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

154116Apollonij Pergæi

143[Figure 143]

Ergo quadratum I C æquale eſt duplo trianguli N F M cum duplo
11e trianguli D I N, & c. Quoniam quadratum I C æquale eſt duplo trianguli I
C F, ſeu duplo trianguli I F E vna cum duplo trianguli E F C; eſtque duplum
trianguli E D M æquale duplo trianguli E C F; igitur quadratum I C æquale
eſt duplo trianguli I F E vna cum duplo trianguli E M D: ĳs vero triangulis
æquatur duplum trianguli N F M vna cum duplo trianguli D I N; igitur qua-
dratum I C æquale eſt duplo trianguli N F M vna cum duplo trianguli D I N:
eſt vero quadratum I D æquale duplo trianguli D I N; igitur exceſſus quadrati
I C ſupra quadratum I D eſt triangulum N F M bis ſumptum; ſcilicet exem-
plar applicatum ad latus tranſuerſum D C.

SECTIO DECIMASEPTIMA
Continens XIX. XX. XXI. XXII. XXIII.
XXIV. & XXV. Propoſ. Apollonij.

PROPOSITIO XIX.

SI menſura E C ſumatur in axe minori ellipſis A B C, ſitque
22a maior comparata; erit maximus omniũ ramorũ egredientiũ
ex ſua origine, vt E F, E B, E G; & maximo propinquior,
maior erit remotiore, nempe E F, quàm E B, & E B, quàm E G.

Coniungamus rectas A G, G B, B F,

144[Figure 144]33b F C; & ſecetur C H æqualis compara-
tæ: iungãturque F H, H B, H G.

Et quoniam H C maior eſt, quàm H
F, (16. 17. 18. ex 5.) erit angulus H C
F minor, quàm H F C; & ideo multo
minor erit, quàm E F C, quare E C
maior eſt, quàm E F: & ſic conſtat, quod
E F maior ſit, quàm E B, & E B, quàm
E G, & E G, quàm A E; quod erat
oſtendendum.

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