5548	1	6	issn	issn	PROPN
grhe-5548	1	7	2576	2576	NUM
grhe-5548	1	8	-	-	PUNCT
grhe-5548	1	9	196x	196x	PROPN
grhe-5548	1	10	(	(	PUNCT
grhe-5548	1	11	print	print	NOUN
grhe-5548	1	12	)	)	PUNCT
grhe-5548	1	13	issn	issn	PROPN
grhe-5548	1	14	2576	2576	NUM
grhe-5548	1	15	-	-	SYM
grhe-5548	1	16	1951	1951	NUM
grhe-5548	1	17	(	(	PUNCT
grhe-5548	1	18	online	online	ADJ
grhe-5548	1	19	)	)	PUNCT
grhe-5548	1	20	vol	vol	NOUN
grhe-5548	1	21	.	.	PROPN
grhe-5548	2	1	6	6	NUM
grhe-5548	2	2	,	,	PUNCT
grhe-5548	2	3	no	no	INTJ
grhe-5548	2	4	.	.	NOUN
grhe-5548	2	5	2	2	NUM
grhe-5548	2	6	,	,	PUNCT
grhe-5548	2	7	2023	2023	NUM
grhe-5548	2	8	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	NOUN
grhe-5548	2	9	32	32	NUM
grhe-5548	2	10	original	original	ADJ
grhe-5548	2	11	paper	paper	NOUN
grhe-5548	2	12	an	an	DET
grhe-5548	2	13	important	important	ADJ
grhe-5548	2	14	historical	historical	ADJ
grhe-5548	2	15	milestone	milestone	NOUN
grhe-5548	2	16	:	:	PUNCT
grhe-5548	2	17	the	the	DET
grhe-5548	2	18	classification	classification	NOUN
grhe-5548	2	19	of	of	ADP
grhe-5548	2	20	the	the	DET
grhe-5548	2	21	cubic	cubic	ADJ
grhe-5548	2	22	equations	equation	NOUN
grhe-5548	2	23	ilhan	ilhan	PROPN
grhe-5548	2	24	m.	m.	PROPN
grhe-5548	2	25	izmirli	izmirli	NOUN
grhe-5548	2	26	1	1	NUM
grhe-5548	2	27	1	1	NUM
grhe-5548	2	28	george	george	PROPN
grhe-5548	2	29	mason	mason	PROPN
grhe-5548	2	30	university	university	PROPN
grhe-5548	2	31	,	,	PUNCT
grhe-5548	2	32	fairfax	fairfax	NOUN
grhe-5548	2	33	,	,	PUNCT
grhe-5548	2	34	va	va	PROPN
grhe-5548	2	35	,	,	PUNCT
grhe-5548	2	36	usa	usa	PROPN
grhe-5548	2	37	received	receive	VERB
grhe-5548	2	38	:	:	PUNCT
grhe-5548	2	39	january	january	PROPN
grhe-5548	2	40	11	11	NUM
grhe-5548	2	41	,	,	PUNCT
grhe-5548	2	42	2023	2023	NUM
grhe-5548	2	43	accepted	accept	VERB
grhe-5548	2	44	:	:	PUNCT
grhe-5548	2	45	january	january	PROPN
grhe-5548	2	46	23	23	NUM
grhe-5548	2	47	,	,	PUNCT
grhe-5548	2	48	2023	2023	NUM
grhe-5548	2	49	online	online	ADV
grhe-5548	2	50	published	publish	VERB
grhe-5548	2	51	:	:	PUNCT
grhe-5548	2	52	april	april	PROPN
grhe-5548	2	53	13	13	NUM
grhe-5548	2	54	,	,	PUNCT
grhe-5548	2	55	2023	2023	NUM
grhe-5548	2	56	doi:10.22158	doi:10.22158	NOUN
grhe-5548	2	57	/	/	SYM
grhe-5548	2	58	grhe.v6n2p32	grhe.v6n2p32	NOUN
grhe-5548	2	59	url	url	NOUN
grhe-5548	2	60	:	:	PUNCT
grhe-5548	2	61	http://dx.doi.org/10.22158	http://dx.doi.org/10.22158	NOUN
grhe-5548	2	62	/	/	SYM
grhe-5548	2	63	grhe.v6n2p32	grhe.v6n2p32	NOUN
grhe-5548	2	64	abstract	abstract	NOUN
grhe-5548	2	65	this	this	DET
grhe-5548	2	66	article	article	NOUN
grhe-5548	2	67	investigates	investigate	VERB
grhe-5548	2	68	the	the	DET
grhe-5548	2	69	use	use	NOUN
grhe-5548	2	70	of	of	ADP
grhe-5548	2	71	the	the	DET
grhe-5548	2	72	history	history	NOUN
grhe-5548	2	73	of	of	ADP
grhe-5548	2	74	mathematics	mathematic	NOUN
grhe-5548	2	75	as	as	ADP
grhe-5548	2	76	a	a	DET
grhe-5548	2	77	pedagogical	pedagogical	ADJ
grhe-5548	2	78	tool	tool	NOUN
grhe-5548	2	79	for	for	ADP
grhe-5548	2	80	the	the	DET
grhe-5548	2	81	teaching	teaching	NOUN
grhe-5548	2	82	and	and	CCONJ
grhe-5548	2	83	learning	learning	NOUN
grhe-5548	2	84	of	of	ADP
grhe-5548	2	85	mathematics	mathematic	NOUN
grhe-5548	2	86	,	,	PUNCT
grhe-5548	2	87	using	use	VERB
grhe-5548	2	88	the	the	DET
grhe-5548	2	89	history	history	NOUN
grhe-5548	2	90	of	of	ADP
grhe-5548	2	91	the	the	DET
grhe-5548	2	92	cubic	cubic	ADJ
grhe-5548	2	93	equation	equation	NOUN
grhe-5548	2	94	as	as	ADP
grhe-5548	2	95	a	a	DET
grhe-5548	2	96	specific	specific	ADJ
grhe-5548	2	97	example	example	NOUN
grhe-5548	2	98	.	.	PUNCT
grhe-5548	3	1	cubic	cubic	ADJ
grhe-5548	3	2	equations	equation	NOUN
grhe-5548	3	3	arise	arise	VERB
grhe-5548	3	4	intrinsically	intrinsically	ADV
grhe-5548	3	5	in	in	ADP
grhe-5548	3	6	many	many	ADJ
grhe-5548	3	7	applications	application	NOUN
grhe-5548	3	8	in	in	ADP
grhe-5548	3	9	natural	natural	ADJ
grhe-5548	3	10	sciences	science	NOUN
grhe-5548	3	11	and	and	CCONJ
grhe-5548	3	12	mathematics	mathematic	NOUN
grhe-5548	3	13	.	.	PUNCT
grhe-5548	4	1	for	for	ADP
grhe-5548	4	2	example	example	NOUN
grhe-5548	4	3	,	,	PUNCT
grhe-5548	4	4	in	in	ADP
grhe-5548	4	5	physics	physics	NOUN
grhe-5548	4	6	,	,	PUNCT
grhe-5548	4	7	the	the	DET
grhe-5548	4	8	solutions	solution	NOUN
grhe-5548	4	9	of	of	ADP
grhe-5548	4	10	the	the	DET
grhe-5548	4	11	equations	equation	NOUN
grhe-5548	4	12	of	of	ADP
grhe-5548	4	13	state	state	NOUN
grhe-5548	4	14	in	in	ADP
grhe-5548	4	15	thermodynamics	thermodynamic	NOUN
grhe-5548	4	16	,	,	PUNCT
grhe-5548	4	17	or	or	CCONJ
grhe-5548	4	18	the	the	DET
grhe-5548	4	19	computation	computation	NOUN
grhe-5548	4	20	of	of	ADP
grhe-5548	4	21	the	the	DET
grhe-5548	4	22	speed	speed	NOUN
grhe-5548	4	23	of	of	ADP
grhe-5548	4	24	seismic	seismic	ADJ
grhe-5548	4	25	rayleigh	rayleigh	PROPN
grhe-5548	4	26	waves	wave	NOUN
grhe-5548	4	27	require	require	VERB
grhe-5548	4	28	the	the	DET
grhe-5548	4	29	solutions	solution	NOUN
grhe-5548	4	30	of	of	ADP
grhe-5548	4	31	cubic	cubic	ADJ
grhe-5548	4	32	equations	equation	NOUN
grhe-5548	4	33	.	.	PUNCT
grhe-5548	5	1	in	in	ADP
grhe-5548	5	2	mathematics	mathematic	NOUN
grhe-5548	5	3	,	,	PUNCT
grhe-5548	5	4	they	they	PRON
grhe-5548	5	5	are	be	AUX
grhe-5548	5	6	instrumental	instrumental	ADJ
grhe-5548	5	7	in	in	ADP
grhe-5548	5	8	solving	solve	VERB
grhe-5548	5	9	the	the	DET
grhe-5548	5	10	quartic	quartic	ADJ
grhe-5548	5	11	equations	equation	NOUN
grhe-5548	5	12	,	,	PUNCT
grhe-5548	5	13	for	for	ADP
grhe-5548	5	14	in	in	ADP
grhe-5548	5	15	the	the	DET
grhe-5548	5	16	process	process	NOUN
grhe-5548	5	17	,	,	PUNCT
grhe-5548	5	18	these	these	PRON
grhe-5548	5	19	are	be	AUX
grhe-5548	5	20	reduced	reduce	VERB
grhe-5548	5	21	to	to	ADP
grhe-5548	5	22	cubic	cubic	ADJ
grhe-5548	5	23	equations	equation	NOUN
grhe-5548	5	24	.	.	PUNCT
grhe-5548	6	1	the	the	DET
grhe-5548	6	2	impossibility	impossibility	NOUN
grhe-5548	6	3	of	of	ADP
grhe-5548	6	4	trisecting	trisect	VERB
grhe-5548	6	5	an	an	DET
grhe-5548	6	6	angle	angle	NOUN
grhe-5548	6	7	or	or	CCONJ
grhe-5548	6	8	doubling	double	VERB
grhe-5548	6	9	a	a	DET
grhe-5548	6	10	cube	cube	NOUN
grhe-5548	6	11	using	use	VERB
grhe-5548	6	12	only	only	ADV
grhe-5548	6	13	a	a	DET
grhe-5548	6	14	straightedge	straightedge	NOUN
grhe-5548	6	15	and	and	CCONJ
grhe-5548	6	16	compass	compass	NOUN
grhe-5548	6	17	is	be	AUX
grhe-5548	6	18	equivalent	equivalent	ADJ
grhe-5548	6	19	to	to	ADP
grhe-5548	6	20	solving	solve	VERB
grhe-5548	6	21	some	some	DET
grhe-5548	6	22	cubic	cubic	ADJ
grhe-5548	6	23	equations	equation	NOUN
grhe-5548	6	24	.	.	PUNCT
grhe-5548	7	1	as	as	SCONJ
grhe-5548	7	2	the	the	DET
grhe-5548	7	3	name	name	NOUN
grhe-5548	7	4	implies	imply	VERB
grhe-5548	7	5	,	,	PUNCT
grhe-5548	7	6	the	the	DET
grhe-5548	7	7	cubic	cubic	ADJ
grhe-5548	7	8	spline	spline	PROPN
grhe-5548	7	9	approximation	approximation	NOUN
grhe-5548	7	10	,	,	PUNCT
grhe-5548	7	11	an	an	DET
grhe-5548	7	12	important	important	ADJ
grhe-5548	7	13	tool	tool	NOUN
grhe-5548	7	14	in	in	ADP
grhe-5548	7	15	numerical	numerical	ADJ
grhe-5548	7	16	analysis	analysis	NOUN
grhe-5548	7	17	,	,	PUNCT
grhe-5548	7	18	also	also	ADV
grhe-5548	7	19	entails	entail	VERB
grhe-5548	7	20	working	work	VERB
grhe-5548	7	21	with	with	ADP
grhe-5548	7	22	cubic	cubic	ADJ
grhe-5548	7	23	functions	function	NOUN
grhe-5548	7	24	.	.	PUNCT
grhe-5548	8	1	although	although	SCONJ
grhe-5548	8	2	cubic	cubic	ADJ
grhe-5548	8	3	equations	equation	NOUN
grhe-5548	8	4	were	be	AUX
grhe-5548	8	5	explored	explore	VERB
grhe-5548	8	6	by	by	ADP
grhe-5548	8	7	the	the	DET
grhe-5548	8	8	ancient	ancient	ADJ
grhe-5548	8	9	babylonian	babylonian	ADJ
grhe-5548	8	10	,	,	PUNCT
grhe-5548	8	11	greek	greek	ADJ
grhe-5548	8	12	,	,	PUNCT
grhe-5548	8	13	chinese	chinese	PROPN
grhe-5548	8	14	,	,	PUNCT
grhe-5548	8	15	indian	indian	ADJ
grhe-5548	8	16	,	,	PUNCT
grhe-5548	8	17	and	and	CCONJ
grhe-5548	8	18	egyptian	egyptian	ADJ
grhe-5548	8	19	scholars	scholar	NOUN
grhe-5548	8	20	,	,	PUNCT
grhe-5548	8	21	it	it	PRON
grhe-5548	8	22	took	take	VERB
grhe-5548	8	23	the	the	DET
grhe-5548	8	24	collective	collective	ADJ
grhe-5548	8	25	work	work	NOUN
grhe-5548	8	26	of	of	ADP
grhe-5548	8	27	many	many	ADJ
grhe-5548	8	28	well	well	ADV
grhe-5548	8	29	-	-	PUNCT
grhe-5548	8	30	known	know	VERB
grhe-5548	8	31	mathematicians	mathematician	NOUN
grhe-5548	8	32	such	such	ADJ
grhe-5548	8	33	as	as	ADP
grhe-5548	8	34	diophantus	diophantus	NOUN
grhe-5548	8	35	,	,	PUNCT
grhe-5548	8	36	archimedes	archimede	NOUN
grhe-5548	8	37	,	,	PUNCT
grhe-5548	8	38	fibonacci	fibonacci	NOUN
grhe-5548	8	39	,	,	PUNCT
grhe-5548	8	40	del	del	X
grhe-5548	8	41	ferro	ferro	NOUN
grhe-5548	8	42	,	,	PUNCT
grhe-5548	8	43	khayyam	khayyam	PROPN
grhe-5548	8	44	,	,	PUNCT
grhe-5548	8	45	tartaglia	tartaglia	PROPN
grhe-5548	8	46	,	,	PUNCT
grhe-5548	8	47	cardano	cardano	NOUN
grhe-5548	8	48	,	,	PUNCT
grhe-5548	8	49	viète	viète	NOUN
grhe-5548	8	50	,	,	PUNCT
grhe-5548	8	51	descartes	descarte	NOUN
grhe-5548	8	52	,	,	PUNCT
grhe-5548	8	53	and	and	CCONJ
grhe-5548	8	54	lagrange	lagrange	NOUN
grhe-5548	8	55	to	to	PART
grhe-5548	8	56	finally	finally	ADV
grhe-5548	8	57	obtain	obtain	VERB
grhe-5548	8	58	a	a	DET
grhe-5548	8	59	full	full	ADJ
grhe-5548	8	60	solution	solution	NOUN
grhe-5548	8	61	.	.	PUNCT
grhe-5548	9	1	our	our	PRON
grhe-5548	9	2	goal	goal	NOUN
grhe-5548	9	3	in	in	ADP
grhe-5548	9	4	this	this	DET
grhe-5548	9	5	paper	paper	NOUN
grhe-5548	9	6	is	be	AUX
grhe-5548	9	7	to	to	PART
grhe-5548	9	8	investigate	investigate	VERB
grhe-5548	9	9	one	one	NUM
grhe-5548	9	10	of	of	ADP
grhe-5548	9	11	the	the	DET
grhe-5548	9	12	most	most	ADV
grhe-5548	9	13	formidable	formidable	ADJ
grhe-5548	9	14	steps	step	NOUN
grhe-5548	9	15	in	in	ADP
grhe-5548	9	16	this	this	DET
grhe-5548	9	17	extensive	extensive	ADJ
grhe-5548	9	18	and	and	CCONJ
grhe-5548	9	19	prolific	prolific	ADJ
grhe-5548	9	20	history	history	NOUN
grhe-5548	9	21	,	,	PUNCT
grhe-5548	9	22	namely	namely	ADV
grhe-5548	9	23	the	the	DET
grhe-5548	9	24	complete	complete	ADJ
grhe-5548	9	25	classification	classification	NOUN
grhe-5548	9	26	of	of	ADP
grhe-5548	9	27	the	the	DET
grhe-5548	9	28	cubic	cubic	ADJ
grhe-5548	9	29	equations	equation	NOUN
grhe-5548	9	30	by	by	ADP
grhe-5548	9	31	omar	omar	PROPN
grhe-5548	9	32	khayyam	khayyam	PROPN
grhe-5548	9	33	in	in	ADP
grhe-5548	9	34	eleventh	eleventh	ADJ
grhe-5548	9	35	century	century	NOUN
grhe-5548	9	36	,	,	PUNCT
grhe-5548	9	37	who	who	PRON
grhe-5548	9	38	was	be	AUX
grhe-5548	9	39	the	the	DET
grhe-5548	9	40	first	first	ADJ
grhe-5548	9	41	scholar	scholar	NOUN
grhe-5548	9	42	to	to	PART
grhe-5548	9	43	classify	classify	VERB
grhe-5548	9	44	cubic	cubic	ADJ
grhe-5548	9	45	equation	equation	NOUN
grhe-5548	9	46	and	and	CCONJ
grhe-5548	9	47	hence	hence	ADV
grhe-5548	9	48	facilitate	facilitate	VERB
grhe-5548	9	49	a	a	DET
grhe-5548	9	50	methodical	methodical	ADJ
grhe-5548	9	51	and	and	CCONJ
grhe-5548	9	52	logical	logical	ADJ
grhe-5548	9	53	approach	approach	NOUN
grhe-5548	9	54	to	to	ADP
grhe-5548	9	55	obtaining	obtain	VERB
grhe-5548	9	56	a	a	DET
grhe-5548	9	57	general	general	ADJ
grhe-5548	9	58	solution	solution	NOUN
grhe-5548	9	59	.	.	PUNCT
grhe-5548	10	1	keywords	keyword	VERB
grhe-5548	10	2	cubic	cubic	ADJ
grhe-5548	10	3	equation	equation	NOUN
grhe-5548	10	4	,	,	PUNCT
grhe-5548	10	5	monic	monic	ADJ
grhe-5548	10	6	polynomial	polynomial	ADJ
grhe-5548	10	7	,	,	PUNCT
grhe-5548	10	8	classification	classification	NOUN
grhe-5548	10	9	of	of	ADP
grhe-5548	10	10	cubic	cubic	ADJ
grhe-5548	10	11	equations	equation	NOUN
grhe-5548	10	12	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	10	13	global	global	ADJ
grhe-5548	10	14	research	research	NOUN
grhe-5548	10	15	in	in	ADP
grhe-5548	10	16	higher	high	ADJ
grhe-5548	10	17	education	education	NOUN
grhe-5548	10	18	vol	vol	NOUN
grhe-5548	10	19	.	.	PROPN
grhe-5548	11	1	6	6	NUM
grhe-5548	11	2	,	,	PUNCT
grhe-5548	11	3	no	no	INTJ
grhe-5548	11	4	.	.	NOUN
grhe-5548	11	5	2	2	NUM
grhe-5548	11	6	,	,	PUNCT
grhe-5548	11	7	2023	2023	NUM
grhe-5548	11	8	33	33	NUM
grhe-5548	11	9	published	publish	VERB
grhe-5548	11	10	by	by	ADP
grhe-5548	11	11	scholink	scholink	PROPN
grhe-5548	11	12	inc	inc	PROPN
grhe-5548	11	13	.	.	PROPN
grhe-5548	11	14	1	1	NUM
grhe-5548	11	15	.	.	PUNCT
grhe-5548	11	16	introduction	introduction	NOUN
grhe-5548	11	17	history	history	NOUN
grhe-5548	11	18	of	of	ADP
grhe-5548	11	19	mathematics	mathematics	NOUN
grhe-5548	11	20	is	be	AUX
grhe-5548	11	21	more	more	ADJ
grhe-5548	11	22	than	than	ADP
grhe-5548	11	23	a	a	DET
grhe-5548	11	24	few	few	ADJ
grhe-5548	11	25	amusing	amusing	ADJ
grhe-5548	11	26	and	and	CCONJ
grhe-5548	11	27	enjoyable	enjoyable	ADJ
grhe-5548	11	28	anecdotes	anecdote	NOUN
grhe-5548	11	29	and/or	and/or	CCONJ
grhe-5548	11	30	some	some	DET
grhe-5548	11	31	unverifiable	unverifiable	ADJ
grhe-5548	11	32	apocrypha	apocrypha	NOUN
grhe-5548	11	33	.	.	PUNCT
grhe-5548	12	1	indeed	indeed	ADV
grhe-5548	12	2	,	,	PUNCT
grhe-5548	12	3	it	it	PRON
grhe-5548	12	4	is	be	AUX
grhe-5548	12	5	an	an	DET
grhe-5548	12	6	account	account	NOUN
