Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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0101
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DEIIS QVAE VEH. IN AQVA.
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ad quadratum bd: </
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<
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xml:space
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<
s
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xml:space
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">quam habet portio ad humidum in
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grauitate, eandem quadratum nt habet ad bd quadratũ,
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ex iis, quæ dicta ſunt: </
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<
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">conſtat n t lineæ ψ æqualem eſſe,
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quare & </
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nes a n z, a g q
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ſunt æquales. </
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<
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quoniam in por
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tionibus æquali
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bus, & </
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<
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xml:space
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">ſimilibus
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a g q l, a n z l, ab
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extremitatibus
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baſiũ ductæ ſunt
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a q, a z, quæ æ-
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quales portiões
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abſcindunt: </
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<
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ſpicuum eſt an-
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gulos facere æ-
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quales cum por
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tionum diame-
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tris: </
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<
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<
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lorum n fs, g ω c, angulos, qui ad f ω æquales eſſe: </
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<
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xml:space
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æquales inter ſe, s b, c b; </
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xml:space
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<
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</
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">cũq; </
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">g h dupla ſit ipſius h i, erit n χ minor, quàm
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duplaipſius χ t. </
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m K protrahatur ad e. </
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erit punctum K: </
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">partis eius, quæ eſt in humido, punctũ m: </
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<
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eius autem, quæ extra humidum in linea protracta, quod
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ſit e. </
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>
<
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">ergo ex proxime demonſtratis patet, nõ manere por
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tionem, ſed inclinari adeo, ut baſis nullo modo ſuperficiẽ
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humidi contingat. </
s
>
<
s
xml:id
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xml:space
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">At uero portionem conſiſtere ita, uta-
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xis cum ſuperficie humidi faciat angulum angulo φ mino-
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rem, ſic demonſtrabitur. </
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>
<
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">conſiſtat enim, ſi fieri poteſt, ut
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non faciat angulum minorem angulo φ: </
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<
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ponantur; </
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">ut in ſubiecta figura. </
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