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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153115Conicor. Lib. V. ſimilia; pariterque duo triangula E F C, T b F ſimilia erunt; & propterea S a
ad a F eandem æqualitatis proportionem habebit, quàm I C habebat ad C F, ſi-
militer T b ad b F eandem proportionem habebit, quàm E C ad C F, ſeu quàm
latus tranſuerſum D C ad eius latus rectum: eſtvero T b æqualis S a, ſeu a F;
ergo F a ad F b eandem proportionem habet, quàm latus tranſuerſum D C ad
eius latus rectum; & comparando antecedentes ad differentias terminorum. ,
11Lem. 1.
huius. erit F a, ſeu b T ad b a, vt latus tranſuerſum D C ad differentiam eiuſdem
tranſuerſi, & recti lateris; quare parallelogrammũ rectangulum S b, erit exem-
22Defin. 9.
huius. plar applicatum ad abſciſſam O C.

141[Figure 141]

Igitur I C maior eſt, quàm I H, & I H, quàm I K, & c. Eo quod abſciſ-
33d ſa O C minor eſt, quàm C P, & C P minor, quàm C E: ſuntque prædictæ ab-
ſciſſæ latera homologa exemplarium, quæ ad eaſdem abſciſſas applicantur; at-
44Defin. 9.
huius. que prædicta exemplaria ſimilia ſunt inter ſe, cum circa angulos rectos latera
habeant eandem proportionem, quàm latus tranſuerſum D C ad differentiam.
eiuſdem tranſuerſi, & recti lateris; quare exceſſus quadrati I C ſupra quadra-
tum I H minus eſt exceſſu eiuſdem quadrati I C ſupra quadratum I K; & ad
huc minus exceſſu quadrati I C ſupra quadratum I B, & propterea recta I C
minori exceſſu ipſam I H ſuperabit, quàm ipſam I K; & adhuc minori exceſ-
ſu ſuperabit I K, quàm excedat I B; & ideo I C maior erit, quàm I H, & I
H maior, quàm I K, & I K maior, quàm I B.

142[Figure 142]

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