grhe-5548	12	7	of	of	ADP
grhe-5548	12	8	the	the	DET
grhe-5548	12	9	process	process	NOUN
grhe-5548	12	10	of	of	ADP
grhe-5548	12	11	development	development	NOUN
grhe-5548	12	12	of	of	ADP
grhe-5548	12	13	the	the	DET
grhe-5548	12	14	discipline	discipline	NOUN
grhe-5548	12	15	over	over	ADP
grhe-5548	12	16	long	long	ADJ
grhe-5548	12	17	periods	period	NOUN
grhe-5548	12	18	of	of	ADP
grhe-5548	12	19	time	time	NOUN
grhe-5548	12	20	and	and	CCONJ
grhe-5548	12	21	in	in	ADP
grhe-5548	12	22	different	different	ADJ
grhe-5548	12	23	places	place	NOUN
grhe-5548	12	24	using	use	VERB
grhe-5548	12	25	a	a	DET
grhe-5548	12	26	variety	variety	NOUN
grhe-5548	12	27	of	of	ADP
grhe-5548	12	28	valid	valid	ADJ
grhe-5548	12	29	ways	way	NOUN
grhe-5548	12	30	of	of	ADP
grhe-5548	12	31	constructing	construct	VERB
grhe-5548	12	32	concepts	concept	NOUN
grhe-5548	12	33	and	and	CCONJ
grhe-5548	12	34	proofs	proof	NOUN
grhe-5548	12	35	.	.	PUNCT
grhe-5548	13	1	as	as	ADP
grhe-5548	13	2	such	such	ADJ
grhe-5548	13	3	,	,	PUNCT
grhe-5548	13	4	it	it	PRON
grhe-5548	13	5	fosters	foster	VERB
grhe-5548	13	6	flexibility	flexibility	NOUN
grhe-5548	13	7	and	and	CCONJ
grhe-5548	13	8	creativity	creativity	NOUN
grhe-5548	13	9	in	in	ADP
grhe-5548	13	10	the	the	DET
grhe-5548	13	11	learners	learner	NOUN
grhe-5548	13	12	,	,	PUNCT
grhe-5548	13	13	and	and	CCONJ
grhe-5548	13	14	provides	provide	VERB
grhe-5548	13	15	them	they	PRON
grhe-5548	13	16	with	with	ADP
grhe-5548	13	17	crucial	crucial	ADJ
grhe-5548	13	18	sources	source	NOUN
grhe-5548	13	19	of	of	ADP
grhe-5548	13	20	inspiration	inspiration	NOUN
grhe-5548	13	21	,	,	PUNCT
grhe-5548	13	22	insight	insight	NOUN
grhe-5548	13	23	,	,	PUNCT
grhe-5548	13	24	and	and	CCONJ
grhe-5548	13	25	motivation	motivation	NOUN
grhe-5548	13	26	.	.	PUNCT
grhe-5548	14	1	it	it	PRON
grhe-5548	14	2	also	also	ADV
grhe-5548	14	3	presents	present	VERB
grhe-5548	14	4	mathematics	mathematic	NOUN
grhe-5548	14	5	within	within	ADP
grhe-5548	14	6	a	a	DET
grhe-5548	14	7	context	context	NOUN
grhe-5548	14	8	that	that	PRON
grhe-5548	14	9	corroborates	corroborate	VERB
grhe-5548	14	10	the	the	DET
grhe-5548	14	11	notion	notion	NOUN
grhe-5548	14	12	that	that	SCONJ
grhe-5548	14	13	this	this	DET
grhe-5548	14	14	discipline	discipline	NOUN
grhe-5548	14	15	is	be	AUX
grhe-5548	14	16	a	a	DET
grhe-5548	14	17	dynamic	dynamic	ADJ
grhe-5548	14	18	,	,	PUNCT
grhe-5548	14	19	continuously	continuously	ADV
grhe-5548	14	20	transmuting	transmute	VERB
grhe-5548	14	21	field	field	NOUN
grhe-5548	14	22	of	of	ADP
grhe-5548	14	23	study	study	NOUN
grhe-5548	14	24	that	that	PRON
grhe-5548	14	25	is	be	AUX
grhe-5548	14	26	open	open	ADJ
grhe-5548	14	27	to	to	ADP
grhe-5548	14	28	refutation	refutation	NOUN
grhe-5548	14	29	and	and	CCONJ
grhe-5548	14	30	revision	revision	NOUN
grhe-5548	14	31	;	;	PUNCT
grhe-5548	14	32	in	in	ADP
grhe-5548	14	33	other	other	ADJ
grhe-5548	14	34	words	word	NOUN
grhe-5548	14	35	,	,	PUNCT
grhe-5548	14	36	it	it	PRON
grhe-5548	14	37	humanizes	humanize	VERB
grhe-5548	14	38	mathematics	mathematic	NOUN
grhe-5548	14	39	(	(	PUNCT
grhe-5548	14	40	bidwell	bidwell	PROPN
grhe-5548	14	41	,	,	PUNCT
grhe-5548	14	42	1993	1993	NUM
grhe-5548	14	43	)	)	PUNCT
grhe-5548	14	44	.	.	PUNCT
grhe-5548	15	1	it	it	PRON
grhe-5548	15	2	is	be	AUX
grhe-5548	15	3	now	now	ADV
grhe-5548	15	4	well	well	ADV
grhe-5548	15	5	accepted	accept	VERB
grhe-5548	15	6	that	that	SCONJ
grhe-5548	15	7	inclusion	inclusion	NOUN
grhe-5548	15	8	of	of	ADP
grhe-5548	15	9	the	the	DET
grhe-5548	15	10	history	history	NOUN
grhe-5548	15	11	of	of	ADP
grhe-5548	15	12	mathematics	mathematic	NOUN
grhe-5548	15	13	in	in	ADP
grhe-5548	15	14	the	the	DET
grhe-5548	15	15	classroom	classroom	NOUN
grhe-5548	15	16	not	not	PART
grhe-5548	15	17	only	only	ADV
grhe-5548	15	18	refines	refine	VERB
grhe-5548	15	19	problem	problem	NOUN
grhe-5548	15	20	-	-	PUNCT
grhe-5548	15	21	solving	solve	VERB
grhe-5548	15	22	skills	skill	NOUN
grhe-5548	15	23	and	and	CCONJ
grhe-5548	15	24	helps	help	VERB
grhe-5548	15	25	students	student	NOUN
grhe-5548	15	26	make	make	VERB
grhe-5548	15	27	useful	useful	ADJ
grhe-5548	15	28	mathematical	mathematical	ADJ
grhe-5548	15	29	connections	connection	NOUN
grhe-5548	15	30	(	(	PUNCT
grhe-5548	15	31	jankvist	jankvist	NOUN
grhe-5548	15	32	,	,	PUNCT
grhe-5548	15	33	2009	2009	NUM
grhe-5548	15	34	)	)	PUNCT
grhe-5548	15	35	,	,	PUNCT
grhe-5548	15	36	but	but	CCONJ
grhe-5548	15	37	it	it	PRON
grhe-5548	15	38	also	also	ADV
grhe-5548	15	39	emphasizes	emphasize	VERB
grhe-5548	15	40	the	the	DET
grhe-5548	15	41	interaction	interaction	NOUN
grhe-5548	15	42	between	between	ADP
grhe-5548	15	43	mathematics	mathematic	NOUN
grhe-5548	15	44	and	and	CCONJ
grhe-5548	15	45	society	society	NOUN
grhe-5548	15	46	(	(	PUNCT
grhe-5548	15	47	wilson	wilson	PROPN
grhe-5548	15	48	&	&	CCONJ
grhe-5548	15	49	chauvot	chauvot	PROPN
grhe-5548	15	50	,	,	PUNCT
grhe-5548	15	51	2000	2000	NUM
grhe-5548	15	52	)	)	PUNCT
grhe-5548	15	53	.	.	PUNCT
grhe-5548	16	1	to	to	PART
grhe-5548	16	2	sum	sum	VERB
grhe-5548	16	3	up	up	ADP
grhe-5548	16	4	,	,	PUNCT
grhe-5548	16	5	history	history	NOUN
grhe-5548	16	6	,	,	PUNCT
grhe-5548	16	7	introduced	introduce	VERB
grhe-5548	16	8	in	in	ADP
grhe-5548	16	9	a	a	DET
grhe-5548	16	10	dynamic	dynamic	ADJ
grhe-5548	16	11	and	and	CCONJ
grhe-5548	16	12	vigorous	vigorous	ADJ
grhe-5548	16	13	manner	manner	NOUN
grhe-5548	16	14	,	,	PUNCT
grhe-5548	16	15	has	have	VERB
grhe-5548	16	16	an	an	DET
grhe-5548	16	17	essentially	essentially	ADV
grhe-5548	16	18	fundamental	fundamental	ADJ
grhe-5548	16	19	role	role	NOUN
grhe-5548	16	20	to	to	PART
grhe-5548	16	21	play	play	VERB
grhe-5548	16	22	in	in	ADP
grhe-5548	16	23	today	today	NOUN
grhe-5548	16	24	’s	’s	PART
grhe-5548	16	25	mathematics	mathematics	NOUN
grhe-5548	16	26	classrooms	classroom	NOUN
grhe-5548	16	27	.	.	PUNCT
grhe-5548	17	1	it	it	PRON
grhe-5548	17	2	demystifies	demystify	VERB
grhe-5548	17	3	and	and	CCONJ
grhe-5548	17	4	clarifies	clarify	VERB
grhe-5548	17	5	mathematics	mathematic	NOUN
grhe-5548	17	6	by	by	ADP
grhe-5548	17	7	showing	show	VERB
grhe-5548	17	8	that	that	SCONJ
grhe-5548	17	9	it	it	PRON
grhe-5548	17	10	is	be	AUX
grhe-5548	17	11	the	the	DET
grhe-5548	17	12	creation	creation	NOUN
grhe-5548	17	13	of	of	ADP
grhe-5548	17	14	human	human	ADJ
grhe-5548	17	15	beings	being	NOUN
grhe-5548	17	16	and	and	CCONJ
grhe-5548	17	17	thus	thus	ADV
grhe-5548	17	18	broadens	broaden	VERB
grhe-5548	17	19	the	the	DET
grhe-5548	17	20	knowledge	knowledge	NOUN
grhe-5548	17	21	that	that	PRON
grhe-5548	17	22	students	student	NOUN
grhe-5548	17	23	construct	construct	VERB
grhe-5548	17	24	in	in	ADP
grhe-5548	17	25	a	a	DET
grhe-5548	17	26	mathematics	mathematics	NOUN
grhe-5548	17	27	class	class	NOUN
grhe-5548	17	28	(	(	PUNCT
grhe-5548	17	29	marshall	marshall	PROPN
grhe-5548	17	30	&	&	CCONJ
grhe-5548	17	31	rich	rich	PROPN
grhe-5548	17	32	,	,	PUNCT
grhe-5548	17	33	2000	2000	NUM
grhe-5548	17	34	)	)	PUNCT
grhe-5548	17	35	.	.	PUNCT
grhe-5548	18	1	2	2	X
grhe-5548	18	2	.	.	X
grhe-5548	18	3	methodology	methodology	NOUN
grhe-5548	18	4	to	to	PART
grhe-5548	18	5	accentuate	accentuate	VERB
grhe-5548	18	6	these	these	DET
grhe-5548	18	7	points	point	NOUN
grhe-5548	18	8	,	,	PUNCT
grhe-5548	18	9	in	in	ADP
grhe-5548	18	10	this	this	DET
grhe-5548	18	11	paper	paper	NOUN
grhe-5548	18	12	,	,	PUNCT
grhe-5548	18	13	we	we	PRON
grhe-5548	18	14	will	will	AUX
grhe-5548	18	15	deal	deal	VERB
grhe-5548	18	16	with	with	ADP
grhe-5548	18	17	a	a	DET
grhe-5548	18	18	specific	specific	ADJ
grhe-5548	18	19	example	example	NOUN
grhe-5548	18	20	:	:	PUNCT
grhe-5548	18	21	the	the	DET
grhe-5548	18	22	historical	historical	ADJ
grhe-5548	18	23	development	development	NOUN
grhe-5548	18	24	of	of	ADP
grhe-5548	18	25	the	the	DET
grhe-5548	18	26	solution	solution	NOUN
grhe-5548	18	27	of	of	ADP
grhe-5548	18	28	the	the	DET
grhe-5548	18	29	cubic	cubic	ADJ
grhe-5548	18	30	equation	equation	NOUN
grhe-5548	18	31	.	.	PUNCT
grhe-5548	19	1	there	there	PRON
grhe-5548	19	2	are	be	VERB
grhe-5548	19	3	different	different	ADJ
grhe-5548	19	4	ways	way	NOUN
grhe-5548	19	5	of	of	ADP
grhe-5548	19	6	using	use	VERB
grhe-5548	19	7	history	history	NOUN
grhe-5548	19	8	in	in	ADP
grhe-5548	19	9	the	the	DET
grhe-5548	19	10	classroom	classroom	NOUN
grhe-5548	19	11	(	(	PUNCT
grhe-5548	19	12	bidwell	bidwell	PROPN
grhe-5548	19	13	,	,	PUNCT
grhe-5548	19	14	1993	1993	NUM
grhe-5548	19	15	)	)	PUNCT
grhe-5548	19	16	.	.	PUNCT
grhe-5548	20	1	for	for	ADP
grhe-5548	20	2	example	example	NOUN
grhe-5548	20	3	,	,	PUNCT
grhe-5548	20	4	we	we	PRON
grhe-5548	20	5	can	can	AUX
grhe-5548	20	6	inject	inject	VERB
grhe-5548	20	7	anecdotal	anecdotal	ADJ
grhe-5548	20	8	material	material	NOUN
grhe-5548	20	9	as	as	SCONJ
grhe-5548	20	10	the	the	DET
grhe-5548	20	11	course	course	NOUN
grhe-5548	20	12	is	be	AUX
grhe-5548	20	13	presented	present	VERB
grhe-5548	20	14	,	,	PUNCT
grhe-5548	20	15	that	that	ADV
grhe-5548	20	16	is	is	ADV
grhe-5548	20	17	,	,	PUNCT
grhe-5548	20	18	we	we	PRON
grhe-5548	20	19	can	can	AUX
grhe-5548	20	20	make	make	VERB
grhe-5548	20	21	historical	historical	ADJ
grhe-5548	20	22	references	reference	NOUN
grhe-5548	20	23	to	to	ADP
grhe-5548	20	24	coursework	coursework	NOUN
grhe-5548	20	25	while	while	SCONJ
grhe-5548	20	26	it	it	PRON
grhe-5548	20	27	is	be	AUX
grhe-5548	20	28	being	be	AUX
grhe-5548	20	29	covered	cover	VERB
grhe-5548	20	30	.	.	PUNCT
grhe-5548	21	1	our	our	PRON
grhe-5548	21	2	methodological	methodological	ADJ
grhe-5548	21	3	approach	approach	NOUN
grhe-5548	21	4	is	be	AUX
grhe-5548	21	5	somewhat	somewhat	ADV
grhe-5548	21	6	different	different	ADJ
grhe-5548	21	7	:	:	PUNCT
grhe-5548	21	8	we	we	PRON
grhe-5548	21	9	aim	aim	VERB
grhe-5548	21	10	to	to	PART
grhe-5548	21	11	make	make	VERB
grhe-5548	21	12	the	the	DET
grhe-5548	21	13	accurate	accurate	ADJ
grhe-5548	21	14	historical	historical	ADJ
grhe-5548	21	15	developments	development	NOUN
grhe-5548	21	16	of	of	ADP
grhe-5548	21	17	a	a	DET
grhe-5548	21	18	topic	topic	NOUN
grhe-5548	21	19	(	(	PUNCT
grhe-5548	21	20	namely	namely	ADV
grhe-5548	21	21	the	the	DET
grhe-5548	21	22	categorization	categorization	NOUN
grhe-5548	21	23	of	of	ADP
grhe-5548	21	24	the	the	DET
grhe-5548	21	25	cubic	cubic	ADJ
grhe-5548	21	26	equation	equation	NOUN
grhe-5548	21	27	)	)	PUNCT
grhe-5548	21	28	a	a	DET
grhe-5548	21	29	part	part	NOUN
grhe-5548	21	30	of	of	ADP
grhe-5548	21	31	the	the	DET
grhe-5548	21	32	course	course	NOUN
grhe-5548	21	33	(	(	PUNCT
grhe-5548	21	34	algebra	algebra	NOUN
grhe-5548	21	35	or	or	CCONJ
grhe-5548	21	36	pre	pre	NOUN
grhe-5548	21	37	-	-	NOUN
grhe-5548	21	38	calculus	calculus	ADJ
grhe-5548	21	39	)	)	PUNCT
grhe-5548	21	40	.	.	PUNCT
grhe-5548	22	1	this	this	PRON
grhe-5548	22	2	is	be	AUX
grhe-5548	22	3	what	what	PRON
grhe-5548	22	4	the	the	DET
grhe-5548	22	5	example	example	NOUN
grhe-5548	22	6	given	give	VERB
grhe-5548	22	7	in	in	ADP
grhe-5548	22	8	this	this	DET
grhe-5548	22	9	article	article	NOUN
grhe-5548	22	10	is	be	AUX
grhe-5548	22	11	trying	try	VERB
grhe-5548	22	12	to	to	PART
grhe-5548	22	13	achieve	achieve	VERB
grhe-5548	22	14	.	.	PUNCT
grhe-5548	23	1	as	as	SCONJ
grhe-5548	23	2	is	be	AUX
grhe-5548	23	3	well	well	ADV
grhe-5548	23	4	known	know	VERB
grhe-5548	23	5	,	,	PUNCT
grhe-5548	23	6	today	today	NOUN
grhe-5548	23	7	,	,	PUNCT
grhe-5548	23	8	using	use	VERB
grhe-5548	23	9	basic	basic	ADJ
grhe-5548	23	10	algebraic	algebraic	ADJ
grhe-5548	23	11	tools	tool	NOUN
grhe-5548	23	12	,	,	PUNCT
grhe-5548	23	13	the	the	DET
grhe-5548	23	14	roots	root	NOUN
grhe-5548	23	15	of	of	ADP
grhe-5548	23	16	the	the	DET
grhe-5548	23	17	cubic	cubic	ADJ
grhe-5548	23	18	equation	equation	NOUN
grhe-5548	23	19	can	can	AUX
grhe-5548	23	20	easily	easily	ADV
grhe-5548	23	21	be	be	AUX
grhe-5548	23	22	computed	compute	VERB
grhe-5548	23	23	.	.	PUNCT
grhe-5548	24	1	in	in	ADP
grhe-5548	24	2	fact	fact	NOUN
grhe-5548	24	3	,	,	PUNCT
grhe-5548	24	4	using	use	VERB
grhe-5548	24	5	cardano	cardano	PROPN
grhe-5548	24	6	’s	’s	PART
grhe-5548	24	7	formula	formula	NOUN
grhe-5548	24	8	we	we	PRON
grhe-5548	24	9	have	have	VERB
grhe-5548	24	10	in	in	ADP
grhe-5548	24	11	case	case	NOUN
grhe-5548	24	12	an	an	DET
grhe-5548	24	13	approximate	approximate	ADJ
grhe-5548	24	14	solution	solution	NOUN
grhe-5548	24	15	is	be	AUX
grhe-5548	24	16	needed	need	VERB
grhe-5548	24	17	,	,	PUNCT
grhe-5548	24	18	we	we	PRON
grhe-5548	24	19	let	let	VERB
grhe-5548	24	20	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	24	21	global	global	ADJ
grhe-5548	24	22	research	research	NOUN
grhe-5548	24	23	in	in	ADP
grhe-5548	24	24	higher	high	ADJ
grhe-5548	24	25	education	education	NOUN
grhe-5548	24	26	vol	vol	NOUN
grhe-5548	24	27	.	.	PROPN
grhe-5548	25	1	6	6	NUM
grhe-5548	25	2	,	,	PUNCT
grhe-5548	25	3	no	no	INTJ
grhe-5548	25	4	.	.	NOUN
grhe-5548	25	5	2	2	NUM
grhe-5548	25	6	,	,	PUNCT
grhe-5548	25	7	2023	2023	NUM
grhe-5548	25	8	34	34	NUM
grhe-5548	25	9	published	publish	VERB
grhe-5548	25	10	by	by	ADP
grhe-5548	25	11	scholink	scholink	PROPN
grhe-5548	25	12	inc	inc	PROPN
grhe-5548	25	13	.	.	PROPN
