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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209171Conicor. Lib. VI. Q ſimile eſt M K S,

231[Figure 231] quare angulus G æ-
qualis eſt angulo M,
& propterea periphe-
riæ E F Q, & K F S,
quibus inſiſtunt, æ-
quales erunt, quod
eſt abſurdũ: eſt enim
E F Q maior, quàm
K F S; ergo duo triã-
gula A B C, D E F
in omnibus figuris
ſunt ſimilia. Quod e-
rat oſtendendum.

PROPOSITIO
Præmiſſa VI.

DEinde ſint duo anguli B, E qualeſcunque; ſed angulus
11a A B H, vel C B H æqualis angulo D E I, aut F E I:
& ſupponantur reliqua omnia iam dicta.

Quia proportio C H in H A ad quadratum H B ſuppoſita eſt, vt F I
in I D ad quadratum I E, & H C, vel H A ad H B eſt, vt F I, vel D I
ad I E; erit etiam H A ad H B, vt I D ad I E, & duo anguli H, I ſunt
æquales; igitur triangulum H B A, aut H B C ſimile eſt triangulo E D
I, aut E F I, quare duo triangula A B C, D E F ſimilia ſunt; Et hoc
erat oſtendendum.

Notæ in Propoſit. Præmiſſas
I. II. III. IV. & V.

AFferuntur in hac ſectione aliquæ propoſitiones ſimul coaceruatæ, quæ lem-
maticæ ſunt, & vſum habent in ſequentibus propoſitionibus; ſanè conij-
citur ex hoc titulo PRAEMISS AE rubeis characteribus inſcripto, huiuſmodi lẽ-
mata T extui Apollonij ab Arabico Interprete, vel ab aliquo alio ſuperaddita fuiſſe;
licet Pappus Alexandrinus libro 7. afferat eadem ferè lemmata, tanquã propria,
& conferentia ad Apollonij ſexti libri intelligentiam.

Poteſt tamen propoſitio vniuerſalis breuius exponi hac ratione. Si à vertici-
bus duorum triangulorum à duobus circulis compræhenſorum rectæ lineæ ductæ
efficiant cum baſibus angulos æquales; atque eorundem ſegmentorum inter baſim,
& peripheriam interceptorum quadrata ad rectangula ſub factis ſegmentis

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