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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160122Apollonij Pergæi C S V cum duplo trianguli F S V; ideſt quadratum I B æquale eſt duplo trian-
guli I S C cum duplo trianguli F S V; & quoniam propter parallelas C S, &
G V, triangulum I C S ſimile eſt iſoſcelio, & rectangulo triangulo I G V, erit,
quadratum I C æquale duplo trianguli I C S iſoſcelei, & rectanguli in C; ergo
exceſſus quadrati I B ſupra quadratum I C æquale eſt duplo trianguli F S V;
eſt verò rectangulum, cuius baſis F S, altitudo verò C G æquale duplo trianguli
F S V; atque buiuſmodi rectangulum eſt exemplar applicatum ad abſciſſam G
C, vt in notis prop. 16. 17. & 18. litera c. oſtenſum eſt igitur quadrati I B
exceßus ſupra quadratum I C eſt exemplar applicatum ad abſciſſam G C: Simili

153[Figure 153] modo quadratum I K oſtendetur æquale duplo trianguli I C S vna cum duplo
trapezĳ L T S F; atque dupli trianguli I C S cum duplo trianguli F S V ex-
ceſſus ſupra duplum trianguli I C S cum duplo trapezĳ L T S F eſt duplum
trianguli L T V; ergo quadrati I B exceſſus ſupra quadratum I K eſt duplum
trianguli L T V, ſeu exemplar applicatum ad G P differentiam abſciſſarum.
Poſtea quia triangula ſimilia E C F, E D M ſunt æqualia, cum eorum bomologa
latera E C, E D æqualia ſint; ergo addito communi triangulo I E V, erit trian-
gulum E C F cum triangulo E I V, ſeu triangulũ I C S cum triangulo F S V
æquale duobus triaugulis E D M, & I E V, ſeu duobus triangulis M V N, &
N I D: erat autem quadratum I B æquale duplo trianguli I C S cum duplo tri-
anguli F S V; igitur quadratum I B æquale erit duplo trianguli M N V cum
duplo trianguli N I D; eſtque quadratum I D æquale duplo trianguli iſoſcelei,
rectanguli I D N; igitur quadratum I B ſuperat quadratum I D, eſtque exceſ-
ſus duplum trianguli M N V ſeu exemplar applicatum ad G D. Tandem quia
quadratum I Q æquale eſt duplo trianguli iſoſcelei rectanguli I Q X, atque
quadratum Q A æquale eſt duplo trapezĳ Q M; igitur quadratũ bypotbenuſæ I
A æquale eſt duplo trianguli I D N cum duplo trapezĳ X N M Z; ergo exceſ-
ſus quadrati I A ſupra quadratnm I D æqualis eſt duplo trapezĳ X N M Z; exceſ-
ſus autem trianguli N M V ſupra trapezium N Z eſt triangulum X Z V; &
erat quadrati I B exceſſus ſupra quadratum I D, triangulum ipſum M V N bis
ſumptum. Igitur quadrati I B exceſſus ſupra quadratum I A eſt duplum trian-
guli X Z V, ſeu exemplar applicatum ad G Q. Quod autem exemplaria æqualia
ſint prædictis triangulis bis ſumptis, oſtenſum eſt in prop. 6. buius.

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