Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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ipſius PV, vnà cum duabus tertiis quadrati eiuſdem dif
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ferentiæ, ad quadratum PV, ita eſt reliquum ſolidi ZV
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dempto fruſto PKLV ad ſolidum ZV; erit vt rectangu
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lum DES, vnà cum duabus tertiis quadrati ES, ad DS
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quadratum, ita ſolidi ZV reliquum dempto fruſto PK
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LV ad ſolidum ZV: ſed vt quadratum DS ad quadra
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tum DB, hoc eſt vt quadratum SV ad quadratum BG,
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ideſt ad quadratum SX, ita eſt ſolidum ZV, ad ſolidum
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FX; ex æquali igitur, vt rectangulum DES, vnà cum
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duabus tertiis ES quadrati, ad quadratum BD, ita eſt
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reliquum ſolidi ZV, dem
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pto ſolido PKLV ad ſo
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lidum FX: ſed vt rectan
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gulum BSR ad quadra
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tum BD, ita eſt, eadem
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ratione, qua in præcedenti
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theoremate vtebamur, re
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liquum ſolidi FX dem
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pto ſolido ZV, ad ſoli
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dum FX; vt igitur prima
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cum quinta ad ſecundam,
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ita tertia cum ſexta ad
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quartam; videlicet, vt duo
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rectangula BSR, DES, vnà cum duabus tertiis quadra
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ti ES ad quadratum BD, ita erit totum reliquum cylin
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dri, vel portionis cylindricæ FX dempto fruſto PKLV:
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hoc eſt ſphæræ, vel ſphæroidis portio AQTC ad cylin
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drum, vel portionem cylindricam FX. </
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ſtrandum erat. </
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