Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE IIS QVAE VEH. IN AQVA.
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<
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">Cum ergo tres portiones ſint a p o i, a ei, atd, con-
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tentæ rectis lineis, & </
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">, ſimiles, & </
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">inæquales, quæ contingunt ſe ſe ſuper
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unam quamque baſim.</
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<
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">] _Poſt ea uerba, ſuper unamquanque_
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_baſim, in trans latione aliqua deſiderari uidentur. </
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<
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">Ad borum autem_
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_demonſtrationem non nulla præmittere oportet, quæ etiam ad alia,_
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_quæ ſequuntur, neceſſaria erunt._</
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<
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<
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">Sit recta linea a b, quam ſecent duæ lineæ inter ſeſe
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æquidiſtantes a c, d e, ita ut quam proportionem ba-
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bet a b ad b d, eandern haheat a c ad de. </
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neam, quæ c b puncta coniungit, etiam per ipſum e
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tr anſire.</
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">SI enim fieri poteſt, non tranſeat pere, ſed nel ſupra, uel infra.
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<
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">tranſeat primum infra, ut per f. </
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">erunt triangula a b c, d b f inter ſe
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ſimilia. </
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">quare ut a b ad b d, ita a c ad d f. </
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">ſed ut a b ad bd, ita
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erat a c ad d e. </
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<
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">ergo d f ipſi d e æqualis erit, uidelicet pars to-
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ti, quod eſt
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cbſurdum.
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<
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ſurdum ſe
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quetur, ſi
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linea c b
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ſupra e pú
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ctum tran
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ſire pona-
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tur. </
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<
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c b etiam
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per e ne-
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ceſſario tranſibit. </
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<
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