Apollonius <Pergaeus> - Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

11678Apollonij Pergæi

MONITVM.

ANtequam huius Decimætertiæ Sectionis explicationes, atque
emendationes aggrediamur, vt Notæ breuiores, clarioreſque
reddentatur, & teſtus Arabici menda facilius corrigi poſſent, operæ
pretium duximus (amice lector) Lemmata ſequentia præmittere.

LEMMA IX.

Si ad coniſectionem, atque ad vnum quadrantem ellipſis A B C à
concurſu D nullus ramus duci poſsit, qui ſit breuiſecans; Dico, quod
quilibet ſecans ramus D B cum tangente H B G per eius terminum B
ducta efficit angulum D B H ad partes verticis A acutum, & D B
G, qui deinceps eſt, obtuſum.

Quoniam nullus ramus ex concurſu

98[Figure 98] D ad ſectionem A C ductus eſt breui-
ſecans, erit (ex conuerſa propoſitionis
49. 50. 51. 52. huius) menſura A E
aut non maior ſemiſſe lateris recti, aut
perpendicularis D E maior Trutina,
quæ ſit F, & ideo quilibet ramus ſe-
cans D B cadit ſupra breuiſsimam ex
puncto B ad axim ductam, eſt verò
breuiſsima ex puncto B ad axim ducta
perpendicularis ad G B H tangentem
1129. 30.
huius. ſectionem in B; ergo angulus D B H,
verticem A reſpiciens eſt acutus, & qui deinceps eſt D B G erit obtuſus.

LEMMA X.

Iiſdem poſitis, ſi à concurſu D vnicus tantum ramus D B breuiſe-
cans ad ſectionem A B duci poteſt; Dico, quod quilibet alius ramus
ſecans D 1 ſupra, vel infra breuiſecantem D B poſitus efficit cum recta
L I H tangente ſectionem in I angulum D I L, verticem reſpicien-
tem, acutum, & D I H, qui deinceps eſt, obtuſum.

Nam ex conuerſa propoſitione 51. & 52. huius perpendicularis D E æqualis
crit Trutinæ F, & ideo quilibet ramus D I poſitus ſupra, velinſra

Page concordance

Text layer

Text normalization

Search

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52

Scan	Original
61	23
62	24
63	25
64	26
65	27
66	28
67	29
68	30
69	31
70	32
71	33
72	34
73	35
74	36
75	37
76	38
77	39
78	40
79	41
80	42
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52