grhe-5548	25	14	and	and	CCONJ
grhe-5548	25	15	apply	apply	VERB
grhe-5548	25	16	newton	newton	PROPN
grhe-5548	25	17	-	-	PUNCT
grhe-5548	25	18	raphson	raphson	NOUN
grhe-5548	25	19	recursion	recursion	NOUN
grhe-5548	25	20	formula	formula	NOUN
grhe-5548	25	21	that	that	PRON
grhe-5548	25	22	is	be	AUX
grhe-5548	25	23	,	,	PUNCT
grhe-5548	25	24	we	we	PRON
grhe-5548	25	25	iterate	iterate	VERB
grhe-5548	25	26	until	until	ADP
grhe-5548	25	27	,	,	PUNCT
grhe-5548	25	28	where	where	SCONJ
grhe-5548	25	29	is	be	AUX
grhe-5548	25	30	a	a	DET
grhe-5548	25	31	given	give	VERB
grhe-5548	25	32	tolerance	tolerance	NOUN
grhe-5548	25	33	.	.	PUNCT
grhe-5548	26	1	in	in	ADP
grhe-5548	26	2	this	this	DET
grhe-5548	26	3	paper	paper	NOUN
grhe-5548	26	4	,	,	PUNCT
grhe-5548	26	5	we	we	PRON
grhe-5548	26	6	are	be	AUX
grhe-5548	26	7	interested	interested	ADJ
grhe-5548	26	8	in	in	ADP
grhe-5548	26	9	one	one	NUM
grhe-5548	26	10	particular	particular	ADJ
grhe-5548	26	11	stage	stage	NOUN
grhe-5548	26	12	in	in	ADP
grhe-5548	26	13	the	the	DET
grhe-5548	26	14	long	long	ADJ
grhe-5548	26	15	journey	journey	NOUN
grhe-5548	26	16	that	that	PRON
grhe-5548	26	17	started	start	VERB
grhe-5548	26	18	with	with	ADP
grhe-5548	26	19	some	some	DET
grhe-5548	26	20	cuneiform	cuneiform	NOUN
grhe-5548	26	21	tablets	tablet	NOUN
grhe-5548	26	22	and	and	CCONJ
grhe-5548	26	23	ended	end	VERB
grhe-5548	26	24	up	up	ADP
grhe-5548	26	25	with	with	ADP
grhe-5548	26	26	not	not	PART
grhe-5548	26	27	only	only	ADV
grhe-5548	26	28	the	the	DET
grhe-5548	26	29	general	general	ADJ
grhe-5548	26	30	solution	solution	NOUN
grhe-5548	26	31	techniques	technique	NOUN
grhe-5548	26	32	,	,	PUNCT
grhe-5548	26	33	but	but	CCONJ
grhe-5548	26	34	also	also	ADV
grhe-5548	26	35	the	the	DET
grhe-5548	26	36	invention	invention	NOUN
grhe-5548	26	37	of	of	ADP
grhe-5548	26	38	complex	complex	ADJ
grhe-5548	26	39	numbers	number	NOUN
grhe-5548	26	40	:	:	PUNCT
grhe-5548	26	41	specifically	specifically	ADV
grhe-5548	26	42	,	,	PUNCT
grhe-5548	26	43	the	the	DET
grhe-5548	26	44	important	important	ADJ
grhe-5548	26	45	step	step	NOUN
grhe-5548	26	46	of	of	ADP
grhe-5548	26	47	classification	classification	NOUN
grhe-5548	26	48	of	of	ADP
grhe-5548	26	49	the	the	DET
grhe-5548	26	50	cubic	cubic	ADJ
grhe-5548	26	51	equations	equation	NOUN
grhe-5548	26	52	.	.	PUNCT
grhe-5548	27	1	3	3	X
grhe-5548	27	2	.	.	X
grhe-5548	27	3	a	a	DET
grhe-5548	27	4	brief	brief	ADJ
grhe-5548	27	5	history	history	NOUN
grhe-5548	27	6	cubic	cubic	ADJ
grhe-5548	27	7	equations	equation	NOUN
grhe-5548	27	8	were	be	AUX
grhe-5548	27	9	known	know	VERB
grhe-5548	27	10	to	to	ADP
grhe-5548	27	11	the	the	DET
grhe-5548	27	12	ancient	ancient	ADJ
grhe-5548	27	13	babylonian	babylonian	ADJ
grhe-5548	27	14	,	,	PUNCT
grhe-5548	27	15	greek	greek	ADJ
grhe-5548	27	16	,	,	PUNCT
grhe-5548	27	17	chinese	chinese	PROPN
grhe-5548	27	18	,	,	PUNCT
grhe-5548	27	19	indian	indian	ADJ
grhe-5548	27	20	,	,	PUNCT
grhe-5548	27	21	and	and	CCONJ
grhe-5548	27	22	egyptian	egyptian	ADJ
grhe-5548	27	23	mathematicians	mathematician	NOUN
grhe-5548	27	24	(	(	PUNCT
grhe-5548	27	25	van	van	PROPN
grhe-5548	27	26	der	der	PROPN
grhe-5548	27	27	waerden	waerden	VERB
grhe-5548	27	28	,	,	PUNCT
grhe-5548	27	29	1983	1983	NUM
grhe-5548	27	30	)	)	PUNCT
grhe-5548	27	31	.	.	PUNCT
grhe-5548	28	1	indeed	indeed	ADV
grhe-5548	28	2	,	,	PUNCT
grhe-5548	28	3	babylonians	babylonians	PROPN
grhe-5548	28	4	had	have	VERB
grhe-5548	28	5	extensive	extensive	ADJ
grhe-5548	28	6	tables	table	NOUN
grhe-5548	28	7	for	for	ADP
grhe-5548	28	8	calculating	calculate	VERB
grhe-5548	28	9	cubes	cube	NOUN
grhe-5548	28	10	and	and	CCONJ
grhe-5548	28	11	cube	cube	NOUN
grhe-5548	28	12	roots	root	NOUN
grhe-5548	28	13	(	(	PUNCT
grhe-5548	28	14	cooke	cooke	PROPN
grhe-5548	28	15	,	,	PUNCT
grhe-5548	28	16	2012	2012	NUM
grhe-5548	28	17	)	)	PUNCT
grhe-5548	28	18	.	.	PUNCT
grhe-5548	29	1	the	the	DET
grhe-5548	29	2	greek	greek	PROPN
grhe-5548	29	3	involvement	involvement	NOUN
grhe-5548	29	4	with	with	ADP
grhe-5548	29	5	the	the	DET
grhe-5548	29	6	cubic	cubic	ADJ
grhe-5548	29	7	equations	equation	NOUN
grhe-5548	29	8	grew	grow	VERB
grhe-5548	29	9	out	out	ADP
grhe-5548	29	10	of	of	ADP
grhe-5548	29	11	their	their	PRON
grhe-5548	29	12	desire	desire	NOUN
grhe-5548	29	13	to	to	PART
grhe-5548	29	14	solve	solve	VERB
grhe-5548	29	15	the	the	DET
grhe-5548	29	16	problems	problem	NOUN
grhe-5548	29	17	of	of	ADP
grhe-5548	29	18	doubling	doubling	NOUN
grhe-5548	29	19	of	of	ADP
grhe-5548	29	20	the	the	DET
grhe-5548	29	21	cube	cube	NOUN
grhe-5548	29	22	and	and	CCONJ
grhe-5548	29	23	trisection	trisection	NOUN
grhe-5548	29	24	of	of	ADP
grhe-5548	29	25	an	an	DET
grhe-5548	29	26	angle	angle	NOUN
grhe-5548	29	27	(	(	PUNCT
grhe-5548	29	28	kline	kline	PROPN
grhe-5548	29	29	,	,	PUNCT
grhe-5548	29	30	1990	1990	NUM
grhe-5548	29	31	)	)	PUNCT
grhe-5548	29	32	.	.	PUNCT
grhe-5548	30	1	archimedes	archimedes	PROPN
grhe-5548	30	2	(	(	PUNCT
grhe-5548	30	3	c.	c.	PROPN
grhe-5548	30	4	287	287	NUM
grhe-5548	30	5	bce	bce	PROPN
grhe-5548	30	6	-	-	PUNCT
grhe-5548	30	7	c.	c.	PROPN
grhe-5548	30	8	212	212	NUM
grhe-5548	30	9	bce	bce	NOUN
grhe-5548	30	10	)	)	PUNCT
grhe-5548	30	11	in	in	ADP
grhe-5548	30	12	his	his	PRON
grhe-5548	30	13	on	on	ADP
grhe-5548	30	14	the	the	DET
grhe-5548	30	15	sphere	sphere	NOUN
grhe-5548	30	16	and	and	CCONJ
grhe-5548	30	17	cylinder	cylinder	PROPN
grhe-5548	30	18	ii	ii	PROPN
grhe-5548	30	19	,	,	PUNCT
grhe-5548	30	20	dealt	deal	VERB
grhe-5548	30	21	with	with	ADP
grhe-5548	30	22	the	the	DET
grhe-5548	30	23	doubling	doubling	NOUN
grhe-5548	30	24	of	of	ADP
grhe-5548	30	25	the	the	DET
grhe-5548	30	26	cube	cube	NOUN
grhe-5548	30	27	problem	problem	NOUN
grhe-5548	30	28	and	and	CCONJ
grhe-5548	30	29	reduced	reduce	VERB
grhe-5548	30	30	the	the	DET
grhe-5548	30	31	problem	problem	NOUN
grhe-5548	30	32	to	to	ADP
grhe-5548	30	33	the	the	DET
grhe-5548	30	34	solution	solution	NOUN
grhe-5548	30	35	of	of	ADP
grhe-5548	30	36	some	some	DET
grhe-5548	30	37	cubic	cubic	ADJ
grhe-5548	30	38	equations	equation	NOUN
grhe-5548	30	39	of	of	ADP
grhe-5548	30	40	the	the	DET
grhe-5548	30	41	type	type	NOUN
grhe-5548	30	42	and	and	CCONJ
grhe-5548	30	43	(	(	PUNCT
grhe-5548	30	44	katz	katz	PROPN
grhe-5548	30	45	,	,	PUNCT
grhe-5548	30	46	2004	2004	NUM
grhe-5548	30	47	)	)	PUNCT
grhe-5548	30	48	.	.	PUNCT
grhe-5548	31	1	it	it	PRON
grhe-5548	31	2	was	be	AUX
grhe-5548	31	3	also	also	ADV
grhe-5548	31	4	shown	show	VERB
grhe-5548	31	5	that	that	SCONJ
grhe-5548	31	6	the	the	DET
grhe-5548	31	7	angle	angle	NOUN
grhe-5548	31	8	trisection	trisection	NOUN
grhe-5548	31	9	problem	problem	NOUN
grhe-5548	31	10	could	could	AUX
grhe-5548	31	11	be	be	AUX
grhe-5548	31	12	written	write	VERB
grhe-5548	31	13	as	as	ADP
grhe-5548	31	14	or	or	CCONJ
grhe-5548	31	15	equivalently	equivalently	ADV
grhe-5548	31	16	as	as	ADP
grhe-5548	31	17	another	another	DET
grhe-5548	31	18	cubic	cubic	ADJ
grhe-5548	31	19	equation	equation	NOUN
grhe-5548	31	20	.	.	PUNCT
grhe-5548	32	1	in	in	ADP
grhe-5548	32	2	the	the	DET
grhe-5548	32	3	3rd	3rd	ADJ
grhe-5548	32	4	century	century	NOUN
grhe-5548	32	5	ad	ad	NOUN
grhe-5548	32	6	,	,	PUNCT
grhe-5548	32	7	diophantus	diophantus	NOUN
grhe-5548	32	8	(	(	PUNCT
grhe-5548	32	9	200	200	NUM
grhe-5548	32	10	-	-	SYM
grhe-5548	32	11	284	284	NUM
grhe-5548	32	12	)	)	PUNCT
grhe-5548	32	13	,	,	PUNCT
grhe-5548	32	14	in	in	ADP
grhe-5548	32	15	his	his	PRON
grhe-5548	32	16	famous	famous	ADJ
grhe-5548	32	17	book	book	NOUN
grhe-5548	32	18	arithmetica	arithmetica	NOUN
grhe-5548	32	19	,	,	PUNCT
grhe-5548	32	20	proposed	propose	VERB
grhe-5548	32	21	the	the	DET
grhe-5548	32	22	following	follow	VERB
grhe-5548	32	23	interesting	interesting	ADJ
grhe-5548	32	24	problem	problem	NOUN
grhe-5548	32	25	:	:	PUNCT
grhe-5548	32	26	find	find	VERB
grhe-5548	32	27	a	a	DET
grhe-5548	32	28	right	right	ADV
grhe-5548	32	29	-	-	PUNCT
grhe-5548	32	30	angled	angle	VERB
grhe-5548	32	31	triangle	triangle	NOUN
grhe-5548	32	32	such	such	ADJ
grhe-5548	32	33	that	that	SCONJ
grhe-5548	32	34	its	its	PRON
grhe-5548	32	35	area	area	NOUN
grhe-5548	32	36	added	add	VERB
grhe-5548	32	37	to	to	ADP
grhe-5548	32	38	one	one	NUM
grhe-5548	32	39	of	of	ADP
grhe-5548	32	40	the	the	DET
grhe-5548	32	41	perpendicular	perpendicular	ADJ
grhe-5548	32	42	sides	side	NOUN
grhe-5548	32	43	makes	make	VERB
grhe-5548	32	44	a	a	DET
grhe-5548	32	45	square	square	NOUN
grhe-5548	32	46	,	,	PUNCT
grhe-5548	32	47	while	while	SCONJ
grhe-5548	32	48	its	its	PRON
grhe-5548	32	49	perimeter	perimeter	NOUN
grhe-5548	32	50	is	be	AUX
grhe-5548	32	51	a	a	DET
grhe-5548	32	52	cube	cube	NOUN
grhe-5548	32	53	.	.	PUNCT
grhe-5548	33	1	it	it	PRON
grhe-5548	33	2	was	be	AUX
grhe-5548	33	3	shown	show	VERB
grhe-5548	33	4	by	by	ADP
grhe-5548	33	5	diophantus	diophantus	NOUN
grhe-5548	33	6	that	that	PRON
grhe-5548	33	7	the	the	DET
grhe-5548	33	8	solution	solution	NOUN
grhe-5548	33	9	of	of	ADP
grhe-5548	33	10	this	this	DET
grhe-5548	33	11	problem	problem	NOUN
grhe-5548	33	12	required	require	VERB
grhe-5548	33	13	finding	find	VERB
grhe-5548	33	14	the	the	DET
grhe-5548	33	15	solution	solution	NOUN
grhe-5548	33	16	of	of	ADP
grhe-5548	33	17	the	the	DET
grhe-5548	33	18	equation	equation	NOUN
grhe-5548	33	19	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	33	20	global	global	ADJ
grhe-5548	33	21	research	research	NOUN
grhe-5548	33	22	in	in	ADP
grhe-5548	33	23	higher	high	ADJ
grhe-5548	33	24	education	education	NOUN
grhe-5548	33	25	vol	vol	NOUN
grhe-5548	33	26	.	.	PROPN
grhe-5548	34	1	6	6	NUM
grhe-5548	34	2	,	,	PUNCT
grhe-5548	34	3	no	no	INTJ
grhe-5548	34	4	.	.	NOUN
grhe-5548	34	5	2	2	NUM
grhe-5548	34	6	,	,	PUNCT
grhe-5548	34	7	2023	2023	NUM
grhe-5548	34	8	35	35	NUM
grhe-5548	34	9	published	publish	VERB
grhe-5548	34	10	by	by	ADP
grhe-5548	34	11	scholink	scholink	PROPN
grhe-5548	34	12	inc	inc	PROPN
grhe-5548	34	13	.	.	PROPN
grhe-5548	34	14	diophantus	diophantus	PROPN
grhe-5548	34	15	found	find	VERB
grhe-5548	34	16	the	the	DET
grhe-5548	34	17	solution	solution	NOUN
grhe-5548	34	18	to	to	ADP
grhe-5548	34	19	this	this	DET
grhe-5548	34	20	equation	equation	NOUN
grhe-5548	34	21	to	to	PART
grhe-5548	34	22	be	be	AUX
grhe-5548	34	23	(	(	PUNCT
grhe-5548	34	24	heath	heath	PROPN
grhe-5548	34	25	,	,	PUNCT
grhe-5548	34	26	2009	2009	NUM
grhe-5548	34	27	)	)	PUNCT
grhe-5548	34	28	.	.	PUNCT
grhe-5548	35	1	we	we	PRON
grhe-5548	35	2	also	also	ADV
grhe-5548	35	3	know	know	VERB
grhe-5548	35	4	that	that	SCONJ
grhe-5548	35	5	in	in	ADP
grhe-5548	35	6	the	the	DET
grhe-5548	35	7	7th	7th	ADJ
grhe-5548	35	8	century	century	NOUN
grhe-5548	35	9	,	,	PUNCT
grhe-5548	35	10	the	the	DET
grhe-5548	35	11	chinese	chinese	ADJ
grhe-5548	35	12	mathematician	mathematician	NOUN
grhe-5548	35	13	xiaotong	xiaotong	PROPN
grhe-5548	35	14	solved	solve	VERB
grhe-5548	35	15	some	some	DET
grhe-5548	35	16	cubic	cubic	ADJ
grhe-5548	35	17	equations	equation	NOUN
grhe-5548	35	18	of	of	ADP
grhe-5548	35	19	the	the	DET
grhe-5548	35	20	form	form	NOUN
grhe-5548	35	21	(	(	PUNCT
grhe-5548	35	22	van	van	PROPN
grhe-5548	35	23	der	der	PROPN
grhe-5548	35	24	waerden	waerden	ADJ
grhe-5548	35	25	,	,	PUNCT
grhe-5548	35	26	1985	1985	NUM
grhe-5548	35	27	)	)	PUNCT
grhe-5548	35	28	.	.	PUNCT
grhe-5548	36	1	however	however	ADV
grhe-5548	36	2	,	,	PUNCT
grhe-5548	36	3	it	it	PRON
grhe-5548	36	4	should	should	AUX
grhe-5548	36	5	be	be	AUX
grhe-5548	36	6	noted	note	VERB
grhe-5548	36	7	that	that	SCONJ
grhe-5548	36	8	all	all	PRON
grhe-5548	36	9	of	of	ADP
grhe-5548	36	10	the	the	DET
grhe-5548	36	11	above	above	ADJ
grhe-5548	36	12	solutions	solution	NOUN
grhe-5548	36	13	were	be	AUX
grhe-5548	36	14	based	base	VERB
grhe-5548	36	15	on	on	ADP
grhe-5548	36	16	ad	ad	X
grhe-5548	36	17	hoc	hoc	X
grhe-5548	36	18	arguments	argument	NOUN
grhe-5548	36	19	and	and	CCONJ
grhe-5548	36	20	applied	apply	VERB
grhe-5548	36	21	only	only	ADV
grhe-5548	36	22	to	to	ADP
grhe-5548	36	23	specific	specific	ADJ
grhe-5548	36	24	problems	problem	NOUN
grhe-5548	36	25	and	and	CCONJ
grhe-5548	36	26	specific	specific	ADJ
grhe-5548	36	27	equations	equation	NOUN
grhe-5548	36	28	.	.	PUNCT
grhe-5548	37	1	no	no	DET
grhe-5548	37	2	attempts	attempt	NOUN
grhe-5548	37	3	were	be	AUX
grhe-5548	37	4	made	make	VERB
grhe-5548	37	5	to	to	PART
grhe-5548	37	6	obtain	obtain	VERB
grhe-5548	37	7	a	a	DET
grhe-5548	37	8	general	general	ADJ
grhe-5548	37	9	method	method	NOUN
grhe-5548	37	10	for	for	ADP
grhe-5548	37	11	solving	solve	VERB
grhe-5548	37	12	the	the	DET
grhe-5548	37	13	cubic	cubic	ADJ
grhe-5548	37	14	equation	equation	NOUN
grhe-5548	37	15	.	.	PUNCT
grhe-5548	38	1	this	this	PRON
grhe-5548	38	2	all	all	PRON
grhe-5548	38	3	changed	change	VERB
grhe-5548	38	4	in	in	ADP
grhe-5548	38	5	the	the	DET
grhe-5548	38	6	11th	11th	ADJ
grhe-5548	38	7	century	century	NOUN
grhe-5548	38	8	,	,	PUNCT
grhe-5548	38	9	when	when	SCONJ
grhe-5548	38	10	the	the	DET
grhe-5548	38	11	persian	persian	ADJ
grhe-5548	38	12	poet	poet	NOUN
grhe-5548	38	13	-	-	PUNCT
grhe-5548	38	14	mathematician	mathematician	ADJ
