Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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<
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xml:space
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">COROLLARIVM VIII.</
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<
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">octaua diſcimus à data ſphæra, vel ſphæroide, vel ſo-
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lido quocunque genito ex circulo, vel ellipſi, iuxta regulam, quę
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ſit vna ex ordinatim applicatis, abſcindere portionem, quæ ad ſoli-
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dum ſimilare ſibi genitum ex triangulo in eadem baſi, & </
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<
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">circa eun-
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dem axim, vel diametrum cum portione conſtituto, habeat datam
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rationem, quam oportet eſſe maiorem ſexquialtera; </
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<
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">quæ omniaibi
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clarè patent, & </
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<
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">COROLL. IX. SECTIO PRIOR.</
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">nona patet ratio, quam
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fig-0285-01
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0285-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0285-01
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habet ſolidum ſimilare genitum ex
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circulo, vel ellipſi, iuxta regulam pri-
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mum axim, vel diametrum, ad ſolidum
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ſimilare genitum ex eodem, iuxta ſe-
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cundum axim, vel diametrum tamquam
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regulam, ſiue hæc ſolida ſint ſphæra, vel
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ſphæroides, vel tantum ſolida ſimilaria,
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quæ in his appoſitis figuris clarè patent,
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in quarum vna conſpici poteſt ſphęroi-
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des prolatum, in altera oblongum, præ-
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dicta autem ratio eſt ea, quam habet
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prima axis, vel diameter ad ſecundam
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axim, vel diametrum: </
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<
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">quę etiam pro re-
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liquis ſolidis ad inuicem ſimilaribus ma-
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nifeſta ſunt.</
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">SECTIO POSTERIOR.</
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<
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">IN Corollario autem eiuſdem Theorematis colligimus eſſe notam
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rationem omnium quadratorum duarum portionum circuli, vel
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ellipſis abſeiſlarum per lineas, quarum vna ſit parallela primo, alte-
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ra ſecundo axi, vel diametro, quales ſint in appoſitis figuris portio-
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nes, BMS, VPX, vnde etiam nota eritratio ſolidorum ſimilarium,
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BMS, VPX, exipſis genitorum, vnumiuxta regulam, BS, alte-
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rum iuxta regulam, VX, ſiue ſint hæc portiones ſphæræ, velſphæ-
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roidis, ſiue ſolida ſimilaria genita ex portionibus, BMS, VFX.</
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