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

224186Apollonij Pergæi

LEMMA VIII.

SI duo hyperbolica, aut elliptica ſegmenta A B C, D E F fuerint
ſimilia, quorum baſes A C, D F efficiant cum diametrorum ab-
ſciſsis B M, E O angulos æquales M, & O; ſintque eorum tranſ-
uerſa latera T B, Z E, recta vero B L, E Q. Dico figuras eorum;
ſiue rectangula T B L, & Z E Q ſimilia eße.

Secentur ſegmentorum abſciſſæ M B, O E proportionaliter in N, P, & per
ea puncta ducantur ordinatim ad diametros applicatæ G N, I P æquidiſtantes
baſibus, efficientes abſciſſas B N, E P, coniunganturq; duæ rectæ lineæ T L, Z
Q ſecantes rectas lineas N H, M V, P K, O S æquidiſtantes lateribus rectis B
L, E Q in punctis H, V,

251[Figure 251] K, S, atque à punctis H, &
K ducantur rectæ lineæ H X,
K R parallelæ diametris occur-
rentes ipſis M V, O S in X,
11Defin. 7.
huius.& R. Quoniam ſegmenta ſup-
ponuntur ſimilia erit A M ad
M B, vt D O ad O E, & G
N ad N B erit vt I P ad P
E, atque quadratum A M, ſeu
ei æquale rectangulum B M V,
2212. 13.
lib. 1. ad quadratum M B eandem
proportionem habebit, quàm,
33Ibidem. quadratum D O, ſeu ei æquale
rectangulum E O S ad quadratum O E; ſed vt rectangulum B M V ad quadra-
tum M B ita eſt M V ad M B (cum M B ſit eorum altitudo communis) pari-
terque vt rectangulum E O S ad quadratum O E, ita eſt O S ad O E; quare
M V ad M B eandem proportionem habebit, quàm O S ad O E; non aliter oſten-
detur N H ad N B eandem proportionem

252[Figure 252] habere, quàm P K ad P E: erat autem
44Lem. 1.
lib. 5. M B ad B N vt O E ad E P; ergo compa-
rando antecedentes, & poſtea conſequentes
ad differentias terminorum erit B M ad M
N vt E O ad O P; atque B N ad N M eã-
dem proportionem habebit, quàm E P ad P
O. Quare ex æquali V M ad M N erit vt
S O ad O P, atque H N ad N M erit vt K
P ad P O; & differentia ipſarum V M &
H N ideſt X V ad M N, ſeu ad X H ean-
dem proportionem habebit, quàm differentia ipſarum S O, & K P, ideſt S R
ad O P, ſeu ad R K; quapropter V X ad X H erit vt S R ad R K; ſed quia
X V, L B inter ſe, nec non X H, & B T ſunt parallelæ, atq; etiam S R, Q E
inter ſe, nec nõ R K, & E Z ſunt æquidiſtantes; erunt triangula V X H, & L

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