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

Table of contents

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[141.] PROPOSITIO XXXIII. XXXIV.
[142.] PROPOSITIO XXXV.
[143.] PROPOSITIO XXXVI.
[144.] PROPOSITIO XXXVII. XLVI.
[145.] PROPOSITIO XXXVIII.
[146.] PR OPOSITIO XXXIX.
[147.] PROPOSITIO XXXX.
[148.] PROPOSITIO XXXXVII.
[149.] PROPOSITIO XXXXVIII.
[150.] Notæ in Propoſit. XXXII.
[151.] Notæ in Propoſit. XXXIII. XXXIV.
[152.] Notæ in Propoſit. XXXV.
[153.] Notæ in Prop. XXXVI.
[154.] Notæ in Prop. XXXVIII.
[155.] Notæ in Propoſit. XXXIX.
[156.] Notæ in Propoſit. XXXXVIII.
[157.] LIBRI QVINTI FINIS.
[158.] APOLLONII PERGAEI CONICORVM LIB VI. DEFINITIONES. I.
[159.] II.
[160.] III.
[161.] IV.
[163.] VI.
[164.] VII.
[165.] VIII.
[166.] IX.
[167.] NOTÆ.
[168.] MONITVM.
[169.] SECTIO PRIMA Continens Propoſit. I. II. IV. & X. PROPOSITIO I.
[170.] PROPOSITIO II.
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242204Apollonij Pergæi Quoniam O L ad L I oſtenſa fuit, vt Q M ad M K; atque prius oſtenſa ſuit
B L ad L I, vt E M ad M K;
ergo inuertendo I L ad L B erit, vt K M ad
M E;
& propterea ex æqualitate O L ad L B erit vt Q M ad M E; ſed B L
11ex 12.
huius.
ad L N eſt, vt E M ad M P;
igitur ex æqualitate O L ad L N erit vt Q M
ad M P;
ſuntque duo anguli L, & M recti; ergo triangula O L N, & Q M P
æquiangula erunt;
& propterea anguli O, & Qæquales inter ſe erunt; ſed quia
contingentes verticales V e, &
γ f parallelæ ſunt or dinatim applicatis N A, P
D ad diametros V R, &
γ S; igitur angulus V e B æqualis erit angulo N O L;
pariterque angulus γ f E æqualis erit angulo P Q M; & propterea anguli e, &
f æquales erunt inter ſe.
Ergo propter ſimilitudinem duarum ſectionum T Z in Z e ad quadra-
22d tum Z V eandem proportionem habebit quàm X a in a f ad quadratum
a Y, &
angulus e æqualis eſt angulo f; igitur V e T ſimile eſt Y f X,
&
pariter, & c. Quoniam in ſectionibus ſimilibus V B, & γ E axes tranſuerſi
3312. huius. lateribus rectis proportionales ſunt, &
ductæ ſunt ad axes ordinatim applicatæ
V Z, γ a, &
contingentes V e, γ f, eſtque rectangulum T Z e ad quadratum
4437. lib. 1. Z V, vt latus tranſuerſum ad rectum, pariterque rectangulum X a f ad qua-
dratum a γ, vt axis tranſuerſus ad erectum;
igitur rectangulũ T Z e adqua-
dratum Z V eandem proportionem habet, quàm rectangulum X a f ad quadra-
tum a γ, &
à verticibus V, γ duorum triangulorum V e T, & γ f X ductæ
ſunt ad baſes rectæ linæ V Z, γ a efficientes angulos rectos, cum ordinatim
276[Figure 276] applicatæ ſint ad axes;
atque angulus V e Z oſtenſus eſt æqualis angulo γ f a,
igitur tertius angulus Z V e æqualis erit tertio angulo a γ f;
& ideo duo triã-
55Propof. 6
præmiſſ.
gula V T e, &
γ X f ſimilia erunt inter ſe: & propterea circa angulos æquales
T, &
X latus e T ad T V eandem proportionem habebit, quàm f X ad X γ:
cumque duæ contingentes verticales V e, γ f parallelæ ſint ordinatim applicatis
N A, &
P D ad diametros V R, γ S, erit O e ad R V, vt e T ad T V; pa-
riterque Q f ad S γ erit, vt f X ad X r:
erat autem e T ad T V, vt f X ad
X γ;
igitur pariter O e ad R V eandem proportionem habebit, quàm Q f ad
6612. huius. S γ;
ſed B I ad I A eſt, vt E K ad K D.

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