grhe-5548	38	15	-	-	PUNCT
grhe-5548	38	16	astronomer	astronomer	NOUN
grhe-5548	38	17	-	-	PUNCT
grhe-5548	38	18	philosopher	philosopher	NOUN
grhe-5548	38	19	,	,	PUNCT
grhe-5548	38	20	omar	omar	PROPN
grhe-5548	38	21	khayyam	khayyam	PROPN
grhe-5548	38	22	(	(	PUNCT
grhe-5548	38	23	1048	1048	NUM
grhe-5548	38	24	-	-	SYM
grhe-5548	38	25	1131	1131	NUM
grhe-5548	38	26	)	)	PUNCT
grhe-5548	38	27	,	,	PUNCT
grhe-5548	38	28	made	make	VERB
grhe-5548	38	29	significant	significant	ADJ
grhe-5548	38	30	progress	progress	NOUN
grhe-5548	38	31	in	in	ADP
grhe-5548	38	32	the	the	DET
grhe-5548	38	33	theory	theory	NOUN
grhe-5548	38	34	of	of	ADP
grhe-5548	38	35	cubic	cubic	ADJ
grhe-5548	38	36	equations	equation	NOUN
grhe-5548	38	37	.	.	PUNCT
grhe-5548	39	1	first	first	ADV
grhe-5548	39	2	of	of	ADP
grhe-5548	39	3	all	all	PRON
grhe-5548	39	4	,	,	PUNCT
grhe-5548	39	5	he	he	PRON
grhe-5548	39	6	realized	realize	VERB
grhe-5548	39	7	that	that	SCONJ
grhe-5548	39	8	a	a	DET
grhe-5548	39	9	cubic	cubic	ADJ
grhe-5548	39	10	equation	equation	NOUN
grhe-5548	39	11	could	could	AUX
grhe-5548	39	12	have	have	VERB
grhe-5548	39	13	more	more	ADJ
grhe-5548	39	14	than	than	ADP
grhe-5548	39	15	one	one	NUM
grhe-5548	39	16	solution	solution	NOUN
grhe-5548	39	17	.	.	PUNCT
grhe-5548	40	1	secondly	secondly	ADV
grhe-5548	40	2	,	,	PUNCT
grhe-5548	40	3	in	in	ADP
grhe-5548	40	4	his	his	PRON
grhe-5548	40	5	fil	fil	X
grhe-5548	40	6	birâhini	birâhini	PROPN
grhe-5548	40	7	-	-	PUNCT
grhe-5548	40	8	al	al	PROPN
grhe-5548	40	9	-	-	PUNCT
grhe-5548	40	10	el	el	PROPN
grhe-5548	40	11	-	-	PUNCT
grhe-5548	40	12	mesâil	mesâil	NOUN
grhe-5548	40	13	-	-	PUNCT
grhe-5548	40	14	el	el	NOUN
grhe-5548	40	15	-	-	PUNCT
grhe-5548	40	16	cebr	cebr	ADJ
grhe-5548	40	17	vel	vel	PROPN
grhe-5548	40	18	mukabele	mukabele	NOUN
grhe-5548	40	19	,	,	PUNCT
grhe-5548	40	20	he	he	PRON
grhe-5548	40	21	wrote	write	VERB
grhe-5548	40	22	a	a	DET
grhe-5548	40	23	complete	complete	ADJ
grhe-5548	40	24	classification	classification	NOUN
grhe-5548	40	25	of	of	ADP
grhe-5548	40	26	cubic	cubic	ADJ
grhe-5548	40	27	equations	equation	NOUN
grhe-5548	40	28	.	.	PUNCT
grhe-5548	41	1	thirdly	thirdly	ADV
grhe-5548	41	2	,	,	PUNCT
grhe-5548	41	3	in	in	ADP
grhe-5548	41	4	the	the	DET
grhe-5548	41	5	same	same	ADJ
grhe-5548	41	6	book	book	NOUN
grhe-5548	41	7	,	,	PUNCT
grhe-5548	41	8	he	he	PRON
grhe-5548	41	9	proposed	propose	VERB
grhe-5548	41	10	some	some	DET
grhe-5548	41	11	general	general	ADJ
grhe-5548	41	12	geometric	geometric	ADJ
grhe-5548	41	13	solutions	solution	NOUN
grhe-5548	41	14	that	that	PRON
grhe-5548	41	15	involved	involve	VERB
grhe-5548	41	16	intersecting	intersect	VERB
grhe-5548	41	17	certain	certain	ADJ
grhe-5548	41	18	conic	conic	ADJ
grhe-5548	41	19	sections	section	NOUN
grhe-5548	41	20	(	(	PUNCT
grhe-5548	41	21	katz	katz	PROPN
grhe-5548	41	22	,	,	PUNCT
grhe-5548	41	23	2004	2004	NUM
grhe-5548	41	24	)	)	PUNCT
grhe-5548	41	25	.	.	PUNCT
grhe-5548	42	1	khayyam	khayyam	PROPN
grhe-5548	42	2	’s	’s	PART
grhe-5548	42	3	general	general	ADJ
grhe-5548	42	4	geometric	geometric	ADJ
grhe-5548	42	5	solution	solution	NOUN
grhe-5548	42	6	of	of	ADP
grhe-5548	42	7	the	the	DET
grhe-5548	42	8	cubic	cubic	NOUN
grhe-5548	42	9	as	as	ADV
grhe-5548	42	10	well	well	ADV
grhe-5548	42	11	as	as	ADP
grhe-5548	42	12	his	his	PRON
grhe-5548	42	13	contributions	contribution	NOUN
grhe-5548	42	14	to	to	ADP
grhe-5548	42	15	literature	literature	NOUN
grhe-5548	42	16	,	,	PUNCT
grhe-5548	42	17	philosophy	philosophy	NOUN
grhe-5548	42	18	,	,	PUNCT
grhe-5548	42	19	astronomy	astronomy	NOUN
grhe-5548	42	20	,	,	PUNCT
grhe-5548	42	21	geometry	geometry	NOUN
grhe-5548	42	22	,	,	PUNCT
grhe-5548	42	23	and	and	CCONJ
grhe-5548	42	24	sciences	science	NOUN
grhe-5548	42	25	will	will	AUX
grhe-5548	42	26	be	be	AUX
grhe-5548	42	27	analyzed	analyze	VERB
grhe-5548	42	28	in	in	ADP
grhe-5548	42	29	detail	detail	NOUN
grhe-5548	42	30	in	in	ADP
grhe-5548	42	31	another	another	DET
grhe-5548	42	32	paper	paper	NOUN
grhe-5548	42	33	.	.	PUNCT
grhe-5548	43	1	here	here	ADV
grhe-5548	43	2	,	,	PUNCT
grhe-5548	43	3	we	we	PRON
grhe-5548	43	4	are	be	AUX
grhe-5548	43	5	only	only	ADV
grhe-5548	43	6	interested	interested	ADJ
grhe-5548	43	7	in	in	ADP
grhe-5548	43	8	his	his	PRON
grhe-5548	43	9	classification	classification	NOUN
grhe-5548	43	10	of	of	ADP
grhe-5548	43	11	the	the	DET
grhe-5548	43	12	cubic	cubic	ADJ
grhe-5548	43	13	equation	equation	NOUN
grhe-5548	43	14	.	.	PUNCT
grhe-5548	44	1	for	for	ADP
grhe-5548	44	2	,	,	PUNCT
grhe-5548	44	3	it	it	PRON
grhe-5548	44	4	is	be	AUX
grhe-5548	44	5	this	this	DET
grhe-5548	44	6	classification	classification	NOUN
grhe-5548	44	7	that	that	PRON
grhe-5548	44	8	provided	provide	VERB
grhe-5548	44	9	the	the	DET
grhe-5548	44	10	much	much	ADV
grhe-5548	44	11	needed	need	VERB
grhe-5548	44	12	background	background	NOUN
grhe-5548	44	13	for	for	ADP
grhe-5548	44	14	the	the	DET
grhe-5548	44	15	works	work	NOUN
grhe-5548	44	16	of	of	ADP
grhe-5548	44	17	fibonacci	fibonacci	NOUN
grhe-5548	44	18	(	(	PUNCT
grhe-5548	44	19	1170	1170	NUM
grhe-5548	44	20	-	-	SYM
grhe-5548	44	21	1250	1250	NUM
grhe-5548	44	22	)	)	PUNCT
grhe-5548	44	23	,	,	PUNCT
grhe-5548	45	1	[	[	X
grhe-5548	45	2	19	19	NUM
grhe-5548	45	3	]	]	PUNCT
grhe-5548	45	4	,	,	PUNCT
grhe-5548	45	5	scipione	scipione	NOUN
grhe-5548	45	6	del	del	NOUN
grhe-5548	45	7	ferro	ferro	NOUN
grhe-5548	45	8	(	(	PUNCT
grhe-5548	45	9	1465	1465	NUM
grhe-5548	45	10	-	-	SYM
grhe-5548	45	11	1526	1526	NUM
grhe-5548	45	12	)	)	PUNCT
grhe-5548	45	13	,	,	PUNCT
grhe-5548	45	14	niccolò	niccolò	VERB
grhe-5548	45	15	fontana	fontana	PROPN
grhe-5548	45	16	tartaglia	tartaglia	PROPN
grhe-5548	45	17	(	(	PUNCT
grhe-5548	45	18	1500	1500	NUM
grhe-5548	45	19	-	-	SYM
grhe-5548	45	20	1557	1557	NUM
grhe-5548	45	21	)	)	PUNCT
grhe-5548	45	22	,	,	PUNCT
grhe-5548	45	23	gerolamo	gerolamo	PROPN
grhe-5548	45	24	cardano	cardano	X
grhe-5548	45	25	(	(	PUNCT
grhe-5548	45	26	1501	1501	NUM
grhe-5548	45	27	-	-	SYM
grhe-5548	45	28	1576	1576	NUM
grhe-5548	45	29	)	)	PUNCT
grhe-5548	45	30	,	,	PUNCT
grhe-5548	45	31	françois	françois	PROPN
grhe-5548	45	32	viète	viète	NOUN
grhe-5548	45	33	(	(	PUNCT
grhe-5548	45	34	1540	1540	NUM
grhe-5548	45	35	-	-	SYM
grhe-5548	45	36	1603	1603	NUM
grhe-5548	45	37	)	)	PUNCT
grhe-5548	45	38	and	and	CCONJ
grhe-5548	45	39	rené	rené	PROPN
grhe-5548	45	40	descartes	descartes	PROPN
grhe-5548	45	41	(	(	PUNCT
grhe-5548	45	42	1596	1596	NUM
grhe-5548	45	43	-	-	SYM
grhe-5548	45	44	1650	1650	NUM
grhe-5548	45	45	)	)	PUNCT
grhe-5548	45	46	(	(	PUNCT
grhe-5548	45	47	note	note	NOUN
grhe-5548	45	48	1	1	NUM
grhe-5548	45	49	)	)	PUNCT
grhe-5548	45	50	en	en	ADP
grhe-5548	45	51	route	route	NOUN
grhe-5548	45	52	to	to	ADP
grhe-5548	45	53	the	the	DET
grhe-5548	45	54	complete	complete	ADJ
grhe-5548	45	55	solution	solution	NOUN
grhe-5548	45	56	of	of	ADP
grhe-5548	45	57	the	the	DET
grhe-5548	45	58	cubic	cubic	NOUN
grhe-5548	45	59	.	.	PUNCT
grhe-5548	46	1	4	4	X
grhe-5548	46	2	.	.	X
grhe-5548	46	3	omar	omar	PROPN
grhe-5548	46	4	khayyam	khayyam	PROPN
grhe-5548	46	5	’s	’s	PART
grhe-5548	46	6	life	life	NOUN
grhe-5548	46	7	and	and	CCONJ
grhe-5548	46	8	work	work	NOUN
grhe-5548	46	9	omar	omar	PROPN
grhe-5548	46	10	khayyam	khayyam	PROPN
grhe-5548	46	11	(	(	PUNCT
grhe-5548	46	12	whose	whose	DET
grhe-5548	46	13	full	full	ADJ
grhe-5548	46	14	name	name	NOUN
grhe-5548	46	15	was	be	AUX
grhe-5548	46	16	ebu	ebu	NOUN
grhe-5548	46	17	hafs	hafs	PROPN
grhe-5548	46	18	omar	omar	PROPN
grhe-5548	46	19	ibn	ibn	PROPN
grhe-5548	46	20	-	-	PUNCT
grhe-5548	46	21	i	i	PRON
grhe-5548	46	22	ibrahim	ibrahim	PROPN
grhe-5548	46	23	el	el	PROPN
grhe-5548	46	24	khayyami	khayyami	PROPN
grhe-5548	46	25	)	)	PUNCT
grhe-5548	46	26	was	be	AUX
grhe-5548	46	27	born	bear	VERB
grhe-5548	46	28	in	in	ADP
grhe-5548	46	29	nishapur	nishapur	NOUN
grhe-5548	46	30	in	in	ADP
grhe-5548	46	31	northeastern	northeastern	ADJ
grhe-5548	46	32	iran	iran	PROPN
grhe-5548	46	33	in	in	ADP
grhe-5548	46	34	1048	1048	NUM
grhe-5548	46	35	.	.	PUNCT
grhe-5548	47	1	khayyam	khayyam	PROPN
grhe-5548	47	2	came	come	VERB
grhe-5548	47	3	from	from	ADP
grhe-5548	47	4	a	a	DET
grhe-5548	47	5	middle	middle	ADJ
grhe-5548	47	6	-	-	PUNCT
grhe-5548	47	7	class	class	NOUN
grhe-5548	47	8	family	family	NOUN
grhe-5548	47	9	.	.	PUNCT
grhe-5548	48	1	the	the	DET
grhe-5548	48	2	patronymic	patronymic	ADJ
grhe-5548	48	3	khayyam	khayyam	PROPN
grhe-5548	48	4	(	(	PUNCT
grhe-5548	48	5	or	or	CCONJ
grhe-5548	48	6	khayyami	khayyami	NOUN
grhe-5548	48	7	)	)	PUNCT
grhe-5548	48	8	meaning	mean	VERB
grhe-5548	48	9	“	"	PUNCT
grhe-5548	48	10	tent	tent	NOUN
grhe-5548	48	11	maker	maker	NOUN
grhe-5548	48	12	”	"	PUNCT
grhe-5548	48	13	implies	imply	VERB
grhe-5548	48	14	that	that	SCONJ
grhe-5548	48	15	at	at	ADV
grhe-5548	48	16	least	least	ADJ
grhe-5548	48	17	one	one	NUM
grhe-5548	48	18	of	of	ADP
grhe-5548	48	19	his	his	PRON
grhe-5548	48	20	ancestors	ancestor	NOUN
grhe-5548	48	21	must	must	AUX
grhe-5548	48	22	have	have	AUX
grhe-5548	48	23	been	be	AUX
grhe-5548	48	24	a	a	DET
grhe-5548	48	25	tent	tent	NOUN
grhe-5548	48	26	maker	maker	NOUN
grhe-5548	48	27	.	.	PUNCT
grhe-5548	49	1	he	he	PRON
grhe-5548	49	2	was	be	AUX
grhe-5548	49	3	educated	educate	VERB
grhe-5548	49	4	in	in	ADP
grhe-5548	49	5	nishapur	nishapur	NOUN
grhe-5548	49	6	by	by	ADP
grhe-5548	49	7	some	some	PRON
grhe-5548	49	8	of	of	ADP
grhe-5548	49	9	the	the	DET
grhe-5548	49	10	leading	lead	VERB
grhe-5548	49	11	scholars	scholar	NOUN
grhe-5548	49	12	and	and	CCONJ
grhe-5548	49	13	scientists	scientist	NOUN
grhe-5548	49	14	of	of	ADP
grhe-5548	49	15	time	time	NOUN
grhe-5548	49	16	such	such	ADJ
grhe-5548	49	17	as	as	ADP
grhe-5548	49	18	nasȋr	nasȋr	NOUN
grhe-5548	49	19	-	-	PUNCT
grhe-5548	49	20	ed	ed	NOUN
grhe-5548	49	21	-	-	PUNCT
grhe-5548	49	22	din	din	NOUN
grhe-5548	49	23	sheih	sheih	PROPN
grhe-5548	49	24	muhammad	muhammad	PROPN
grhe-5548	49	25	mansur	mansur	PROPN
grhe-5548	49	26	and	and	CCONJ
grhe-5548	49	27	muvaffak	muvaffak	PROPN
grhe-5548	49	28	-	-	PUNCT
grhe-5548	49	29	üd	üd	NOUN
grhe-5548	49	30	-	-	PUNCT
grhe-5548	49	31	din	din	NOUN
grhe-5548	49	32	abdullatif	abdullatif	PROPN
grhe-5548	49	33	ibn	ibn	PROPN
grhe-5548	49	34	-	-	PUNCT
grhe-5548	49	35	ül	ül	ADP
grhe-5548	49	36	lübâd	lübâd	NOUN
grhe-5548	49	37	,	,	PUNCT
grhe-5548	49	38	and	and	CCONJ
grhe-5548	49	39	the	the	DET
grhe-5548	49	40	renowned	renowned	ADJ
grhe-5548	49	41	theologian	theologian	ADJ
grhe-5548	49	42	hâce	hâce	PROPN
grhe-5548	49	43	ali	ali	PROPN
grhe-5548	49	44	.	.	PUNCT
grhe-5548	50	1	he	he	PRON
grhe-5548	50	2	died	die	VERB
grhe-5548	50	3	in	in	ADP
grhe-5548	50	4	the	the	DET
grhe-5548	50	5	same	same	ADJ
grhe-5548	50	6	city	city	NOUN
grhe-5548	50	7	in	in	ADP
grhe-5548	50	8	1131	1131	NUM
grhe-5548	50	9	.	.	PUNCT
grhe-5548	51	1	for	for	ADP
grhe-5548	51	2	more	more	ADJ
grhe-5548	51	3	information	information	NOUN
grhe-5548	51	4	on	on	ADP
grhe-5548	51	5	his	his	PRON
grhe-5548	51	6	life	life	NOUN
grhe-5548	51	7	and	and	CCONJ
grhe-5548	51	8	major	major	ADJ
grhe-5548	51	9	works	work	NOUN
grhe-5548	51	10	,	,	PUNCT
grhe-5548	51	11	please	please	INTJ
grhe-5548	51	12	see	see	VERB
grhe-5548	51	13	dilgan	dilgan	ADJ
grhe-5548	51	14	(	(	PUNCT
grhe-5548	51	15	1964	1964	NUM
grhe-5548	51	16	)	)	PUNCT
grhe-5548	51	17	.	.	PUNCT
grhe-5548	52	1	khayyam	khayyam	PROPN
grhe-5548	52	2	was	be	AUX
grhe-5548	52	3	introduced	introduce	VERB
grhe-5548	52	4	to	to	ADP
grhe-5548	52	5	western	western	ADJ
grhe-5548	52	6	world	world	NOUN
grhe-5548	52	7	in	in	ADP
grhe-5548	52	8	the	the	DET
grhe-5548	52	9	first	first	ADJ
grhe-5548	52	10	half	half	NOUN
grhe-5548	52	11	of	of	ADP
grhe-5548	52	12	nineteenth	nineteenth	ADJ
grhe-5548	52	13	century	century	NOUN
grhe-5548	52	14	by	by	ADP
grhe-5548	52	15	the	the	DET
grhe-5548	52	16	translations	translation	NOUN
grhe-5548	52	17	of	of	ADP
grhe-5548	52	18	two	two	NUM
grhe-5548	52	19	of	of	ADP
grhe-5548	52	20	his	his	PRON
grhe-5548	52	21	major	major	ADJ
grhe-5548	52	22	works	work	NOUN
grhe-5548	52	23	.	.	PUNCT
grhe-5548	53	1	one	one	NUM
grhe-5548	53	2	was	be	AUX
grhe-5548	53	3	an	an	DET
grhe-5548	53	4	1851	1851	NUM
grhe-5548	53	5	translation	translation	NOUN
grhe-5548	53	6	of	of	ADP
grhe-5548	53	7	his	his	PRON
grhe-5548	53	8	work	work	NOUN
grhe-5548	53	9	in	in	ADP
grhe-5548	53	10	algebra	algebra	PROPN
grhe-5548	53	11	(	(	PUNCT
grhe-5548	53	12	fil	fil	X
grhe-5548	53	13	birâhini	birâhini	PROPN
grhe-5548	53	14	-	-	PUNCT
grhe-5548	53	15	al	al	PROPN
grhe-5548	53	16	-	-	PUNCT
grhe-5548	53	17	el	el	PROPN
grhe-5548	53	18	-	-	PUNCT
grhe-5548	53	19	mesâil	mesâil	NOUN
grhe-5548	53	20	-	-	PUNCT
grhe-5548	53	21	el	el	NOUN
grhe-5548	53	22	-	-	PUNCT
grhe-5548	53	23	cebr	cebr	ADJ
grhe-5548	53	24	vel	vel	PROPN
grhe-5548	53	25	mukabele	mukabele	PROPN
grhe-5548	53	26	)	)	PUNCT
grhe-5548	53	27	by	by	ADP
grhe-5548	53	28	franz	franz	PROPN
grhe-5548	53	29	woepcke	woepcke	NOUN
grhe-5548	53	30	(	(	PUNCT
grhe-5548	53	31	1826	1826	NUM
grhe-5548	53	32	-	-	SYM
grhe-5548	53	33	1864	1864	NUM
grhe-5548	53	34	)	)	PUNCT
grhe-5548	53	35	as	as	ADP
