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

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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

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