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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page |< < of 291 > >|
<archimedes>
<text>
<body>
<chap>
<p type="main">
<s id="id001678">
no de, & eleuetur ex a, & manifeſtum eſt, quod inſidebit per totam
<lb/>
lineam c f ipſi plano, & proportio grauitatis totius ſuſpenſi in com
<lb/>
paratione ad grauitatem eius, qui inuertit, eſt, uelut proportio par­
<lb/>
tis terminatæ ad lineam c f uerſus eum, qui eleuat ad partem, quæ
<lb/>
ultra eſt, cum uerò hæ partes notæ ſint iuxta perpendiculum ex
<lb/>
centro grauitatis, manifeſtum eſt, quod ſciemus pondus corporis
<lb/>
a b cf, dum inuertitur in quo cunque ſitu ad pondus eius, dum ſu­
<lb/>
ſpenditur, & clarum eſt, quòd cùm centrum, & medium grauitatis
<lb/>
fuerint in una linea per c f, tunc nulla erit grauitas.</s>
</p>
<p type="margin">
<s id="id001679">
<margin.target id="marg339"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
40.</s>
</p>
<p type="main">
<s id="id001680">Propoſitio nonageſima octaua.</s>
</p>
<p type="main">
<s id="id001681">Proportionem ponderum æqualium per differentiam angulo­
<lb/>
rum inuenire.
<lb/>
<arrow.to.target n="marg340"/>
</s>
</p>
<p type="margin">
<s id="id001682">
<margin.target id="marg340"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id001683">Sit a b, quæ ſi appenſa eſſet ad æquidi­
<lb/>
<lb/>
ſtantem terræ ſuperficiei, nulla ui poſſet ele</s>
</p>
<p type="main">
<s id="id001684">
<arrow.to.target n="marg341"/>
<lb/>
uari, inflectatur ergo ad c punctum, omiſſa
<lb/>
c g, & manifeſtum eſt, quod ſi b c inſiſteret
<lb/>
<arrow.to.target n="marg342"/>
<lb/>
ad perpendiculum, ponderaret a c ſi eſſet in
<lb/>
æquilibrio, ponatur ergo accliuis in c d per
<lb/>
notum angulum. </s>
<s id="id001685">Quia igitur b c ad c a no­
<lb/>
ta eſt, erit dicta ſuperiùs notum pondus
<lb/>
b h, poſita h c æquali c a, quare totius a b,
<lb/>
& iam fuit e k notum, & punctus d notus:
<lb/>
hoc enim infrà demonſtrabitur, qualis igitur proportio lineæ
<lb/>
<arrow.to.target n="marg343"/>
<lb/>
tranſuerſæ dl ad lineam deſcendentem d m, talis differentiæ pon­
<lb/>
derum c m, & c e, id eſt partis ad partem. </s>
<s id="id001686">hæc autem inferiùs de­
<lb/>
monſtrabuntur. </s>
<s id="id001687">Neque enim abſurdum eſt in materijs miſtis, ali­
<lb/>
<arrow.to.target n="marg344"/>
<lb/>
quando uti nondum demonſtratis cum fuerint mathematica, quia
<lb/>
obtinent principij rationem, quod etiam facit Archimedes. </s>
<s id="id001688">Ma­
<lb/>
nifeſtum eſt autem, quod in angulo m c d recti dimidio, propor­
<lb/>
tio media erit. </s>
<s id="id001689">Sed hoc bifariam contingere poteſt ſcilicet, ut ſit
<lb/>
media, per quantitatem, & per proportionem, eſt autem media, ut
<lb/>
<arrow.to.target n="marg345"/>
<lb/>
demonſtrabitur infrà ſecundum proportionem l d ad l e, propo­
<lb/>
natur ergo c e b, erit latus quadrati <02> 72, igitur latus octogoni eſt
<lb/>
<02> v: 72 m: <02> 2592, & latus reſidui <02> v: 72 p: <02> 2592. quadrata er­
<lb/>
go partium baſis differunt in <02> 10368. Quare partes baſis ſunt
<lb/>
6 p: <02> 18, & 6 m: <02> 18 ſcilicet l e, l d autem eſt <02> 18, igitur differen­
<lb/>
tia, & proportio eſt, qualis <02> 18 ad 6 m: <02> 18 fermê, ut 17 ad 7, & ta­
<lb/>
lis eſt proportio ponderis c d ad pondus c e ratione in crementi,
<lb/>
ſeu differentiæ. </s>
<s id="id001690">Vt ſi pondus in c e eſſet decem librarum in c in </s>
</p>
</chap>
</body>
</text>
</archimedes>