grhe-5548	53	36	l’algèbre	l’algèbre	PROPN
grhe-5548	53	37	d’omar	d’omar	PROPN
grhe-5548	53	38	al	al	PROPN
grhe-5548	53	39	khayyamȋ	khayyamȋ	PROPN
grhe-5548	53	40	and	and	CCONJ
grhe-5548	53	41	the	the	DET
grhe-5548	53	42	other	other	ADJ
grhe-5548	53	43	was	be	AUX
grhe-5548	53	44	the	the	DET
grhe-5548	53	45	1859	1859	NUM
grhe-5548	53	46	translation	translation	NOUN
grhe-5548	53	47	of	of	ADP
grhe-5548	53	48	his	his	PRON
grhe-5548	53	49	poetry	poetry	NOUN
grhe-5548	53	50	(	(	PUNCT
grhe-5548	53	51	rubaiyat	rubaiyat	PROPN
grhe-5548	53	52	)	)	PUNCT
grhe-5548	53	53	by	by	ADP
grhe-5548	53	54	the	the	DET
grhe-5548	53	55	well	well	ADV
grhe-5548	53	56	-	-	PUNCT
grhe-5548	53	57	known	know	VERB
grhe-5548	53	58	english	english	ADJ
grhe-5548	53	59	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	53	60	global	global	ADJ
grhe-5548	53	61	research	research	NOUN
grhe-5548	53	62	in	in	ADP
grhe-5548	53	63	higher	high	ADJ
grhe-5548	53	64	education	education	NOUN
grhe-5548	53	65	vol	vol	NOUN
grhe-5548	53	66	.	.	PROPN
grhe-5548	54	1	6	6	NUM
grhe-5548	54	2	,	,	PUNCT
grhe-5548	54	3	no	no	INTJ
grhe-5548	54	4	.	.	NOUN
grhe-5548	54	5	2	2	NUM
grhe-5548	54	6	,	,	PUNCT
grhe-5548	54	7	2023	2023	NUM
grhe-5548	54	8	36	36	NUM
grhe-5548	54	9	published	publish	VERB
grhe-5548	54	10	by	by	ADP
grhe-5548	54	11	scholink	scholink	PROPN
grhe-5548	54	12	inc	inc	PROPN
grhe-5548	54	13	.	.	PROPN
grhe-5548	54	14	poet	poet	PROPN
grhe-5548	54	15	and	and	CCONJ
grhe-5548	54	16	writer	writer	PROPN
grhe-5548	54	17	edward	edward	PROPN
grhe-5548	54	18	fitzgerald	fitzgerald	PROPN
grhe-5548	54	19	(	(	PUNCT
grhe-5548	54	20	1809	1809	NUM
grhe-5548	54	21	-	-	SYM
grhe-5548	54	22	1883	1883	NUM
grhe-5548	54	23	)	)	PUNCT
grhe-5548	54	24	as	as	ADP
grhe-5548	54	25	the	the	DET
grhe-5548	54	26	rubaiyat	rubaiyat	NOUN
grhe-5548	54	27	of	of	ADP
grhe-5548	54	28	omar	omar	PROPN
grhe-5548	54	29	khayyam	khayyam	PROPN
grhe-5548	54	30	.	.	PUNCT
grhe-5548	55	1	his	his	PRON
grhe-5548	55	2	philosophical	philosophical	ADJ
grhe-5548	55	3	thoughts	thought	NOUN
grhe-5548	55	4	have	have	AUX
grhe-5548	55	5	been	be	AUX
grhe-5548	55	6	compared	compare	VERB
grhe-5548	55	7	to	to	ADP
grhe-5548	55	8	epicure	epicure	NOUN
grhe-5548	55	9	,	,	PUNCT
grhe-5548	55	10	voltaire	voltaire	NOUN
grhe-5548	55	11	,	,	PUNCT
grhe-5548	55	12	and	and	CCONJ
grhe-5548	55	13	schopenhauer	schopenhauer	PROPN
grhe-5548	55	14	(	(	PUNCT
grhe-5548	55	15	dilgan	dilgan	ADJ
grhe-5548	55	16	,	,	PUNCT
grhe-5548	55	17	1964	1964	NUM
grhe-5548	55	18	)	)	PUNCT
grhe-5548	55	19	.	.	PUNCT
grhe-5548	56	1	khayyam	khayyam	PROPN
grhe-5548	56	2	’s	’s	PART
grhe-5548	56	3	fil	fil	PROPN
grhe-5548	56	4	birâhini	birâhini	PROPN
grhe-5548	56	5	-	-	PUNCT
grhe-5548	56	6	al	al	PROPN
grhe-5548	56	7	-	-	PUNCT
grhe-5548	56	8	el	el	PROPN
grhe-5548	56	9	-	-	PUNCT
grhe-5548	56	10	mesâil	mesâil	NOUN
grhe-5548	56	11	-	-	PUNCT
grhe-5548	56	12	el	el	NOUN
grhe-5548	56	13	-	-	PUNCT
grhe-5548	56	14	cebr	cebr	VERB
grhe-5548	56	15	vel	vel	PROPN
grhe-5548	56	16	mukabele	mukabele	NOUN
grhe-5548	56	17	comprised	comprise	VERB
grhe-5548	56	18	five	five	NUM
grhe-5548	56	19	sections	section	NOUN
grhe-5548	56	20	.	.	PUNCT
grhe-5548	57	1	the	the	DET
grhe-5548	57	2	first	first	ADJ
grhe-5548	57	3	section	section	NOUN
grhe-5548	57	4	contained	contain	VERB
grhe-5548	57	5	a	a	DET
grhe-5548	57	6	preface	preface	NOUN
grhe-5548	57	7	and	and	CCONJ
grhe-5548	57	8	gave	give	VERB
grhe-5548	57	9	some	some	DET
grhe-5548	57	10	basic	basic	ADJ
grhe-5548	57	11	definitions	definition	NOUN
grhe-5548	57	12	.	.	PUNCT
grhe-5548	58	1	in	in	ADP
grhe-5548	58	2	the	the	DET
grhe-5548	58	3	second	second	ADJ
grhe-5548	58	4	section	section	NOUN
grhe-5548	58	5	,	,	PUNCT
grhe-5548	58	6	khayyam	khayyam	PROPN
grhe-5548	58	7	discussed	discuss	VERB
grhe-5548	58	8	first	first	ADJ
grhe-5548	58	9	and	and	CCONJ
grhe-5548	58	10	second	second	ADJ
grhe-5548	58	11	degree	degree	NOUN
grhe-5548	58	12	equations	equation	NOUN
grhe-5548	58	13	and	and	CCONJ
grhe-5548	58	14	in	in	ADP
grhe-5548	58	15	the	the	DET
grhe-5548	58	16	third	third	NOUN
grhe-5548	58	17	,	,	PUNCT
grhe-5548	58	18	he	he	PRON
grhe-5548	58	19	talked	talk	VERB
grhe-5548	58	20	about	about	ADP
grhe-5548	58	21	cubic	cubic	ADJ
grhe-5548	58	22	equations	equation	NOUN
grhe-5548	58	23	.	.	PUNCT
grhe-5548	59	1	fourth	fourth	ADJ
grhe-5548	59	2	and	and	CCONJ
grhe-5548	59	3	fifth	fifth	ADJ
grhe-5548	59	4	sections	section	NOUN
grhe-5548	59	5	involved	involve	VERB
grhe-5548	59	6	equations	equation	NOUN
grhe-5548	59	7	that	that	PRON
grhe-5548	59	8	contained	contain	VERB
grhe-5548	59	9	powers	power	NOUN
grhe-5548	59	10	of	of	ADP
grhe-5548	59	11	unknown	unknown	NOUN
grhe-5548	59	12	in	in	ADP
grhe-5548	59	13	the	the	DET
grhe-5548	59	14	denominator	denominator	NOUN
grhe-5548	59	15	and	and	CCONJ
grhe-5548	59	16	some	some	DET
grhe-5548	59	17	additional	additional	ADJ
grhe-5548	59	18	remarks	remark	NOUN
grhe-5548	59	19	on	on	ADP
grhe-5548	59	20	basic	basic	ADJ
grhe-5548	59	21	rules	rule	NOUN
grhe-5548	59	22	of	of	ADP
grhe-5548	59	23	algebra	algebra	NOUN
grhe-5548	59	24	.	.	PUNCT
grhe-5548	60	1	it	it	PRON
grhe-5548	60	2	must	must	AUX
grhe-5548	60	3	be	be	AUX
grhe-5548	60	4	mentioned	mention	VERB
grhe-5548	60	5	that	that	SCONJ
grhe-5548	60	6	khayyam	khayyam	PROPN
grhe-5548	60	7	,	,	PUNCT
grhe-5548	60	8	like	like	ADP
grhe-5548	60	9	his	his	PRON
grhe-5548	60	10	contemporaries	contemporary	NOUN
grhe-5548	60	11	,	,	PUNCT
grhe-5548	60	12	considered	consider	VERB
grhe-5548	60	13	only	only	ADV
grhe-5548	60	14	equations	equation	NOUN
grhe-5548	60	15	whose	whose	DET
grhe-5548	60	16	coefficients	coefficient	NOUN
grhe-5548	60	17	and	and	CCONJ
grhe-5548	60	18	roots	root	NOUN
grhe-5548	60	19	were	be	AUX
grhe-5548	60	20	positive	positive	ADJ
grhe-5548	60	21	numbers	number	NOUN
grhe-5548	60	22	and	and	CCONJ
grhe-5548	60	23	if	if	SCONJ
grhe-5548	60	24	an	an	DET
grhe-5548	60	25	equation	equation	NOUN
grhe-5548	60	26	did	do	AUX
grhe-5548	60	27	not	not	PART
grhe-5548	60	28	have	have	VERB
grhe-5548	60	29	positive	positive	ADJ
grhe-5548	60	30	roots	root	NOUN
grhe-5548	60	31	,	,	PUNCT
grhe-5548	60	32	he	he	PRON
grhe-5548	60	33	classified	classify	VERB
grhe-5548	60	34	them	they	PRON
grhe-5548	60	35	as	as	ADP
grhe-5548	60	36	unsolvable	unsolvable	ADJ
grhe-5548	60	37	.	.	PUNCT
grhe-5548	61	1	it	it	PRON
grhe-5548	61	2	is	be	AUX
grhe-5548	61	3	interesting	interesting	ADJ
grhe-5548	61	4	to	to	PART
grhe-5548	61	5	note	note	VERB
grhe-5548	61	6	that	that	SCONJ
grhe-5548	61	7	for	for	ADP
grhe-5548	61	8	the	the	DET
grhe-5548	61	9	first	first	ADJ
grhe-5548	61	10	time	time	NOUN
grhe-5548	61	11	,	,	PUNCT
grhe-5548	61	12	khayyam	khayyam	PROPN
grhe-5548	61	13	established	establish	VERB
grhe-5548	61	14	some	some	DET
grhe-5548	61	15	relationships	relationship	NOUN
grhe-5548	61	16	between	between	ADP
grhe-5548	61	17	roots	root	NOUN
grhe-5548	61	18	and	and	CCONJ
grhe-5548	61	19	the	the	DET
grhe-5548	61	20	coefficients	coefficient	NOUN
grhe-5548	61	21	of	of	ADP
grhe-5548	61	22	an	an	DET
grhe-5548	61	23	equation	equation	NOUN
grhe-5548	61	24	.	.	PUNCT
grhe-5548	62	1	for	for	ADP
grhe-5548	62	2	example	example	NOUN
grhe-5548	62	3	,	,	PUNCT
grhe-5548	62	4	in	in	ADP
grhe-5548	62	5	the	the	DET
grhe-5548	62	6	equation	equation	NOUN
grhe-5548	62	7	where	where	SCONJ
grhe-5548	62	8	,	,	PUNCT
grhe-5548	62	9	he	he	PRON
grhe-5548	62	10	showed	show	VERB
grhe-5548	62	11	that	that	SCONJ
grhe-5548	62	12	there	there	PRON
grhe-5548	62	13	would	would	AUX
grhe-5548	62	14	be	be	AUX
grhe-5548	62	15	two	two	NUM
grhe-5548	62	16	positive	positive	ADJ
grhe-5548	62	17	roots	root	NOUN
grhe-5548	62	18	if	if	SCONJ
grhe-5548	62	19	and	and	CCONJ
grhe-5548	62	20	no	no	DET
grhe-5548	62	21	positive	positive	ADJ
grhe-5548	62	22	roots	root	NOUN
grhe-5548	62	23	(	(	PUNCT
grhe-5548	62	24	i.e.	i.e.	X
grhe-5548	62	25	,	,	PUNCT
grhe-5548	62	26	in	in	ADP
grhe-5548	62	27	his	his	PRON
grhe-5548	62	28	terms	term	NOUN
grhe-5548	62	29	,	,	PUNCT
grhe-5548	62	30	no	no	DET
grhe-5548	62	31	solutions	solution	NOUN
grhe-5548	62	32	)	)	PUNCT
grhe-5548	62	33	if	if	SCONJ
grhe-5548	62	34	.	.	PUNCT
grhe-5548	63	1	in	in	ADP
grhe-5548	63	2	the	the	DET
grhe-5548	63	3	case	case	NOUN
grhe-5548	63	4	,	,	PUNCT
grhe-5548	63	5	he	he	PRON
grhe-5548	63	6	showed	show	VERB
grhe-5548	63	7	that	that	SCONJ
grhe-5548	63	8	the	the	DET
grhe-5548	63	9	equation	equation	NOUN
grhe-5548	63	10	may	may	AUX
grhe-5548	63	11	or	or	CCONJ
grhe-5548	63	12	may	may	AUX
grhe-5548	63	13	not	not	PART
grhe-5548	63	14	have	have	VERB
grhe-5548	63	15	positive	positive	ADJ
grhe-5548	63	16	roots	root	NOUN
grhe-5548	63	17	.	.	PUNCT
grhe-5548	64	1	indeed	indeed	ADV
grhe-5548	64	2	,	,	PUNCT
grhe-5548	64	3	some	some	DET
grhe-5548	64	4	simple	simple	ADJ
grhe-5548	64	5	examples	example	NOUN
grhe-5548	64	6	show	show	VERB
grhe-5548	64	7	this	this	PRON
grhe-5548	64	8	to	to	PART
grhe-5548	64	9	be	be	AUX
grhe-5548	64	10	the	the	DET
grhe-5548	64	11	case	case	NOUN
grhe-5548	64	12	.	.	PUNCT
grhe-5548	65	1	for	for	ADP
grhe-5548	65	2	example	example	NOUN
grhe-5548	65	3	,	,	PUNCT
grhe-5548	65	4	it	it	PRON
grhe-5548	65	5	can	can	AUX
grhe-5548	65	6	easily	easily	ADV
grhe-5548	65	7	be	be	AUX
grhe-5548	65	8	verified	verify	VERB
grhe-5548	65	9	that	that	SCONJ
grhe-5548	65	10	with	with	ADP
grhe-5548	65	11	,	,	PUNCT
grhe-5548	65	12	the	the	DET
grhe-5548	65	13	equation	equation	NOUN
grhe-5548	65	14	has	have	VERB
grhe-5548	65	15	no	no	DET
grhe-5548	65	16	positive	positive	ADJ
grhe-5548	65	17	roots	root	NOUN
grhe-5548	65	18	;	;	PUNCT
grhe-5548	65	19	with	with	ADP
grhe-5548	65	20	,	,	PUNCT
grhe-5548	65	21	it	it	PRON
grhe-5548	65	22	has	have	VERB
grhe-5548	65	23	one	one	NUM
grhe-5548	65	24	positive	positive	ADJ
grhe-5548	65	25	root	root	NOUN
grhe-5548	65	26	;	;	PUNCT
grhe-5548	65	27	and	and	CCONJ
grhe-5548	65	28	with	with	ADP
grhe-5548	65	29	,	,	PUNCT
grhe-5548	65	30	it	it	PRON
grhe-5548	65	31	has	have	VERB
grhe-5548	65	32	two	two	NUM
grhe-5548	65	33	positive	positive	ADJ
grhe-5548	65	34	roots	root	NOUN
grhe-5548	65	35	.	.	PUNCT
grhe-5548	66	1	5	5	X
grhe-5548	66	2	.	.	X
grhe-5548	66	3	khayyam	khayyam	PROPN
grhe-5548	66	4	’s	’s	PART
grhe-5548	66	5	classification	classification	NOUN
grhe-5548	66	6	of	of	ADP
grhe-5548	66	7	the	the	DET
grhe-5548	66	8	cubic	cubic	ADJ
grhe-5548	66	9	in	in	ADP
grhe-5548	66	10	section	section	NOUN
grhe-5548	66	11	three	three	NUM
grhe-5548	66	12	of	of	ADP
grhe-5548	66	13	fil	fil	X
grhe-5548	66	14	birâhini	birâhini	PROPN
grhe-5548	66	15	-	-	PUNCT
grhe-5548	66	16	al	al	PROPN
grhe-5548	66	17	-	-	PUNCT
grhe-5548	66	18	el	el	PROPN
grhe-5548	66	19	-	-	PUNCT
grhe-5548	66	20	mesâil	mesâil	NOUN
grhe-5548	66	21	-	-	PUNCT
grhe-5548	66	22	el	el	NOUN
grhe-5548	66	23	-	-	PUNCT
grhe-5548	66	24	cebr	cebr	ADJ
grhe-5548	66	25	vel	vel	PROPN
grhe-5548	66	26	mukabele	mukabele	PROPN
grhe-5548	66	27	,	,	PUNCT
grhe-5548	66	28	khayyam	khayyam	PROPN
grhe-5548	66	29	divided	divide	VERB
grhe-5548	66	30	cubic	cubic	ADJ
grhe-5548	66	31	equations	equation	NOUN
grhe-5548	66	32	into	into	ADP
grhe-5548	66	33	four	four	NUM
grhe-5548	66	34	major	major	ADJ
grhe-5548	66	35	groups	group	NOUN
grhe-5548	66	36	.	.	PUNCT
grhe-5548	67	1	the	the	DET
grhe-5548	67	2	first	first	ADJ
grhe-5548	67	3	group	group	NOUN
grhe-5548	67	4	consisted	consist	VERB
grhe-5548	67	5	equations	equation	NOUN
grhe-5548	67	6	.	.	PUNCT
grhe-5548	68	1	only	only	ADV
grhe-5548	68	2	two	two	NUM
grhe-5548	68	3	of	of	ADP
grhe-5548	68	4	those	those	PRON
grhe-5548	68	5	could	could	AUX
grhe-5548	68	6	not	not	PART
grhe-5548	68	7	be	be	AUX
grhe-5548	68	8	solved	solve	VERB
grhe-5548	68	9	by	by	ADP
grhe-5548	68	10	the	the	DET
grhe-5548	68	11	geometric	geometric	ADJ
grhe-5548	68	12	method	method	NOUN
grhe-5548	68	13	khayyam	khayyam	PROPN
grhe-5548	68	14	proposed	propose	VERB
grhe-5548	68	15	and	and	CCONJ
grhe-5548	68	16	required	require	VERB
grhe-5548	68	17	other	other	ADJ
grhe-5548	68	18	techniques	technique	NOUN
grhe-5548	68	19	.	.	PUNCT
grhe-5548	69	1	thus	thus	ADV
grhe-5548	69	2	,	,	PUNCT
grhe-5548	69	3	could	could	AUX
grhe-5548	69	4	be	be	AUX
grhe-5548	69	5	solved	solve	VERB
grhe-5548	69	6	by	by	ADP
grhe-5548	69	7	khayyam	khayyam	PROPN
grhe-5548	69	8	’s	’s	PART
grhe-5548	69	9	method	method	NOUN
grhe-5548	69	10	.	.	PUNCT
grhe-5548	70	1	the	the	DET
grhe-5548	70	2	second	second	ADJ
grhe-5548	70	3	group	group	NOUN
grhe-5548	70	4	contained	contain	VERB
grhe-5548	70	5	trinomial	trinomial	ADJ
grhe-5548	70	6	equations	equation	NOUN
grhe-5548	70	7	that	that	PRON
grhe-5548	70	8	had	have	VERB
grhe-5548	70	9	three	three	NUM
grhe-5548	70	10	successive	successive	ADJ
grhe-5548	70	11	powers	power	NOUN
grhe-5548	70	12	(	(	PUNCT
grhe-5548	70	13	,	,	PUNCT
grhe-5548	70	14	and	and	CCONJ
grhe-5548	70	15	constant	constant	ADJ
grhe-5548	70	16	term	term	NOUN
grhe-5548	70	17	or	or	CCONJ
grhe-5548	70	18	,	,	PUNCT
grhe-5548	70	19	and	and	CCONJ
grhe-5548	70	20	)	)	PUNCT
grhe-5548	70	21	.	.	PUNCT
grhe-5548	71	1	there	there	PRON
grhe-5548	71	2	were	be	VERB
grhe-5548	71	3	such	such	ADJ
