Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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DE CENTRO GRAVIT. SOLID.
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<
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xml:space
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">SIT fruſtum pyramidis a e, cuius maior baſis triangu-
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lum a b c, minor d e f: </
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<
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<
s
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xml:space
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">oporteat ipſum plano, quod baſi
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æquidiſtet, ita ſecare, ut ſectio ſit proportionalis inter triã
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gula a b c, d e f. </
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<
s
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xml:space
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portionalis, quæ ſit b g: </
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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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">à puncto g erigatur g h æquidi-
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ſtans b e, ſecansq; </
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<
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xml:space
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<
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xml:space
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">deinde per h ducatur planum
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baſibus æ quidiſtans, cuius ſectio ſit triangulum h _k_ 1. </
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<
s
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xml:space
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triangulum h K l proportionale eſſe inter triangula a b c,
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d e f, hoc eſt triangulum a b c ad
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triangulum h K l eandem habere
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proportionem, quam triãgulum
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h K l ad ipſum d e f. </
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<
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xml:space
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lineæ a b, h K æquidiſtantium pla
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xlink:label
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xml:space
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cimi</
note
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norum ſectiones inter ſe æquidi-
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ſtant: </
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<
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xml:space
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</
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<
s
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xml:space
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">linea h _k_ ipſi g b eſt æqualis: </
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<
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xml:space
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<
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xml:space
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<
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xml:space
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note
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pterea proportionalis inter a b,
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d e. </
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<
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xml:space
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">quare ut a b ad h K, ita eſt h
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ad d e. </
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<
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xml:space
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ad aliam lineam, in qua ſit m. </
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<
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ex æquali ut a b ad d e, ita h k ad
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m. </
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<
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xml:space
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">Et quoniam triangula a b c,
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xml:space
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">9. huius
<
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corol.</
note
>
h K l, d e f ſimilia ſunt; </
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<
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xml:space
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">triangulū
<
lb
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a b c ad triangulum h k l eſt, ut li-
<
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<
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xlink:label
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xlink:href
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note-0173-04a
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xml:space
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">20. ſexti</
note
>
nea a b ad lineam d e: </
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<
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xml:space
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autem h k l ad ipſum d e f eſt, ut h _k_ ad m. </
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<
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<
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">11. quinti</
note
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a b c ad triangulum h k l eandem proportionem habet,
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quam triangulum h K l ad ipſum d e f. </
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<
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">Eodem modo in a-
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liis fruſtis pyramidis idem demonſtrabitur.</
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</
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<
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<
s
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xml:space
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">Sit fruſtum coni, uel coni portionis a d: </
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<
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xml:space
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">& </
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>
<
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xml:space
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">ſecetur plano
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per axem, cuius ſectio ſit a b c d, ita ut maior ipſius baſis ſit
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circulus, uel ellipſis circa diametrum a b; </
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<
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</
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<
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xml:space
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">Rurſus inter lineas a b, c d inueniatur proportionalis b e: </
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<
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& </
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<
s
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xml:space
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">ab e ducta e ſ æquid_i_ſtante b d, quæ lineam c a in f </
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