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
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

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
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72

Scan	Original
81	43
82	44
83	45
84	46
85	47
86	48
87	49
88	50
89	51
90	52
91	53
92	54
93	55
94	56
95	57
96	58
97	59
98	60
99	61
100	62
101	63
102	64
103	65
104	66
105	67
106	68
107	69
108	70
109	71
110	72