grhe-5548	71	4	equations	equation	NOUN
grhe-5548	71	5	and	and	CCONJ
grhe-5548	71	6	these	these	PRON
grhe-5548	71	7	were	be	AUX
grhe-5548	71	8	all	all	ADV
grhe-5548	71	9	solvable	solvable	ADJ
grhe-5548	71	10	by	by	ADP
grhe-5548	71	11	khayyam	khayyam	PROPN
grhe-5548	71	12	’s	’s	PART
grhe-5548	71	13	method	method	NOUN
grhe-5548	71	14	.	.	PUNCT
grhe-5548	72	1	the	the	DET
grhe-5548	72	2	third	third	ADJ
grhe-5548	72	3	group	group	NOUN
grhe-5548	72	4	contained	contain	VERB
grhe-5548	72	5	equations	equation	NOUN
grhe-5548	72	6	that	that	PRON
grhe-5548	72	7	contained	contain	VERB
grhe-5548	72	8	,	,	PUNCT
grhe-5548	72	9	and	and	CCONJ
grhe-5548	72	10	terms	term	NOUN
grhe-5548	72	11	,	,	PUNCT
grhe-5548	72	12	but	but	CCONJ
grhe-5548	72	13	not	not	PART
grhe-5548	72	14	necessarily	necessarily	ADV
grhe-5548	72	15	successively	successively	ADV
grhe-5548	72	16	—	—	PUNCT
grhe-5548	72	17	the	the	DET
grhe-5548	72	18	only	only	ADJ
grhe-5548	72	19	stipulation	stipulation	NOUN
grhe-5548	72	20	was	be	AUX
grhe-5548	72	21	that	that	SCONJ
grhe-5548	72	22	a	a	DET
grhe-5548	72	23	cubic	cubic	ADJ
grhe-5548	72	24	term	term	NOUN
grhe-5548	72	25	had	have	VERB
grhe-5548	72	26	to	to	PART
grhe-5548	72	27	be	be	AUX
grhe-5548	72	28	present	present	ADJ
grhe-5548	72	29	.	.	PUNCT
grhe-5548	73	1	all	all	DET
grhe-5548	73	2	equations	equation	NOUN
grhe-5548	73	3	in	in	ADP
grhe-5548	73	4	this	this	DET
grhe-5548	73	5	group	group	NOUN
grhe-5548	73	6	were	be	AUX
grhe-5548	73	7	solvable	solvable	ADJ
grhe-5548	73	8	by	by	ADP
grhe-5548	73	9	khayyam	khayyam	PROPN
grhe-5548	73	10	’s	’s	PART
grhe-5548	73	11	method	method	NOUN
grhe-5548	73	12	.	.	PUNCT
grhe-5548	74	1	the	the	DET
grhe-5548	74	2	fourth	fourth	ADJ
grhe-5548	74	3	and	and	CCONJ
grhe-5548	74	4	the	the	DET
grhe-5548	74	5	last	last	ADJ
grhe-5548	74	6	group	group	NOUN
grhe-5548	74	7	contained	contain	VERB
grhe-5548	74	8	equations	equation	NOUN
grhe-5548	74	9	with	with	ADP
grhe-5548	74	10	four	four	NUM
grhe-5548	74	11	terms	term	NOUN
grhe-5548	74	12	containing	contain	VERB
grhe-5548	74	13	,	,	PUNCT
grhe-5548	74	14	and	and	CCONJ
grhe-5548	74	15	in	in	ADP
grhe-5548	74	16	a	a	DET
grhe-5548	74	17	successive	successive	ADJ
grhe-5548	74	18	manner	manner	NOUN
grhe-5548	74	19	.	.	PUNCT
grhe-5548	75	1	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	75	2	global	global	ADJ
grhe-5548	75	3	research	research	NOUN
grhe-5548	75	4	in	in	ADP
grhe-5548	75	5	higher	high	ADJ
grhe-5548	75	6	education	education	NOUN
grhe-5548	75	7	vol	vol	NOUN
grhe-5548	75	8	.	.	PROPN
grhe-5548	76	1	6	6	NUM
grhe-5548	76	2	,	,	PUNCT
grhe-5548	76	3	no	no	INTJ
grhe-5548	76	4	.	.	NOUN
grhe-5548	76	5	2	2	NUM
grhe-5548	76	6	,	,	PUNCT
grhe-5548	76	7	2023	2023	NUM
grhe-5548	76	8	37	37	NUM
grhe-5548	76	9	published	publish	VERB
grhe-5548	76	10	by	by	ADP
grhe-5548	76	11	scholink	scholink	PROPN
grhe-5548	76	12	inc	inc	PROPN
grhe-5548	76	13	.	.	PROPN
grhe-5548	76	14	thus	thus	ADV
grhe-5548	76	15	,	,	PUNCT
grhe-5548	76	16	khayyam	khayyam	PROPN
grhe-5548	76	17	’s	’s	PART
grhe-5548	76	18	method	method	NOUN
grhe-5548	76	19	applied	apply	VERB
grhe-5548	76	20	to	to	ADP
grhe-5548	76	21	different	different	ADJ
grhe-5548	76	22	type	type	NOUN
grhe-5548	76	23	of	of	ADP
grhe-5548	76	24	cubic	cubic	ADJ
grhe-5548	76	25	equations	equation	NOUN
grhe-5548	76	26	.	.	PUNCT
grhe-5548	77	1	below	below	ADP
grhe-5548	77	2	we	we	PRON
grhe-5548	77	3	give	give	VERB
grhe-5548	77	4	the	the	DET
grhe-5548	77	5	members	member	NOUN
grhe-5548	77	6	of	of	ADP
grhe-5548	77	7	these	these	DET
grhe-5548	77	8	groups	group	NOUN
grhe-5548	77	9	.	.	PUNCT
grhe-5548	78	1	here	here	ADV
grhe-5548	78	2	,	,	PUNCT
grhe-5548	78	3	are	be	AUX
grhe-5548	78	4	positive	positive	ADJ
grhe-5548	78	5	constants	constant	NOUN
grhe-5548	78	6	.	.	PUNCT
grhe-5548	79	1	group	group	NOUN
grhe-5548	79	2	i	i	PRON
grhe-5548	79	3	(	(	PUNCT
grhe-5548	79	4	not	not	PART
grhe-5548	79	5	solvable	solvable	ADJ
grhe-5548	79	6	by	by	ADP
grhe-5548	79	7	khayyam	khayyam	PROPN
grhe-5548	79	8	’s	’s	PART
grhe-5548	79	9	method	method	NOUN
grhe-5548	79	10	)	)	PUNCT
grhe-5548	79	11	group	group	NOUN
grhe-5548	79	12	ii	ii	PROPN
grhe-5548	79	13	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	79	14	global	global	PROPN
grhe-5548	79	15	research	research	NOUN
grhe-5548	79	16	in	in	ADP
grhe-5548	79	17	higher	high	ADJ
grhe-5548	79	18	education	education	NOUN
grhe-5548	79	19	vol	vol	NOUN
grhe-5548	79	20	.	.	PROPN
grhe-5548	79	21	6	6	NUM
grhe-5548	79	22	,	,	PUNCT
grhe-5548	79	23	no	no	INTJ
grhe-5548	79	24	.	.	NOUN
grhe-5548	79	25	2	2	NUM
grhe-5548	79	26	,	,	PUNCT
grhe-5548	79	27	2023	2023	NUM
grhe-5548	79	28	38	38	NUM
grhe-5548	79	29	published	publish	VERB
grhe-5548	79	30	by	by	ADP
grhe-5548	79	31	scholink	scholink	PROPN
grhe-5548	79	32	inc	inc	PROPN
grhe-5548	79	33	.	.	PROPN
grhe-5548	79	34	group	group	PROPN
grhe-5548	79	35	iii	iii	PROPN
grhe-5548	79	36	group	group	PROPN
grhe-5548	79	37	iv	iv	NUM
grhe-5548	79	38	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	79	39	global	global	ADJ
grhe-5548	79	40	research	research	NOUN
grhe-5548	79	41	in	in	ADP
grhe-5548	79	42	higher	high	ADJ
grhe-5548	79	43	education	education	NOUN
grhe-5548	79	44	vol	vol	NOUN
grhe-5548	79	45	.	.	PROPN
grhe-5548	79	46	6	6	NUM
grhe-5548	79	47	,	,	PUNCT
grhe-5548	79	48	no	no	INTJ
grhe-5548	79	49	.	.	NOUN
grhe-5548	79	50	2	2	NUM
grhe-5548	79	51	,	,	PUNCT
grhe-5548	79	52	2023	2023	NUM
grhe-5548	79	53	39	39	NUM
grhe-5548	79	54	published	publish	VERB
grhe-5548	79	55	by	by	ADP
grhe-5548	79	56	scholink	scholink	PROPN
grhe-5548	79	57	inc	inc	PROPN
grhe-5548	79	58	.	.	PROPN
grhe-5548	79	59	let	let	VERB
grhe-5548	79	60	us	we	PRON
grhe-5548	79	61	give	give	VERB
grhe-5548	79	62	a	a	DET
grhe-5548	79	63	specific	specific	ADJ
grhe-5548	79	64	example	example	NOUN
grhe-5548	79	65	of	of	ADP
grhe-5548	79	66	khayyam	khayyam	PROPN
grhe-5548	79	67	’s	’s	PART
grhe-5548	79	68	method	method	NOUN
grhe-5548	79	69	.	.	PUNCT
grhe-5548	80	1	as	as	SCONJ
grhe-5548	80	2	mentioned	mention	VERB
grhe-5548	80	3	earlier	early	ADV
grhe-5548	80	4	,	,	PUNCT
grhe-5548	80	5	the	the	DET
grhe-5548	80	6	general	general	ADJ
grhe-5548	80	7	method	method	NOUN
grhe-5548	80	8	will	will	AUX
grhe-5548	80	9	be	be	AUX
grhe-5548	80	10	analyzed	analyze	VERB
grhe-5548	80	11	in	in	ADP
grhe-5548	80	12	a	a	DET
grhe-5548	80	13	different	different	ADJ
grhe-5548	80	14	paper	paper	NOUN
grhe-5548	80	15	.	.	PUNCT
grhe-5548	81	1	say	say	VERB
grhe-5548	81	2	,	,	PUNCT
grhe-5548	81	3	for	for	ADP
grhe-5548	81	4	example	example	NOUN
grhe-5548	81	5	,	,	PUNCT
grhe-5548	81	6	we	we	PRON
grhe-5548	81	7	want	want	VERB
grhe-5548	81	8	to	to	PART
grhe-5548	81	9	solve	solve	VERB
grhe-5548	81	10	the	the	DET
grhe-5548	81	11	first	first	ADJ
grhe-5548	81	12	equation	equation	NOUN
grhe-5548	81	13	of	of	ADP
grhe-5548	81	14	group	group	NOUN
grhe-5548	81	15	iii	iii	PROPN
grhe-5548	81	16	of	of	ADP
grhe-5548	81	17	course	course	NOUN
grhe-5548	81	18	,	,	PUNCT
grhe-5548	81	19	since	since	ADV
grhe-5548	81	20	,	,	PUNCT
grhe-5548	81	21	can	can	AUX
grhe-5548	81	22	not	not	PART
grhe-5548	81	23	be	be	AUX
grhe-5548	81	24	zero	zero	NUM
grhe-5548	81	25	.	.	PUNCT
grhe-5548	82	1	khayyam	khayyam	PROPN
grhe-5548	82	2	’s	’s	PART
grhe-5548	82	3	solution	solution	NOUN
grhe-5548	82	4	consisted	consist	VERB
grhe-5548	82	5	of	of	ADP
grhe-5548	82	6	constructing	construct	VERB
grhe-5548	82	7	the	the	DET
grhe-5548	82	8	parabola	parabola	NOUN
grhe-5548	82	9	and	and	CCONJ
grhe-5548	82	10	the	the	DET
grhe-5548	82	11	circle	circle	NOUN
grhe-5548	82	12	with	with	ADP
grhe-5548	82	13	center	center	NOUN
grhe-5548	82	14	at	at	ADP
grhe-5548	82	15	and	and	CCONJ
grhe-5548	82	16	radius	radius	VERB
grhe-5548	82	17	and	and	CCONJ
grhe-5548	82	18	determine	determine	VERB
grhe-5548	82	19	the	the	DET
grhe-5548	82	20	-coordinate	-coordinate	NOUN
grhe-5548	82	21	of	of	ADP
grhe-5548	82	22	the	the	DET
grhe-5548	82	23	intersction	intersction	NOUN
grhe-5548	82	24	.	.	PUNCT
grhe-5548	83	1	for	for	ADP
grhe-5548	83	2	,	,	PUNCT
grhe-5548	83	3	if	if	SCONJ
grhe-5548	83	4	we	we	PRON
grhe-5548	83	5	do	do	VERB
grhe-5548	83	6	that	that	PRON
grhe-5548	83	7	,	,	PUNCT
grhe-5548	83	8	we	we	PRON
grhe-5548	83	9	get	get	VERB
grhe-5548	83	10	the	the	DET
grhe-5548	83	11	second	second	ADJ
grhe-5548	83	12	equation	equation	NOUN
grhe-5548	83	13	becomes	become	VERB
grhe-5548	83	14	that	that	PRON
grhe-5548	83	15	is	be	AUX
grhe-5548	83	16	,	,	PUNCT
grhe-5548	83	17	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	83	18	global	global	ADJ
grhe-5548	83	19	research	research	NOUN
grhe-5548	83	20	in	in	ADP
grhe-5548	83	21	higher	high	ADJ
grhe-5548	83	22	education	education	NOUN
grhe-5548	83	23	vol	vol	NOUN
grhe-5548	83	24	.	.	PROPN
grhe-5548	84	1	6	6	NUM
grhe-5548	84	2	,	,	PUNCT
grhe-5548	84	3	no	no	INTJ
grhe-5548	84	4	.	.	NOUN
grhe-5548	84	5	2	2	NUM
grhe-5548	84	6	,	,	PUNCT
grhe-5548	84	7	2023	2023	NUM
grhe-5548	84	8	40	40	NUM
grhe-5548	84	9	published	publish	VERB
grhe-5548	84	10	by	by	ADP
grhe-5548	84	11	scholink	scholink	PROPN
grhe-5548	84	12	inc	inc	PROPN
grhe-5548	84	13	.	.	PROPN
grhe-5548	84	14	since	since	SCONJ
grhe-5548	84	15	this	this	PRON
grhe-5548	84	16	gives	give	VERB
grhe-5548	84	17	us	we	PRON
grhe-5548	84	18	the	the	DET
grhe-5548	84	19	root	root	NOUN
grhe-5548	84	20	found	find	VERB
grhe-5548	84	21	by	by	ADP
grhe-5548	84	22	this	this	DET
grhe-5548	84	23	method	method	NOUN
grhe-5548	84	24	is	be	AUX
grhe-5548	84	25	the	the	DET
grhe-5548	84	26	real	real	ADJ
grhe-5548	84	27	and	and	CCONJ
grhe-5548	84	28	positive	positive	ADJ
grhe-5548	84	29	root	root	NOUN
grhe-5548	84	30	since	since	SCONJ
grhe-5548	84	31	the	the	DET
grhe-5548	84	32	length	length	NOUN
grhe-5548	84	33	of	of	ADP
grhe-5548	84	34	a	a	DET
grhe-5548	84	35	line	line	NOUN
grhe-5548	84	36	segment	segment	NOUN
grhe-5548	84	37	can	can	AUX
grhe-5548	84	38	not	not	PART
grhe-5548	84	39	be	be	AUX
grhe-5548	84	40	negative	negative	ADJ
grhe-5548	84	41	or	or	CCONJ
grhe-5548	84	42	imaginary	imaginary	ADJ
grhe-5548	84	43	.	.	PUNCT
grhe-5548	85	1	for	for	ADP
grhe-5548	85	2	example	example	NOUN
grhe-5548	85	3	,	,	PUNCT
grhe-5548	85	4	to	to	PART
grhe-5548	85	5	solve	solve	VERB
grhe-5548	85	6	we	we	PRON
grhe-5548	85	7	graph	graph	VERB
grhe-5548	85	8	the	the	DET
grhe-5548	85	9	parabola	parabola	NOUN
grhe-5548	85	10	and	and	CCONJ
grhe-5548	85	11	the	the	DET
grhe-5548	85	12	circle	circle	NOUN
grhe-5548	85	13	and	and	CCONJ
grhe-5548	85	14	note	note	VERB
grhe-5548	85	15	that	that	SCONJ
grhe-5548	85	16	the	the	DET
grhe-5548	85	17	-coordinate	-coordinate	NOUN
grhe-5548	85	18	of	of	ADP
grhe-5548	85	19	intersection	intersection	NOUN
grhe-5548	85	20	of	of	ADP
grhe-5548	85	21	the	the	DET
grhe-5548	85	22	two	two	NUM
grhe-5548	85	23	curves	curve	NOUN
grhe-5548	85	24	for	for	ADP
grhe-5548	85	25	is	be	AUX
grhe-5548	85	26	at	at	ADP
grhe-5548	85	27	,	,	PUNCT
grhe-5548	85	28	which	which	PRON
grhe-5548	85	29	of	of	ADP
grhe-5548	85	30	course	course	NOUN
grhe-5548	85	31	is	be	AUX
grhe-5548	85	32	the	the	DET
grhe-5548	85	33	only	only	ADJ
grhe-5548	85	34	real	real	ADJ
grhe-5548	85	35	positive	positive	ADJ
grhe-5548	85	36	solution	solution	NOUN
grhe-5548	85	37	of	of	ADP
grhe-5548	85	38	the	the	DET
grhe-5548	85	39	equation	equation	NOUN
grhe-5548	85	40	.	.	PUNCT
grhe-5548	86	1	6	6	X
grhe-5548	86	2	.	.	X
grhe-5548	86	3	conclusion	conclusion	NOUN
grhe-5548	86	4	were	be	AUX
grhe-5548	86	5	one	one	NUM
grhe-5548	86	6	to	to	PART
grhe-5548	86	7	choose	choose	VERB
grhe-5548	86	8	to	to	PART
grhe-5548	86	9	adhere	adhere	VERB
grhe-5548	86	10	to	to	ADP
grhe-5548	86	11	the	the	DET
grhe-5548	86	12	instrumentalist	instrumentalist	NOUN
grhe-5548	86	13	or	or	CCONJ
grhe-5548	86	14	mechanical	mechanical	ADJ
grhe-5548	86	15	view	view	NOUN
grhe-5548	86	16	of	of	ADP
grhe-5548	86	17	mathematical	mathematical	ADJ
grhe-5548	86	18	knowledge	knowledge	NOUN
grhe-5548	86	19	and	and	CCONJ
grhe-5548	86	20	instruction	instruction	NOUN
grhe-5548	86	21	,	,	PUNCT
grhe-5548	86	22	one	one	PRON
grhe-5548	86	23	would	would	AUX
grhe-5548	86	24	then	then	ADV
grhe-5548	86	25	equate	equate	VERB
grhe-5548	86	26	computational	computational	ADJ
grhe-5548	86	27	proficiency	proficiency	NOUN
grhe-5548	86	28	with	with	ADP
grhe-5548	86	29	mathematical	mathematical	ADJ
grhe-5548	86	30	understanding	understanding	NOUN
grhe-5548	86	31	.	.	PUNCT
grhe-5548	87	1	in	in	ADP
grhe-5548	87	2	other	other	ADJ
grhe-5548	87	3	words	word	NOUN
grhe-5548	87	4	,	,	PUNCT
grhe-5548	87	5	in	in	ADP
grhe-5548	87	6	this	this	DET
grhe-5548	87	7	particular	particular	ADJ
grhe-5548	87	8	case	case	NOUN
grhe-5548	87	9	,	,	PUNCT
grhe-5548	87	10	one	one	PRON
grhe-5548	87	11	would	would	AUX
grhe-5548	87	12	just	just	ADV
grhe-5548	87	13	give	give	VERB
grhe-5548	87	14	cardano	cardano	PROPN
grhe-5548	87	15	’s	’s	PART
grhe-5548	87	16	formula	formula	NOUN
grhe-5548	87	17	(	(	PUNCT
grhe-5548	87	18	with	with	ADP
grhe-5548	87	19	or	or	CCONJ
grhe-5548	87	20	without	without	ADP
grhe-5548	87	21	proof	proof	NOUN
