Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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nium prædictorum cylindri AE cylindrorum ſupremus
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FE, cuius axis BH, & communis ſectio plani per pun
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ctum H tranſeuntis baſi hemiſphærij cum plano per axim
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BD, ſit recta FGKHMNL. </
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<
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>Quoniam igitur rectan
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gulum DHB bis vna cum duobus quadratis DH, BH,
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æquale eſt BD quadrato: & rectangulum DHB bis
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vna cum quadrato BH, eſt rectangulum ex BD DH tan
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quam vna, & BH; rectangulum ex BD, DH tanquam
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vna & BH, vna cum quadrato DH æquale erit quadra
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to BD, hoc eſt quadrato FH: quorum quadratum KH
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æquale eſt rectangulo ex BD, DH, tanquam vna, & BH;
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reliquum igitur quadrati FH dempto quadrato KH æ
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quale erit reliquo quadrato DH, hoc eſt quadrato GH:
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& quadruplum quadruplo reliquum quadrati FL dempto
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quadrato MK toti GN quadrato, hoc eſt reliquum circu
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li, FL dempto circulo MK, æquale circulo GN. </
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<
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>Qua
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re & GP, cylindrus reliquo cylindri FE dempto QK,
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cylindro æqualis erit, propter æqualitatem altitudinum.
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<
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>Similiter oſtenderemus ſingula reliqua cylindrorum eiuſ
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dem altitudinis, in quos totus cylindrus AE ſectus fuit,
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demptis cylindris hemiſphærio circumſcriptis æqualia eſ
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ſe ſingulis cylindris cono EDR inſcriptis, quæ inter ea
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dem plana interijciuntur. </
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<
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>Tota igitur figura ex prædictis
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cylindrorum reſiduis reliquo cylindri AE, dempto he
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miſphærio inſcripta æqualis erit figuræ cono EDR in
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ſcriptæ: deficit autem vtraque harum figurarum hæc à co
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no ADR, illa à reſiduo cylindri AE dempto hemiſphæ
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rio minori exceſsu magnitudine vtcumque propoſita; re
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liquum igitur cylindri AE dempto hemiſphærio æquale
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eſt cono EDR, ſed conus EDR; hoc eſt conus ABC cylin
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dri AE eſt pars tertia; reliquum igitur cylindri AE dem
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pto hemiſphærio, cylindri AE eſt pars tertia, hoc eſt cylin
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drus AE triplus dicti reſidui:
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AE cylindrus ſeſ
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quialter hemiſphærij ABC: &
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cõuertendo
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, hemiſphærium </
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