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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227189Conicor. Lib. VI. γ: poſtea, quia B

255[Figure 255] L, & D N con-
tingunt ſectiones
in verticibus a-
11Conuerſ.
32. lib. 1. xium efficient an-
gulos V B L, &
γ D N rectos, cũ-
que duo anguli V,
& γ oſtenſi ſint æ-
quales, in trian-
gulis V B L, γ
D N, anguli V
L B, & γ N D
æquales erunt in-
ter ſe, & qui de-
inceps A L R, & C N S ſunt æquales inter ſe; & ideo triangula A R L, & C
S N ſimilia ſunt inter ſe.

Et propterea figuræ earundem diametrorum ſunt ſimiles, & c. Quia
22C ex hypotheſi M A ad A E erat, vt O C ad C F; atque (propter ſimilitudinem
triangulorum A E V, & C F γ) vt E A ad duplam ipſius A V, ſeu ad latus
tranſuerſum A T, ita eſt F C ad duplam ipſius C γ, ſeu ad latus tranſuerſum
C X alterius ſectionis; ergo ex æquali ordinata erit M A ad A T, vt O C ad
C X; oſtenſum autem fuit latus tranſuerſum T A ad A P latus rectum eius ha-
bere eandem proportionem, quàm alterius ſectionis latus tranſuerſum X C ad
eius latus rectum C Q; ergo ex æquali ordinata M A ad A P eandem propor-
tionem habet, quàm O C ad C Q; quare duæ abſciſſæ A M, & O C eandem
proportionem habent ad latera recta, atque ad tranſuerſa earundem diametro-
rum, atque efficiunt baſes H G, & K I cum diametris angulos M, & O æqua-
33Defin. 7.
huius. les inter ſe: propterea quod æquales ſunt angulis E A V, & F C γ æqualibus
(propter æquidiſtantiam rectarum H G, & A E; nec non K I, & C F) igitur
erunt duo ſegmenta H A G, & K C I ſimilia inter ſe.

Quia propter ſimilitudinem duorum ſegmentorum continebunt poten-
44d tes cum ſuis abſciſſis angulos æquales: & erit proportio potẽtium ad ab-
ſciſſa eadem, & proportio abſciſſarum in vna earum ad alia ſimilia eadẽ,
quia V a in a E ad quadratum A a, eſt vt Y c in c F ad quadratum C c,
& duo anguli a, & c ſunt æquales; ergo angulus Y æqualis eſt angulo
V, & angulus C, nempe O æqualis A, nempe M propter ſimilitudinem
duorum ſegmentorum; igitur A E V ſimile eſt Y F C, & angulus E; & c.
In hoc textu nonnulla verba deficiunt, aliqua verò tranſpoſita ſunt, vt nullus
ſenſus colligi poſſit: tamen eum reſtitui poße cenſeo vt ibidem videre eſt. Quo-
niam duo ſegmenta H A G, & K C I ſupponuntur ſimilia efficient diametri A
M, & C O cum baſibus G H, & K I angulos M, & O æquales, licet non rectos;
55Lem. 8.
huius. eruntque figuræ earumdem diametrorum ſimiles inter ſe: & propterea habebit
T A ad eius erectum eandem proportionem, quàm X C ad eius latus rectum;
6615. huius. igitur ſectiones A B, & C D ſimiles ſunt, ideſt ductis axibus V B, & γ D
7747. lib. 2. erunt figuræ axium ſimiles inter ſe: ducuntur verò à punctis A, & C ad axes
8812. huius. ordinatim applicati A a, & C c, atque contingentes A E, & C F; igitur re-
9937. lib. 1.

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