grhe-5548	87	22	)	)	PUNCT
grhe-5548	87	23	and	and	CCONJ
grhe-5548	87	24	use	use	VERB
grhe-5548	87	25	it	it	PRON
grhe-5548	87	26	to	to	PART
grhe-5548	87	27	solve	solve	VERB
grhe-5548	87	28	a	a	DET
grhe-5548	87	29	few	few	ADJ
grhe-5548	87	30	cubic	cubic	ADJ
grhe-5548	87	31	equations	equation	NOUN
grhe-5548	87	32	.	.	PUNCT
grhe-5548	88	1	this	this	PRON
grhe-5548	88	2	,	,	PUNCT
grhe-5548	88	3	of	of	ADP
grhe-5548	88	4	course	course	NOUN
grhe-5548	88	5	,	,	PUNCT
grhe-5548	88	6	would	would	AUX
grhe-5548	88	7	deny	deny	VERB
grhe-5548	88	8	the	the	DET
grhe-5548	88	9	students	student	NOUN
grhe-5548	88	10	the	the	DET
grhe-5548	88	11	true	true	ADJ
grhe-5548	88	12	mathematical	mathematical	ADJ
grhe-5548	88	13	understanding	understanding	NOUN
grhe-5548	88	14	of	of	ADP
grhe-5548	88	15	the	the	DET
grhe-5548	88	16	problem	problem	NOUN
grhe-5548	88	17	:	:	PUNCT
grhe-5548	88	18	all	all	PRON
grhe-5548	88	19	of	of	ADV
grhe-5548	88	20	a	a	PRON
grhe-5548	88	21	sudden	sudden	ADJ
grhe-5548	88	22	,	,	PUNCT
grhe-5548	88	23	somehow	somehow	ADV
grhe-5548	88	24	,	,	PUNCT
grhe-5548	88	25	a	a	DET
grhe-5548	88	26	person	person	NOUN
grhe-5548	88	27	discovered	discover	VERB
grhe-5548	88	28	a	a	DET
grhe-5548	88	29	formula	formula	NOUN
grhe-5548	88	30	,	,	PUNCT
grhe-5548	88	31	and	and	CCONJ
grhe-5548	88	32	all	all	DET
grhe-5548	88	33	one	one	NOUN
grhe-5548	88	34	has	have	VERB
grhe-5548	88	35	to	to	PART
grhe-5548	88	36	do	do	VERB
grhe-5548	88	37	now	now	ADV
grhe-5548	88	38	is	be	AUX
grhe-5548	88	39	to	to	PART
grhe-5548	88	40	substitute	substitute	VERB
grhe-5548	88	41	the	the	DET
grhe-5548	88	42	right	right	ADJ
grhe-5548	88	43	numbers	number	NOUN
grhe-5548	88	44	in	in	ADP
grhe-5548	88	45	the	the	DET
grhe-5548	88	46	right	right	ADJ
grhe-5548	88	47	places	place	NOUN
grhe-5548	88	48	,	,	PUNCT
grhe-5548	88	49	and	and	CCONJ
grhe-5548	88	50	then	then	ADV
grhe-5548	88	51	rely	rely	VERB
grhe-5548	88	52	on	on	ADP
grhe-5548	88	53	the	the	DET
grhe-5548	88	54	calculator	calculator	NOUN
grhe-5548	88	55	.	.	PUNCT
grhe-5548	89	1	the	the	DET
grhe-5548	89	2	instructor	instructor	NOUN
grhe-5548	89	3	,	,	PUNCT
grhe-5548	89	4	with	with	ADP
grhe-5548	89	5	this	this	DET
grhe-5548	89	6	approach	approach	NOUN
grhe-5548	89	7	,	,	PUNCT
grhe-5548	89	8	clearly	clearly	ADV
grhe-5548	89	9	would	would	AUX
grhe-5548	89	10	fail	fail	VERB
grhe-5548	89	11	to	to	PART
grhe-5548	89	12	provide	provide	VERB
grhe-5548	89	13	the	the	DET
grhe-5548	89	14	much	much	ADV
grhe-5548	89	15	needed	need	VERB
grhe-5548	89	16	insight	insight	NOUN
grhe-5548	89	17	to	to	ADP
grhe-5548	89	18	and	and	CCONJ
grhe-5548	89	19	motivation	motivation	NOUN
grhe-5548	89	20	for	for	ADP
grhe-5548	89	21	the	the	DET
grhe-5548	89	22	topic	topic	NOUN
grhe-5548	89	23	that	that	PRON
grhe-5548	89	24	is	be	AUX
grhe-5548	89	25	being	be	AUX
grhe-5548	89	26	covered	cover	VERB
grhe-5548	89	27	.	.	PUNCT
grhe-5548	90	1	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	PROPN
grhe-5548	90	2	global	global	ADJ
grhe-5548	90	3	research	research	NOUN
grhe-5548	90	4	in	in	ADP
grhe-5548	90	5	higher	high	ADJ
grhe-5548	90	6	education	education	NOUN
grhe-5548	90	7	vol	vol	NOUN
grhe-5548	90	8	.	.	PROPN
grhe-5548	91	1	6	6	NUM
grhe-5548	91	2	,	,	PUNCT
grhe-5548	91	3	no	no	INTJ
grhe-5548	91	4	.	.	NOUN
grhe-5548	91	5	2	2	NUM
grhe-5548	91	6	,	,	PUNCT
grhe-5548	91	7	2023	2023	NUM
grhe-5548	91	8	41	41	NUM
grhe-5548	91	9	published	publish	VERB
grhe-5548	91	10	by	by	ADP
grhe-5548	91	11	scholink	scholink	PROPN
grhe-5548	91	12	inc	inc	PROPN
grhe-5548	91	13	.	.	PROPN
grhe-5548	92	1	in	in	ADP
grhe-5548	92	2	contrast	contrast	NOUN
grhe-5548	92	3	,	,	PUNCT
grhe-5548	92	4	the	the	DET
grhe-5548	92	5	historical	historical	ADJ
grhe-5548	92	6	approach	approach	NOUN
grhe-5548	92	7	,	,	PUNCT
grhe-5548	92	8	places	place	VERB
grhe-5548	92	9	problem	problem	NOUN
grhe-5548	92	10	solving	solve	VERB
grhe-5548	92	11	at	at	ADP
grhe-5548	92	12	the	the	DET
grhe-5548	92	13	heart	heart	NOUN
grhe-5548	92	14	of	of	ADP
grhe-5548	92	15	instruction	instruction	NOUN
grhe-5548	92	16	.	.	PUNCT
grhe-5548	93	1	for	for	ADP
grhe-5548	93	2	instance	instance	NOUN
grhe-5548	93	3	,	,	PUNCT
grhe-5548	93	4	in	in	ADP
grhe-5548	93	5	our	our	PRON
grhe-5548	93	6	specific	specific	ADJ
grhe-5548	93	7	example	example	NOUN
grhe-5548	93	8	,	,	PUNCT
grhe-5548	93	9	the	the	DET
grhe-5548	93	10	students	student	NOUN
grhe-5548	93	11	would	would	AUX
grhe-5548	93	12	realize	realize	VERB
grhe-5548	93	13	that	that	SCONJ
grhe-5548	93	14	the	the	DET
grhe-5548	93	15	solution	solution	NOUN
grhe-5548	93	16	of	of	ADP
grhe-5548	93	17	the	the	DET
grhe-5548	93	18	cubic	cubic	ADJ
grhe-5548	93	19	equation	equation	NOUN
grhe-5548	93	20	was	be	AUX
grhe-5548	93	21	developed	develop	VERB
grhe-5548	93	22	over	over	ADP
grhe-5548	93	23	time	time	NOUN
grhe-5548	93	24	and	and	CCONJ
grhe-5548	93	25	through	through	ADP
grhe-5548	93	26	the	the	DET
grhe-5548	93	27	efforts	effort	NOUN
grhe-5548	93	28	of	of	ADP
grhe-5548	93	29	several	several	ADJ
grhe-5548	93	30	scholars	scholar	NOUN
grhe-5548	93	31	of	of	ADP
grhe-5548	93	32	different	different	ADJ
grhe-5548	93	33	ethnic	ethnic	ADJ
grhe-5548	93	34	and	and	CCONJ
grhe-5548	93	35	cultural	cultural	ADJ
grhe-5548	93	36	backgrounds	background	NOUN
grhe-5548	93	37	.	.	PUNCT
grhe-5548	94	1	the	the	DET
grhe-5548	94	2	reasoning	reasoning	NOUN
grhe-5548	94	3	behind	behind	ADP
grhe-5548	94	4	the	the	DET
grhe-5548	94	5	classification	classification	NOUN
grhe-5548	94	6	,	,	PUNCT
grhe-5548	94	7	the	the	DET
grhe-5548	94	8	gist	gist	NOUN
grhe-5548	94	9	of	of	ADP
grhe-5548	94	10	our	our	PRON
grhe-5548	94	11	paper	paper	NOUN
grhe-5548	94	12	,	,	PUNCT
grhe-5548	94	13	would	would	AUX
grhe-5548	94	14	pave	pave	VERB
grhe-5548	94	15	the	the	DET
grhe-5548	94	16	path	path	NOUN
grhe-5548	94	17	to	to	ADP
grhe-5548	94	18	students	student	NOUN
grhe-5548	94	19	’	'	PUNCT
grhe-5548	94	20	ability	ability	NOUN
grhe-5548	94	21	to	to	PART
grhe-5548	94	22	indulge	indulge	VERB
grhe-5548	94	23	in	in	ADP
grhe-5548	94	24	the	the	DET
grhe-5548	94	25	study	study	NOUN
grhe-5548	94	26	of	of	ADP
grhe-5548	94	27	a	a	DET
grhe-5548	94	28	class	class	NOUN
grhe-5548	94	29	of	of	ADP
grhe-5548	94	30	objects	object	NOUN
grhe-5548	94	31	rather	rather	ADV
grhe-5548	94	32	than	than	ADP
grhe-5548	94	33	a	a	DET
grhe-5548	94	34	specific	specific	ADJ
grhe-5548	94	35	object	object	NOUN
grhe-5548	94	36	.	.	PUNCT
grhe-5548	95	1	by	by	ADP
grhe-5548	95	2	taking	take	VERB
grhe-5548	95	3	a	a	DET
grhe-5548	95	4	historical	historical	ADJ
grhe-5548	95	5	approach	approach	NOUN
grhe-5548	95	6	to	to	ADP
grhe-5548	95	7	the	the	DET
grhe-5548	95	8	subject	subject	NOUN
grhe-5548	95	9	,	,	PUNCT
grhe-5548	95	10	students	student	NOUN
grhe-5548	95	11	would	would	AUX
grhe-5548	95	12	learn	learn	VERB
grhe-5548	95	13	that	that	SCONJ
grhe-5548	95	14	the	the	DET
grhe-5548	95	15	classification	classification	NOUN
grhe-5548	95	16	of	of	ADP
grhe-5548	95	17	the	the	DET
grhe-5548	95	18	cubic	cubic	NOUN
grhe-5548	95	19	was	be	AUX
grhe-5548	95	20	indeed	indeed	ADV
grhe-5548	95	21	a	a	DET
grhe-5548	95	22	mathematical	mathematical	ADJ
grhe-5548	95	23	necessity	necessity	NOUN
grhe-5548	95	24	on	on	ADP
grhe-5548	95	25	the	the	DET
grhe-5548	95	26	way	way	NOUN
grhe-5548	95	27	to	to	ADP
grhe-5548	95	28	the	the	DET
grhe-5548	95	29	discovery	discovery	NOUN
grhe-5548	95	30	of	of	ADP
grhe-5548	95	31	the	the	DET
grhe-5548	95	32	general	general	ADJ
grhe-5548	95	33	solution	solution	NOUN
grhe-5548	95	34	.	.	PUNCT
grhe-5548	96	1	as	as	ADP
grhe-5548	96	2	an	an	DET
grhe-5548	96	3	added	add	VERB
grhe-5548	96	4	benefit	benefit	NOUN
grhe-5548	96	5	,	,	PUNCT
grhe-5548	96	6	an	an	DET
grhe-5548	96	7	analysis	analysis	NOUN
grhe-5548	96	8	of	of	ADP
grhe-5548	96	9	the	the	DET
grhe-5548	96	10	historical	historical	ADJ
grhe-5548	96	11	development	development	NOUN
grhe-5548	96	12	of	of	ADP
grhe-5548	96	13	the	the	DET
grhe-5548	96	14	solution	solution	NOUN
grhe-5548	96	15	of	of	ADP
grhe-5548	96	16	the	the	DET
grhe-5548	96	17	cubic	cubic	ADJ
grhe-5548	96	18	shows	show	VERB
grhe-5548	96	19	the	the	DET
grhe-5548	96	20	internationalist	internationalist	ADJ
grhe-5548	96	21	character	character	NOUN
grhe-5548	96	22	of	of	ADP
grhe-5548	96	23	mathematics	mathematic	NOUN
grhe-5548	96	24	.	.	PUNCT
grhe-5548	97	1	as	as	ADP
grhe-5548	97	2	teachers	teacher	NOUN
grhe-5548	97	3	,	,	PUNCT
grhe-5548	97	4	if	if	SCONJ
grhe-5548	97	5	we	we	PRON
grhe-5548	97	6	are	be	AUX
grhe-5548	97	7	,	,	PUNCT
grhe-5548	97	8	as	as	SCONJ
grhe-5548	97	9	we	we	PRON
grhe-5548	97	10	should	should	AUX
grhe-5548	97	11	be	be	AUX
grhe-5548	97	12	,	,	PUNCT
grhe-5548	97	13	concerned	concerned	ADJ
grhe-5548	97	14	about	about	ADP
grhe-5548	97	15	cultural	cultural	ADJ
grhe-5548	97	16	chauvinism	chauvinism	NOUN
grhe-5548	97	17	and	and	CCONJ
grhe-5548	97	18	parochial	parochial	ADJ
grhe-5548	97	19	nationalism	nationalism	NOUN
grhe-5548	97	20	,	,	PUNCT
grhe-5548	97	21	and	and	CCONJ
grhe-5548	97	22	try	try	VERB
grhe-5548	97	23	to	to	PART
grhe-5548	97	24	instill	instill	VERB
grhe-5548	97	25	an	an	DET
grhe-5548	97	26	unbiased	unbiased	ADJ
grhe-5548	97	27	perspective	perspective	NOUN
grhe-5548	97	28	of	of	ADP
grhe-5548	97	29	mathematics	mathematic	NOUN
grhe-5548	97	30	,	,	PUNCT
grhe-5548	97	31	the	the	DET
grhe-5548	97	32	historical	historical	ADJ
grhe-5548	97	33	approach	approach	NOUN
grhe-5548	97	34	is	be	AUX
grhe-5548	97	35	the	the	DET
grhe-5548	97	36	needed	need	VERB
grhe-5548	97	37	panacea	panacea	NOUN
grhe-5548	97	38	to	to	PART
grhe-5548	97	39	convince	convince	VERB
grhe-5548	97	40	learners	learner	NOUN
grhe-5548	97	41	that	that	SCONJ
grhe-5548	97	42	transnational	transnational	ADJ
grhe-5548	97	43	collaboration	collaboration	NOUN
grhe-5548	97	44	,	,	PUNCT
grhe-5548	97	45	universal	universal	ADJ
grhe-5548	97	46	solidarity	solidarity	NOUN
grhe-5548	97	47	,	,	PUNCT
grhe-5548	97	48	and	and	CCONJ
grhe-5548	97	49	fellowship	fellowship	NOUN
grhe-5548	97	50	of	of	ADP
grhe-5548	97	51	scholars	scholar	NOUN
grhe-5548	97	52	have	have	AUX
grhe-5548	97	53	always	always	ADV
grhe-5548	97	54	been	be	AUX
grhe-5548	97	55	the	the	DET
grhe-5548	97	56	epitomes	epitome	NOUN
grhe-5548	97	57	of	of	ADP
grhe-5548	97	58	mathematical	mathematical	ADJ
grhe-5548	97	59	development	development	NOUN
grhe-5548	97	60	.	.	PUNCT
grhe-5548	98	1	it	it	PRON
grhe-5548	98	2	also	also	ADV
grhe-5548	98	3	shows	show	VERB
grhe-5548	98	4	the	the	DET
grhe-5548	98	5	interconnectedness	interconnectedness	NOUN
grhe-5548	98	6	of	of	ADP
grhe-5548	98	7	mathematical	mathematical	ADJ
grhe-5548	98	8	areas	area	NOUN
grhe-5548	98	9	(	(	PUNCT
grhe-5548	98	10	geometry	geometry	NOUN
grhe-5548	98	11	,	,	PUNCT
grhe-5548	98	12	algebra	algebra	NOUN
grhe-5548	98	13	,	,	PUNCT
grhe-5548	98	14	etc	etc	X
grhe-5548	98	15	.	.	X
grhe-5548	98	16	)	)	PUNCT
grhe-5548	98	17	.	.	PUNCT
grhe-5548	99	1	moreover	moreover	ADV
grhe-5548	99	2	,	,	PUNCT
grhe-5548	99	3	it	it	PRON
grhe-5548	99	4	proves	prove	VERB
grhe-5548	99	5	that	that	SCONJ
grhe-5548	99	6	even	even	ADV
grhe-5548	99	7	masters	master	NOUN
grhe-5548	99	8	were	be	AUX
grhe-5548	99	9	prone	prone	ADJ
grhe-5548	99	10	to	to	ADP
grhe-5548	99	11	erroneous	erroneous	ADJ
grhe-5548	99	12	thinking	thinking	NOUN
grhe-5548	99	13	(	(	PUNCT
grhe-5548	99	14	denial	denial	NOUN
grhe-5548	99	15	of	of	ADP
grhe-5548	99	16	negative	negative	ADJ
grhe-5548	99	17	solutions	solution	NOUN
grhe-5548	99	18	)	)	PUNCT
grhe-5548	99	19	and	and	CCONJ
grhe-5548	99	20	hence	hence	ADV
grhe-5548	99	21	shows	show	VERB
grhe-5548	99	22	the	the	DET
grhe-5548	99	23	dangers	danger	NOUN
grhe-5548	99	24	of	of	ADP
grhe-5548	99	25	taking	take	VERB
grhe-5548	99	26	mathematics	mathematic	NOUN
grhe-5548	99	27	as	as	ADP
grhe-5548	99	28	a	a	DET
grhe-5548	99	29	set	set	NOUN
grhe-5548	99	30	of	of	ADP
grhe-5548	99	31	absolute	absolute	ADJ
grhe-5548	99	32	truths	truth	NOUN
grhe-5548	99	33	as	as	SCONJ
grhe-5548	99	34	opposed	oppose	VERB
grhe-5548	99	35	to	to	ADP
grhe-5548	99	36	a	a	DET
grhe-5548	99	37	set	set	NOUN
grhe-5548	99	38	of	of	ADP
grhe-5548	99	39	fallible	fallible	ADJ
grhe-5548	99	40	and	and	CCONJ
grhe-5548	99	41	transmutable	transmutable	ADJ
grhe-5548	99	42	ones	one	NOUN
grhe-5548	99	43	.	.	PUNCT
grhe-5548	100	1	references	reference	NOUN
grhe-5548	100	2	bidwell	bidwell	PROPN
grhe-5548	100	3	,	,	PUNCT
grhe-5548	100	4	j.	j.	PROPN
grhe-5548	100	5	k.	k.	PROPN
grhe-5548	100	6	(	(	PUNCT
grhe-5548	100	7	1993	1993	NUM
grhe-5548	100	8	)	)	PUNCT
grhe-5548	100	9	.	.	PUNCT
grhe-5548	101	1	humanize	humanize	VERB
grhe-5548	101	2	your	your	PRON
grhe-5548	101	3	classroom	classroom	NOUN
grhe-5548	101	4	with	with	ADP
grhe-5548	101	5	the	the	DET
grhe-5548	101	6	history	history	NOUN
grhe-5548	101	7	of	of	ADP
grhe-5548	101	8	mathematics	mathematic	NOUN
grhe-5548	101	9	.	.	PUNCT
grhe-5548	102	1	mathematics	mathematic	NOUN
grhe-5548	102	2	teacher	teacher	NOUN
grhe-5548	102	3	,	,	PUNCT
grhe-5548	102	4	86	86	NUM
grhe-5548	102	5	,	,	PUNCT
grhe-5548	102	6	461	461	NUM
grhe-5548	102	7	-	-	SYM
