Valerio, Luca, De centro gravitatis solidorum, 1604

Table of figures

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              ABCD abſciſsa duobus planis parallelis altero ducto
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              per E, & ſectionem faciente circulum maximum, vel
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              ellipſim per centrum, cuius diameter AED: axis autem
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              portionis ſit EF, cui congruens ſphæræ, vel ſphæroidis axis
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              GFER: ſit autem FE bifariam ſectus in puncto H: &
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              FH bifariam in puncto K, ſitque in EH, ſic enim erit,
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              portionis ABCD centrum grauitatis L. </s>
              <s>Dico eſſe HK
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              ad KL, vt rectangulum GFR, vnà cum duabus tertiis
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              quadrati EF ad quadratum EG. </s>
              <s>Sit enim cylindrus, vel
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              portio cylindrica AM circa axim FE abſciſſa ijſdem pla­
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              nis cum portione AB
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              CD, ex cylindro, vel
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              portione cylindrica cir
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              ca axim GR ſphæ­
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              ræ, vel ſphæroidi AG
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              DR circumſcripta.
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              <s>Quoniam igitur ſolidi
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              AM eſt centrum gra­
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              uitatis H: reliqui au­
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              tem dempta ABCD
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              portione centrum gra­
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              uitatis K: & portionis
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              ABCD ponitur cen­
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              trum grauitatis L; erit
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                <figure id="id.043.01.245.1.jpg" xlink:href="043/01/245/1.jpg" number="179"/>
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              vt portio ABCD ad reliquum ſolidi AM, ita ex con­
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              traria parte KH ad HL. componendo igitur vt in antece­
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              denti, & per conuerſionem rationis, & conuertendo, erit
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              vt portio ABCD ad ſolidum AM; hoc eſt vt rectangu­
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              lum GFR, vnà cum duabus tertiis quadrati EF ad qua­
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              dratum EG, ita HK ad KL. </s>
              <s>Quod demonſtrandum
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              erat. </s>
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