Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
dem circa e z diametrum; a t d uero circa diametrum t h;
Kquæ ſimiles ſint portioni a b l. tranſibit igitur a e i coni
Lſectio per _K_:
& quæ ab r ducta eſt perpendicularis ad b d,
ipſam a e i ſecabit.
ſecet in punctis y g: & per y g ducan
tur ipſi b d æquidiſtantes p y q, o g n, quæ ſecent a t d in
f x.
ducantur poſtremo, & p χ, o φ contingentes ſectionẽ
a p o l in punctis p o.
cũ ergo tres portiones ſint a p o l,
Ma e i, a t d, contentæ rectis lineis, &
rectangulorum cono-
rum ſectionibus;
rectæq, ſimiles, & inæquales, quæ contin
gunt ſe ſe ſuper unamquanque baſim:
à puncto autem n
ſurſum ducta ſit n x g o;
& à q ipſa q fy p: habebit o g ad
g x proportionem compoſitam ex proportione, quam ha
bet i l ad l a;
& ex proportione, quam a d habet ad d i.
Sed i l ad l a
Figure: /permanent/library/4E7V2WGH/figures/0070-01 not scanned
[Figure 43]
habet eandem,
quam duo ad
quinque.
ete-
nim c b ad b d
Neſt, ut ſex ad
quĩdecim;
hoc
eſt ut duo ad
quinque:
& ut
Oc b ad b d, ita
e b ad b a:
&
d z ad d a.
ha-
rum autẽ d z,
Pd a duplæ ſunt
ipſæ l i, l a:
&
Qa d ad d i eã pro
portionem habet, quam quinque ad unum.
ſed proportio
compoſita ex proportione, quam habet duo ad quinque;
& ex proportione, quam quinque ad unum; eſt eadem,
quam habent duo ad unum:
duo autem ad unum duplam
proportionem habent.
dupla eſt igitur g b ipſius g x: &

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