grhe-5548	102	8	464	464	NUM
grhe-5548	102	9	.	.	PUNCT
grhe-5548	103	1	https://doi.org/10.5951/mt.86.6.0461	https://doi.org/10.5951/mt.86.6.0461	PRON
grhe-5548	103	2	cooke	cooke	PROPN
grhe-5548	103	3	,	,	PUNCT
grhe-5548	103	4	r.	r.	PROPN
grhe-5548	103	5	(	(	PUNCT
grhe-5548	103	6	2012	2012	NUM
grhe-5548	103	7	)	)	PUNCT
grhe-5548	103	8	.	.	PUNCT
grhe-5548	104	1	the	the	DET
grhe-5548	104	2	history	history	NOUN
grhe-5548	104	3	of	of	ADP
grhe-5548	104	4	mathematics	mathematic	NOUN
grhe-5548	104	5	:	:	PUNCT
grhe-5548	104	6	a	a	DET
grhe-5548	104	7	brief	brief	ADJ
grhe-5548	104	8	course	course	NOUN
grhe-5548	104	9	(	(	PUNCT
grhe-5548	104	10	3rd	3rd	ADJ
grhe-5548	104	11	ed	ed	NOUN
grhe-5548	104	12	.	.	PUNCT
grhe-5548	104	13	)	)	PUNCT
grhe-5548	104	14	.	.	PUNCT
grhe-5548	105	1	john	john	PROPN
grhe-5548	105	2	wiley	wiley	PROPN
grhe-5548	105	3	&	&	CCONJ
grhe-5548	105	4	sons	son	NOUN
grhe-5548	105	5	.	.	PUNCT
grhe-5548	106	1	dilgan	dilgan	PROPN
grhe-5548	106	2	,	,	PUNCT
grhe-5548	106	3	h.	h.	PROPN
grhe-5548	106	4	(	(	PUNCT
grhe-5548	106	5	1964	1964	NUM
grhe-5548	106	6	)	)	PUNCT
grhe-5548	106	7	.	.	PUNCT
grhe-5548	107	1	șair	șair	PROPN
grhe-5548	107	2	matematikçi	matematikçi	PROPN
grhe-5548	107	3	ömer	ömer	PROPN
grhe-5548	107	4	hayyam	hayyam	PROPN
grhe-5548	107	5	(	(	PUNCT
grhe-5548	107	6	poet	poet	NOUN
grhe-5548	107	7	mathematician	mathematician	PROPN
grhe-5548	107	8	omar	omar	PROPN
grhe-5548	107	9	khayyam	khayyam	PROPN
grhe-5548	107	10	)	)	PUNCT
grhe-5548	107	11	.	.	PUNCT
grhe-5548	108	1	sirketi	sirketi	PROPN
grhe-5548	108	2	mürettibiye	mürettibiye	PROPN
grhe-5548	108	3	basimevi	basimevi	PROPN
grhe-5548	108	4	,	,	PUNCT
grhe-5548	108	5	istanbul	istanbul	PROPN
grhe-5548	108	6	,	,	PUNCT
grhe-5548	108	7	turkey	turkey	PROPN
grhe-5548	108	8	.	.	PUNCT
grhe-5548	109	1	heath	heath	PROPN
grhe-5548	109	2	,	,	PUNCT
grhe-5548	109	3	t.	t.	PROPN
grhe-5548	109	4	l.	l.	PROPN
grhe-5548	109	5	(	(	PUNCT
grhe-5548	109	6	2009	2009	NUM
grhe-5548	109	7	)	)	PUNCT
grhe-5548	109	8	.	.	PUNCT
grhe-5548	110	1	diophantus	diophantus	PROPN
grhe-5548	110	2	of	of	ADP
grhe-5548	110	3	alexandria	alexandria	PROPN
grhe-5548	110	4	:	:	PUNCT
grhe-5548	110	5	a	a	DET
grhe-5548	110	6	study	study	NOUN
grhe-5548	110	7	in	in	ADP
grhe-5548	110	8	the	the	DET
grhe-5548	110	9	history	history	NOUN
grhe-5548	110	10	of	of	ADP
grhe-5548	110	11	greek	greek	ADJ
grhe-5548	110	12	algebra	algebra	NOUN
grhe-5548	110	13	.	.	PUNCT
grhe-5548	111	1	martino	martino	PROPN
grhe-5548	111	2	fine	fine	ADJ
grhe-5548	111	3	books	book	NOUN
grhe-5548	111	4	.	.	PUNCT
grhe-5548	112	1	jankvist	jankvist	PROPN
grhe-5548	112	2	,	,	PUNCT
grhe-5548	112	3	u.	u.	PROPN
grhe-5548	112	4	t.	t.	PROPN
grhe-5548	112	5	(	(	PUNCT
grhe-5548	112	6	2009	2009	NUM
grhe-5548	112	7	)	)	PUNCT
grhe-5548	112	8	.	.	PUNCT
grhe-5548	113	1	a	a	DET
grhe-5548	113	2	characterization	characterization	NOUN
grhe-5548	113	3	of	of	ADP
grhe-5548	113	4	the	the	DET
grhe-5548	113	5	“	"	PUNCT
grhe-5548	113	6	why	why	SCONJ
grhe-5548	113	7	s	s	VERB
grhe-5548	113	8	”	"	PUNCT
grhe-5548	113	9	and	and	CCONJ
grhe-5548	113	10	“	"	PUNCT
grhe-5548	113	11	how	how	SCONJ
grhe-5548	113	12	s	s	X
grhe-5548	113	13	”	"	PUNCT
grhe-5548	113	14	of	of	ADP
grhe-5548	113	15	using	use	VERB
grhe-5548	113	16	history	history	NOUN
grhe-5548	113	17	in	in	ADP
grhe-5548	113	18	mathematics	mathematic	NOUN
grhe-5548	113	19	education	education	NOUN
grhe-5548	113	20	.	.	PUNCT
grhe-5548	114	1	educational	educational	ADJ
grhe-5548	114	2	studies	study	NOUN
grhe-5548	114	3	in	in	ADP
grhe-5548	114	4	mathematics	mathematic	NOUN
grhe-5548	114	5	,	,	PUNCT
grhe-5548	114	6	71(3	71(3	NUM
grhe-5548	114	7	)	)	PUNCT
grhe-5548	114	8	,	,	PUNCT
grhe-5548	114	9	235	235	NUM
grhe-5548	114	10	-	-	SYM
grhe-5548	114	11	261	261	NUM
grhe-5548	114	12	.	.	PUNCT
grhe-5548	115	1	https://doi.org/10.1007/s10649-008-9174-9	https://doi.org/10.1007/s10649-008-9174-9	NUM
grhe-5548	115	2	katz	katz	PROPN
grhe-5548	115	3	,	,	PUNCT
grhe-5548	115	4	v.	v.	PROPN
grhe-5548	115	5	(	(	PUNCT
grhe-5548	115	6	2004	2004	NUM
grhe-5548	115	7	)	)	PUNCT
grhe-5548	115	8	.	.	PUNCT
grhe-5548	116	1	a	a	DET
grhe-5548	116	2	history	history	NOUN
grhe-5548	116	3	of	of	ADP
grhe-5548	116	4	mathematics	mathematic	NOUN
grhe-5548	116	5	.	.	PUNCT
grhe-5548	117	1	boston	boston	PROPN
grhe-5548	117	2	:	:	PUNCT
grhe-5548	117	3	addison	addison	PROPN
grhe-5548	117	4	wesley	wesley	PROPN
grhe-5548	117	5	.	.	PUNCT
grhe-5548	118	1	kline	kline	PROPN
grhe-5548	118	2	,	,	PUNCT
grhe-5548	118	3	m.	m.	NOUN
grhe-5548	118	4	(	(	PUNCT
grhe-5548	118	5	1990	1990	NUM
grhe-5548	118	6	)	)	PUNCT
grhe-5548	118	7	.	.	PUNCT
grhe-5548	119	1	mathematical	mathematical	ADJ
grhe-5548	119	2	thought	thought	NOUN
grhe-5548	119	3	from	from	ADP
grhe-5548	119	4	ancient	ancient	ADJ
grhe-5548	119	5	to	to	ADP
grhe-5548	119	6	modern	modern	ADJ
grhe-5548	119	7	times	time	NOUN
grhe-5548	119	8	.	.	PUNCT
grhe-5548	120	1	oxford	oxford	PROPN
grhe-5548	120	2	university	university	PROPN
grhe-5548	120	3	press	press	NOUN
grhe-5548	120	4	.	.	PUNCT
grhe-5548	121	1	marshall	marshall	PROPN
grhe-5548	121	2	,	,	PUNCT
grhe-5548	121	3	g.	g.	PROPN
grhe-5548	121	4	l.	l.	PROPN
grhe-5548	121	5	,	,	PUNCT
grhe-5548	121	6	&	&	CCONJ
grhe-5548	121	7	rich	rich	PROPN
grhe-5548	121	8	,	,	PUNCT
grhe-5548	121	9	b.	b.	PROPN
grhe-5548	121	10	s.	s.	PROPN
grhe-5548	121	11	(	(	PUNCT
grhe-5548	121	12	2000	2000	NUM
grhe-5548	121	13	)	)	PUNCT
grhe-5548	121	14	.	.	PUNCT
grhe-5548	122	1	the	the	DET
grhe-5548	122	2	role	role	NOUN
grhe-5548	122	3	of	of	ADP
grhe-5548	122	4	history	history	NOUN
grhe-5548	122	5	in	in	ADP
grhe-5548	122	6	a	a	DET
grhe-5548	122	7	mathematics	mathematics	NOUN
grhe-5548	122	8	class	class	NOUN
grhe-5548	122	9	.	.	PUNCT
grhe-5548	123	1	mathematics	mathematic	NOUN
grhe-5548	123	2	teacher	teacher	NOUN
grhe-5548	123	3	,	,	PUNCT
grhe-5548	123	4	93(8	93(8	NUM
grhe-5548	123	5	)	)	PUNCT
grhe-5548	123	6	,	,	PUNCT
grhe-5548	123	7	704	704	NUM
grhe-5548	123	8	-	-	SYM
grhe-5548	123	9	706	706	NUM
grhe-5548	123	10	.	.	PUNCT
grhe-5548	124	1	https://doi.org/10.5951/mt.93.8.0704	https://doi.org/10.5951/mt.93.8.0704	PROPN
grhe-5548	124	2	van	van	PROPN
grhe-5548	124	3	der	der	PROPN
grhe-5548	124	4	waerden	waerden	PROPN
grhe-5548	124	5	,	,	PUNCT
grhe-5548	124	6	b.	b.	PROPN
grhe-5548	124	7	l.	l.	PROPN
grhe-5548	124	8	(	(	PUNCT
grhe-5548	124	9	1983	1983	NUM
grhe-5548	124	10	)	)	PUNCT
grhe-5548	124	11	.	.	PUNCT
grhe-5548	125	1	geometry	geometry	NOUN
grhe-5548	125	2	and	and	CCONJ
grhe-5548	125	3	algebra	algebra	NOUN
grhe-5548	125	4	of	of	ADP
grhe-5548	125	5	ancient	ancient	ADJ
grhe-5548	125	6	civilizations	civilization	NOUN
grhe-5548	125	7	.	.	PUNCT
grhe-5548	126	1	springer	springer	NOUN
grhe-5548	126	2	-	-	PUNCT
grhe-5548	126	3	verlag	verlag	PROPN
grhe-5548	126	4	.	.	PUNCT
grhe-5548	127	1	https://doi.org/10.1007/978-3-642-61779-9	https://doi.org/10.1007/978-3-642-61779-9	PROPN
grhe-5548	127	2	https://doi.org/10.5951/mt.86.6.0461	https://doi.org/10.5951/mt.86.6.0461	PRON
grhe-5548	127	3	https://doi.org/10.1007/s10649-008-9174-9	https://doi.org/10.1007/s10649-008-9174-9	PROPN
grhe-5548	127	4	https://doi.org/10.5951/mt.93.8.0704	https://doi.org/10.5951/mt.93.8.0704	ADV
grhe-5548	127	5	https://doi.org/10.1007/978-3-642-61779-9	https://doi.org/10.1007/978-3-642-61779-9	PROPN
grhe-5548	127	6	www.scholink.org/ojs/index.php/grhe	www.scholink.org/ojs/index.php/grhe	NOUN
grhe-5548	127	7	global	global	ADJ
grhe-5548	127	8	research	research	NOUN
grhe-5548	127	9	in	in	ADP
grhe-5548	127	10	higher	high	ADJ
grhe-5548	127	11	education	education	NOUN
grhe-5548	127	12	vol	vol	NOUN
grhe-5548	127	13	.	.	PROPN
grhe-5548	128	1	6	6	NUM
grhe-5548	128	2	,	,	PUNCT
grhe-5548	128	3	no	no	INTJ
grhe-5548	128	4	.	.	NOUN
grhe-5548	128	5	2	2	NUM
grhe-5548	128	6	,	,	PUNCT
grhe-5548	128	7	2023	2023	NUM
grhe-5548	128	8	42	42	NUM
grhe-5548	128	9	published	publish	VERB
grhe-5548	128	10	by	by	ADP
grhe-5548	128	11	scholink	scholink	PROPN
grhe-5548	128	12	inc	inc	PROPN
grhe-5548	128	13	.	.	PROPN
grhe-5548	128	14	van	van	PROPN
grhe-5548	128	15	der	der	PROPN
grhe-5548	128	16	waerden	waerden	PROPN
grhe-5548	128	17	,	,	PUNCT
grhe-5548	128	18	b.	b.	PROPN
grhe-5548	128	19	l.	l.	PROPN
grhe-5548	128	20	(	(	PUNCT
grhe-5548	128	21	1985	1985	NUM
grhe-5548	128	22	)	)	PUNCT
grhe-5548	128	23	.	.	PUNCT
grhe-5548	129	1	“	"	PUNCT
grhe-5548	129	2	from	from	ADP
grhe-5548	129	3	viète	viète	NOUN
grhe-5548	129	4	to	to	ADP
grhe-5548	129	5	descartes	descartes	PROPN
grhe-5548	129	6	”	"	PUNCT
grhe-5548	129	7	,	,	PUNCT
grhe-5548	129	8	a	a	DET
grhe-5548	129	9	history	history	NOUN
grhe-5548	129	10	of	of	ADP
grhe-5548	129	11	algebra	algebra	NOUN
grhe-5548	129	12	:	:	PUNCT
grhe-5548	129	13	from	from	ADP
grhe-5548	129	14	al	al	PROPN
grhe-5548	129	15	-	-	PUNCT
grhe-5548	129	16	khwārizmī	khwārizmī	PROPN
grhe-5548	129	17	to	to	PART
grhe-5548	129	18	emmy	emmy	VERB
grhe-5548	129	19	noether	noether	PROPN
grhe-5548	129	20	.	.	PUNCT
grhe-5548	130	1	springer	springer	NOUN
grhe-5548	130	2	-	-	PUNCT
grhe-5548	130	3	verlag	verlag	PROPN
grhe-5548	130	4	.	.	PUNCT
grhe-5548	131	1	https://doi.org/10.1007/978-3-642-51599-6_3	https://doi.org/10.1007/978-3-642-51599-6_3	PROPN
grhe-5548	131	2	wilson	wilson	PROPN
grhe-5548	131	3	,	,	PUNCT
grhe-5548	131	4	p.	p.	PROPN
grhe-5548	131	5	s.	s.	PROPN
grhe-5548	131	6	,	,	PUNCT
grhe-5548	131	7	&	&	CCONJ
grhe-5548	131	8	chauvot	chauvot	PROPN
grhe-5548	131	9	,	,	PUNCT
grhe-5548	131	10	j.	j.	PROPN
grhe-5548	131	11	b.	b.	PROPN
grhe-5548	131	12	(	(	PUNCT
grhe-5548	131	13	2000	2000	NUM
grhe-5548	131	14	)	)	PUNCT
grhe-5548	131	15	.	.	PUNCT
grhe-5548	132	1	who	who	PRON
grhe-5548	132	2	?	?	PUNCT
grhe-5548	133	1	how	how	SCONJ
grhe-5548	133	2	?	?	PUNCT
grhe-5548	134	1	what	what	PRON
grhe-5548	134	2	?	?	PUNCT
grhe-5548	135	1	a	a	DET
grhe-5548	135	2	strategy	strategy	NOUN
grhe-5548	135	3	for	for	ADP
grhe-5548	135	4	using	use	VERB
grhe-5548	135	5	history	history	NOUN
grhe-5548	135	6	to	to	PART
grhe-5548	135	7	teach	teach	VERB
grhe-5548	135	8	mathematics	mathematic	NOUN
grhe-5548	135	9	.	.	PUNCT
grhe-5548	136	1	mathematics	mathematic	NOUN
grhe-5548	136	2	teacher	teacher	NOUN
grhe-5548	136	3	,	,	PUNCT
grhe-5548	136	4	93(8	93(8	NUM
grhe-5548	136	5	)	)	PUNCT
grhe-5548	136	6	,	,	PUNCT
grhe-5548	136	7	642	642	NUM
grhe-5548	136	8	-	-	SYM
grhe-5548	136	9	645	645	NUM
grhe-5548	136	10	.	.	PUNCT
grhe-5548	137	1	https://doi.org/10.5951/mt.93.8.0642	https://doi.org/10.5951/mt.93.8.0642	NOUN
grhe-5548	137	2	note	note	NOUN
grhe-5548	137	3	note	note	VERB
grhe-5548	137	4	1	1	NUM
grhe-5548	137	5	.	.	PUNCT
grhe-5548	138	1	in	in	ADP
grhe-5548	138	2	his	his	PRON
grhe-5548	138	3	paper	paper	NOUN
grhe-5548	138	4	,	,	PUNCT
grhe-5548	138	5	réflexions	réflexion	NOUN
grhe-5548	138	6	sur	sur	PROPN
grhe-5548	138	7	la	la	X
grhe-5548	138	8	résolution	résolution	PROPN
grhe-5548	138	9	algébrique	algébrique	PROPN
grhe-5548	138	10	des	des	PROPN
grhe-5548	138	11	équations	équations	PROPN
grhe-5548	138	12	,	,	PUNCT
grhe-5548	138	13	joseph	joseph	PROPN
grhe-5548	138	14	louis	louis	PROPN
grhe-5548	138	15	lagrange	lagrange	PROPN
grhe-5548	138	16	introduced	introduce	VERB
grhe-5548	138	17	a	a	DET
grhe-5548	138	18	new	new	ADJ
grhe-5548	138	19	method	method	NOUN
grhe-5548	138	20	to	to	PART
grhe-5548	138	21	solve	solve	VERB
grhe-5548	138	22	equations	equation	NOUN
grhe-5548	138	23	of	of	ADP
grhe-5548	138	24	low	low	ADJ
grhe-5548	138	25	degree	degree	NOUN
grhe-5548	138	26	in	in	ADP
grhe-5548	138	27	a	a	DET
grhe-5548	138	28	uniform	uniform	ADJ
grhe-5548	138	29	way	way	NOUN
grhe-5548	138	30	,	,	PUNCT
grhe-5548	138	31	with	with	ADP
grhe-5548	138	32	the	the	DET
grhe-5548	138	33	hope	hope	NOUN
grhe-5548	138	34	that	that	SCONJ
grhe-5548	138	35	he	he	PRON
grhe-5548	138	36	could	could	AUX
grhe-5548	138	37	generalize	generalize	VERB
grhe-5548	138	38	it	it	PRON
grhe-5548	138	39	for	for	ADP
grhe-5548	138	40	higher	high	ADJ
grhe-5548	138	41	degrees	degree	NOUN
grhe-5548	138	42	.	.	PUNCT
grhe-5548	139	1	of	of	ADP
grhe-5548	139	2	course	course	NOUN
grhe-5548	139	3	,	,	PUNCT
grhe-5548	139	4	we	we	PRON
grhe-5548	139	5	now	now	ADV
grhe-5548	139	6	know	know	VERB
grhe-5548	139	7	of	of	ADP
grhe-5548	139	8	the	the	DET
grhe-5548	139	9	non	non	NOUN
grhe-5548	139	10	-	-	NOUN
grhe-5548	139	11	existence	existence	NOUN
grhe-5548	139	12	of	of	ADP
grhe-5548	139	13	an	an	DET
grhe-5548	139	14	algebraic	algebraic	ADJ
grhe-5548	139	15	formula	formula	NOUN
grhe-5548	139	16	for	for	ADP
grhe-5548	139	17	degrees	degree	NOUN
grhe-5548	139	18	5	5	NUM
grhe-5548	139	19	and	and	CCONJ
grhe-5548	139	20	higher	high	ADJ
grhe-5548	139	21	(	(	PUNCT
grhe-5548	139	22	abel	abel	PROPN
grhe-5548	139	23	’s	’s	PART
grhe-5548	139	24	theorem	theorem	PROPN
grhe-5548	139	25	)	)	PUNCT
grhe-5548	139	26	.	.	PUNCT
grhe-5548	140	1	https://doi.org/10.1007/978-3-642-51599-6_3	https://doi.org/10.1007/978-3-642-51599-6_3	NOUN
grhe-5548	140	2	https://doi.org/10.5951/mt.93.8.0642	https://doi.org/10.5951/mt.93.8.0642	ADJ