Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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proportionem, quam c e ad e a. </
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babere n o ad o f: </
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<
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<
s
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">reliquas eiuſmodi, at uero b K ad K e eam
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habere proportionem, quam habet c e ad e a, ex eadem quinta. </
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<
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chimedis perſpicue apparet. </
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<
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">at que illud eſt, quod demonſtr andum
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propoſuimus.</
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<
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head
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">Itaque maneant eadem, quæ ſupra: </
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<
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<
s
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">itidem deſcri-
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batur alia portio ſimilis contenta recta linea & </
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<
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">rectan-
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guli coni ſectione d r c; </
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<
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">cuius diameter r s, ut ſecet li-
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neam f g in t: </
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<
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">producaturque s r ad lineam c h in u;
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</
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<
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">cuiſectio a b c occurrat in x, & </
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<
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">e f c in y. </
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<
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">Dico b m
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ad m d proportionem habere compoſitam ex propor-
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tione, quam babet e a ad a c; </
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<
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<
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">ex ea, quam c d ba-
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bet ad de.</
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<
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enim ut ſupra, demonſtrabimus lineam c h con-
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tingere ſectioné d r c in c puncto: </
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<
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<
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">l m ad m d, itêmq; </
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</
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<
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">u y ad y r ita eſſe, ut c d ad d e. </
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<
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">Quoniam igitur lb ad b m eſt,
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ut c e ad e a; </
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">erit componendo, conuertendôq; </
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<
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">bm ad lm, ut e a ad
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a c: </
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<
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<
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">ut lm ad m d, ita c d ad d e. </
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<
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">proportio autem b m ad m d
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compoſita eſt ex proportione, quam habet b m ad l m, & </
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<
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">ex propor
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tione, quam l m habet ad m d. </
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<
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">ergo proportio b m ad m d etiam com
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poſita erit ex proportione, quam habet e a, ad a c; </
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<
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">ex ea, quam
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c d habet ad d e. </
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<
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">Eadem ratione demonſtrabitur o f ad f t; </
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<
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">itêmq; </
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<
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x y ad y r proportionem habere ex eiſdem proportionibus compo-
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ſitam: </
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<
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<
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">ita in aijs. </
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<
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">quod demonſtrare oportebat.</
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<
s
xml:id
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">Ex quibus apparet lineas ſic ductas, quæ inter ſectio
<
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nes a b c, d r c interiiciuntur à ſectione e f c in eandem
<
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proportionem diuidi.</
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