Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...
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              <s id="id001678">
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              no de, & eleuetur ex a, & manifeſtum eſt, quod inſidebit per totam
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              lineam c f ipſi plano, & proportio grauitatis totius ſuſpenſi in com
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              paratione ad grauitatem eius, qui inuertit, eſt, uelut proportio par­
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              tis terminatæ ad lineam c f uerſus eum, qui eleuat ad partem, quæ
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              ultra eſt, cum uerò hæ partes notæ ſint iuxta perpendiculum ex
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              centro grauitatis, manifeſtum eſt, quod ſciemus pondus corporis
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              a b cf, dum inuertitur in quo cunque ſitu ad pondus eius, dum ſu­
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              ſpenditur, & clarum eſt, quòd cùm centrum, & medium grauitatis
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              fuerint in una linea per c f, tunc nulla erit grauitas.</s>
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            <p type="margin">
              <s id="id001679">
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              P
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              er
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              40.</s>
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              <s id="id001680">Propoſitio nonageſima octaua.</s>
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              <s id="id001681">Proportionem ponderum æqualium per differentiam angulo­
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              rum inuenire.
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            <p type="margin">
              <s id="id001682">
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              C
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              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id001683">Sit a b, quæ ſi appenſa eſſet ad æquidi­
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                <figure id="id.015.01.111.1.jpg" xlink:href="015/01/111/1.jpg" number="106"/>
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              ſtantem terræ ſuperficiei, nulla ui poſſet ele</s>
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            <p type="main">
              <s id="id001684">
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              uari, inflectatur ergo ad c punctum, omiſſa
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              c g, & manifeſtum eſt, quod ſi b c inſiſteret
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              ad perpendiculum, ponderaret a c ſi eſſet in
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              æquilibrio, ponatur ergo accliuis in c d per
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              notum angulum. </s>
              <s id="id001685">Quia igitur b c ad c a no­
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              ta eſt, erit dicta ſuperiùs notum pondus
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              b h, poſita h c æquali c a, quare totius a b,
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              & iam fuit e k notum, & punctus d notus:
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              hoc enim infrà demonſtrabitur, qualis igitur proportio lineæ
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              tranſuerſæ dl ad lineam deſcendentem d m, talis differentiæ pon­
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              derum c m, & c e, id eſt partis ad partem. </s>
              <s id="id001686">hæc autem inferiùs de­
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              monſtrabuntur. </s>
              <s id="id001687">Neque enim abſurdum eſt in materijs miſtis, ali­
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              quando uti nondum demonſtratis cum fuerint mathematica, quia
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              obtinent principij rationem, quod etiam facit Archimedes. </s>
              <s id="id001688">Ma­
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              nifeſtum eſt autem, quod in angulo m c d recti dimidio, propor­
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              tio media erit. </s>
              <s id="id001689">Sed hoc bifariam contingere poteſt ſcilicet, ut ſit
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              media, per quantitatem, & per proportionem, eſt autem media, ut
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              demonſtrabitur infrà ſecundum proportionem l d ad l e, propo­
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              natur ergo c e b, erit latus quadrati <02> 72, igitur latus octogoni eſt
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              <02> v: 72 m: <02> 2592, & latus reſidui <02> v: 72 p: <02> 2592. quadrata er­
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              go partium baſis differunt in <02> 10368. Quare partes baſis ſunt
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              6 p: <02> 18, & 6 m: <02> 18 ſcilicet l e, l d autem eſt <02> 18, igitur differen­
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              tia, & proportio eſt, qualis <02> 18 ad 6 m: <02> 18 fermê, ut 17 ad 7, & ta­
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              lis eſt proportio ponderis c d ad pondus c e ratione in crementi,
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              ſeu differentiæ. </s>
              <s id="id001690">Vt ſi pondus in c e eſſet decem librarum in c in </s>
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          </chap>
        </body>
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    </archimedes>