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
51	13
52	14
53	15
54	16
55	17
56	18
57	19
58	20
59	21
60	22
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

13496Apollonij Pergæi

Notæ in Propoſ. LXXIV.

ERgo E F per centrum non tranſit, cadat ſuper C D, & quia produ-
11a cti ſunt ex E duo breuiſecantes; ergo C F excedit dimidium erecti,
& E F æqualis eſt Trutinæ (52. ex 5.) patet itaque, vt antea demonſtra-
uimus, quod E G ſit maximus ramorum, & E C minimus, & c.

118[Figure 118] Quoniam in 11. huius oſtenſum eſt, quod ſemiaxis minor ellipſis eſt ramus bre-
uiſsimus, ergo ſi incidentia perpendicularis E F ſuper axim A C, ideſt punctum
F eſt centrum ellipſis educerentur ex concurſu E tres breuiſecantes, nimirum
E H, E G, & E F producta, quæ eſſet axis minor ellipſis: hoc autem eſt con-
tra hypotheſim, cum ducti ſint ex E duo breuiſecantes: ergo eorum vnus E H
menſuram C F ſecat, quæ minor eſſe debet ſemiſſe axis maioris C D; igitur
ex conuerſa propoſitione 50. huius, menſura C F maior erit ſemiſſe lateris re-
cti, & (ex conuerſa propoſ. 52. huius) erit perpendicularis E F æqualis Tru-
tinæ. Demonſtratio huius propoſitionis neglecta ab Apollonio, propterea quod
eodem ferè modo, ac præcedens oſtendi poteſt, breuiſsimè perficietur in hunc
modum.

Quoniam à concurſu E vnicus tantum breuiſecans E H ad quadrantem C B
22Propoſ.
67. huius. ducitur; igitur C E minimus eſt omnium ramorum cadentium ad ſectionis pe-
ripheriam C B, & E C vertici B propinquior minor eſt remotiore E H, & E
H minor, quàm E B: rurſus, quia ramorum cadentium ex E ad peripheriam
33Ex 29. 30.
huius. B G vnus tantummodo breuiſecans E G conſtituit cum tangente N G

Page concordance

Text layer

Text normalization

Search

Scan	Original
51	13
52	14
53	15
54	16
55	17
56	18
57	19
58	20
59	21
60	22
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

Scan	Original
51	13
52	14
53	15
54	16
55	17
56	18
57	19
58	20
59	21
60	22
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

Scan	Original
51	13
52	14
53	15
54	16
55	17
56	18
57	19
58	20
59	21
60	22
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