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="id002308">
e k, & f a ad a e, ut ſuperficierum ipſa­
<lb/>
<lb/>
rum per primam ſexti Elementorum: at
<lb/>
per præcedentem maior eſt proportio
<lb/>
e d ad d f, quàm a f ad a e, duplicata igi­
<lb/>
tur maior eſt proportio e d ad eam, quę
<lb/>
poteſt ſuper f c ſuperficiem, quam f a ad
<lb/>
a e, igitur maior, quàm a k ad a b ex pri­
<lb/>
ma ſexti Elementorum: igitur per trige
<lb/>
ſimam quartam undecimi. </s>
<s id="id002309">Parallelipe­
<lb/>
dum ex e d in a b maius eſt parallelipedo ex ea, quæ poteſt in f c ſu­
<lb/>
perficiem in ipſam ſuperficiem a k. </s>
<s id="id002310">Si uerò diuiſio facta fuerit in g,
<lb/>
conſtat ex præcedenti, quod minor eſt proportio g e ad e d, quàm
<lb/>
ſit duplicata e a ad a d a g, eam igitur minor proportio eius lineæ,
<lb/>
quæ poteſt in g e ſuperficiem ad e d quam a b ad a h, igitur paralle­
<lb/>
lipedum ex e d in a b eſt maius parallelipedo ex ea, quæ poteſt g c
<lb/>
in a h cum ſit a b ad a h, ut dictum eſt, uelut a e ad a g.
<lb/>
<arrow.to.target n="marg456"/>
</s>
</p>
<p type="margin">
<s id="id002311">
<margin.target id="marg455"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="margin">
<s id="id002312">
<margin.target id="marg456"/>
C
<emph type="italics"/>
or
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002313">Manifeſtum eſt autem, quòd tale corpus eſt æquale duplo cubi
<lb/>
</p>
<p type="main">
<s id="id002314">Propoſitio centeſima trigeſima quinta.</s>
</p>
<p type="main">
<s id="id002315">Si linea in duas partes, quarum una ſit alteri dupla, diuidatur
<lb/>
erit, quod fit ex tertia parte in quadratum reſidui parallelipedum
<lb/>
maius omni parallelipedo, quod ex diuiſione eiuſdem lineæ crea­
<lb/>
ri poſsit.</s>
</p>
<p type="main">
<s id="id002316">
<arrow.to.target n="marg457"/>
</s>
</p>
<p type="margin">
<s id="id002317">
<margin.target id="marg457"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002318">Sit a c dupla b c, & ſit quadratum ad ipſius a c, dico parallelipe­
<lb/>
<lb/>
dum ex b c in a d maius eſſe quouis alio ex
<lb/>
diuiſione lineæ a b ſimiliter creato. </s>
<s id="id002319">Secetur
<lb/>
primo in e, & fiat quadratum a f, eritque per
<lb/>
uigeſimam quintam. </s>
<s id="id002320">Huius proportio c b
<lb/>
ad b c maior duplicata a e ad a c, quare ma­
<lb/>
ior, quam a f ad a d per uigeſimam ſexti Ele
<lb/>
mentorum, igitur per trigeſimam quartam
<lb/>
undecimi, Parallelipedum ex b c in a d maius eſt parallelipedo e b
<lb/>
in a f, quod eſt demonſtrandum. </s>
<s id="id002321">Si uerò diuiſio cadat in g, fiat qua­
<lb/>
dratum a h, et erit per uigeſimamtertiam huius proportio g c ad c b
<lb/>
minor, quam duplicata c a ad a g: igitur minor, quàm a d ad a h, igi­
<lb/>
tur per eandem parallelipedum ex c b in a d maius eſt parallelipe­
<lb/>
do ex g b in a h.</s>
</p>
<p type="main">
<s id="id002322">
<arrow.to.target n="marg458"/>
</s>
</p>
<p type="margin">
<s id="id002323">
<margin.target id="marg458"/>
C
<emph type="italics"/>
or
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002324">Ex hoc liquet quòd parallelipedum illud erit quadruplum cu­
<lb/>
bo minoris partis, & dimidium cubi maioris.</s>
</p>
</chap>
</body>
</text>
</archimedes>