Archimedes
,
Archimedis De insidentibvs aqvae
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DE INSIDENTIBVS AQVAE
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ipſius c, d. </
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<
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xml:space
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">Ipſius autem o, i, dupla eſt, quæ ***, propter ſeptimum tbeore-
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ma primi libri elementorum conoycorum A pollonij. </
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<
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xml:space
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">Eſt ergo quæ o, i,
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minor, quàm x, b. </
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<
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xml:id
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xml:space
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">Quare quæ i, ***, eſt maior, quàm x, r, quæ autem x, r,
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eſt æqualis ipſi f, maior ergo _est_, quæ i, ***, quàm f. </
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<
s
xml:id
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xml:space
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preserve
">Et quoniam ſupponi
<
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tur portio ad humidum iu grauitate habere per portionem, quàm tetra-
<
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gonum, quod ab f, q, ad tetragonum, quod a, b, d. </
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<
s
xml:id
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xml:space
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">Quam autem propor-
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tionem, habet proportio ad humidum in grauitate, hanc habet propor-
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lb
/>
tionem pars ipſius demerſa ad totam portionem, quam autem pars de-
<
lb
/>
merſa ad totam hanc habet tetragonum, quod a, p, m, a tetragonum,
<
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quod ab o, n. </
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<
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xml:space
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">Quam ergo proportionem babet tetragonum, quod a, b, f, q.
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</
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<
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xml:space
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">ad tetragonum, quod a, b, d, hanc proportionem habet tetragonum, quod
<
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a, b, m, b, ad tetragonum quod a, b, o, n, æqualis ergo eſt, quæ f, q, ipſi p,
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m. </
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<
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xml:space
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">Quæ autem p, b, demonstrata eſt eſſe maior, quàm f, palam ergo, quòd
<
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quæ p, m, eſt minor, quàm dupla ipſius b, m. </
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<
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xml:space
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">Sit igitur quæ p, Z, dupla ip
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ſius Z. </
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<
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xml:space
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">m, erit autem t, quidem centrum grauitatis ſolidi, eius auté, quod
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intra bumidum Z. </
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xml:space
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">Reliquam autem magnitudinis centrum grauitatis
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erit in linea Z, t. </
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<
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">Copulata, & </
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">educta, & </
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<
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xml:space
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">educatur ad g, demonſtrabitur
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autem ſimiliter quæ t, b, perpendicularis exiſtens ad ſuperficiem humi-
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di, & </
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<
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xml:space
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">portio quidem quæ intra humidum fertur ad extra humidi, ſecun
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dum perpendicularem ducta per Z, ſuperficiem humidi. </
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>
<
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xml:space
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">Quæ autem ex-
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tra humidum ferretur intra humidum, ſecundum ea, quæ per g, non ma-
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net autem portio, ſecundum ſuppoſitam inclinationem, nec etiam in re-
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ctum restituetur. </
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<
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xml:space
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">palam enim propter hoc quoniam, quæ producuntur
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per Z, g. </
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<
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xml:space
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">quæ quidem per Z, perducit ipſi g,
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l, ad eaſdem partes cadit ad quas eſt, & </
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<
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xml:space
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">ſecundum g. </
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<
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xml:space
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">Quæ autem per
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g, ad eaſdem ipſi Z, g. </
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<
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xml:space
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">palam quòd propter prædicta Z, quidem centrũ
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ſurſum ferretur:</
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xml:space
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">g, autem deorſum. </
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<
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xml:space
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">Quare totius magnitudinis, quæ ex
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parte a, deorſum ferretur, hoc antem erat inutile ad demonstrandum.</
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<
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xml:space
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">Supponatur rurſum alia quidem eadem axis autem portionis ad ſu-
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perficiem humidi faciat angulum minorem eo, qui apud b, minorem au-
<
lb
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tem proportionem habet tetragonum, quod a, p, i, ad tetragonum, quod
<
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ab i, ***, quàm ad a, b, x, ad id, quod a, x, b, & </
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<
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xml:space
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">quæ K, r, ergo ad ***, i, mi
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norem proportionem habet, quàm medietas ipſius K, r, ad x, b. </
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<
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xml:space
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">Eſt ergo
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quæ i, ***, maiorem quàm dupla ipſius x, b, ergo quæ ***, i, minor ipſius
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autem o, i, dupla ergo ***, eſt, quæ o, i, ipſus x, b, eſt autem, & </
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ta, quæ ***, t, æqualis ipſi r, b, & </
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xml:space
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">reliqua minor eſt, quàm ***, r, erit ergo,
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& </
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xml:space
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">quæ p, h, minor, quàm f. </
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xml:space
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">Quæ autem m, p, ipſi f, q, eſt æqualis: </
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<
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xml:space
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">palam
<
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quòd p, m, eſt maior, quàm emiolia ipſius p, b, quæ autẽ p, h, minor, quàm
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lb
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dupla ipſius h, m. </
s
>
<
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xml:id
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xml:space
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">Sit igitur, quæ p, z, ipſius z, m, dupla igitur rurſum. </
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<
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xml:space
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">to
<
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tius quidem cétrum grauitatis erit t, eius autem quod intra humidũ Z.</
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