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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<archimedes>
<text>
<body>
<chap>
<p type="main">
<s id="id002474">
fíunt ex æqualibus lineis: at corpus quod fit ex a b in d g æquale eſt
<lb/>
corporibus quæ fiunt ex a c, c b in ſuperficiem d g at cubus a c con­
<lb/>
tinet duo corpora quę fiunt & a c in d g & g f, igitur cubus a c ſupe­
<lb/>
rat productum ex a b in d g in producto ex a c in f g & ſuperatur ab
<lb/>
eo in producto ex b c in d g, ſuperabatur etiam, ut uiſum eſt, cubus
<lb/>
b c à producto b a in d b in producto b cin c f, igitur cubi a c c b ſu­
<lb/>
perantur à producto a b in ad in producto b c in c f & in d g, quare
<lb/>
in producto b c in f e: ſi quidem f e & f g ſunt æqualia ex ſuppoſito
<lb/>
ſuperant autem in producto ex c b in e f, igitur tantum eſt in in quo
<lb/>
ſuperantur quantum eſt id in quo ſuperant: ergo ſunt æqualia.</s>
</p>
<p type="margin">
<s id="id002475">
<margin.target id="marg480"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
m.</s>
</p>
<p type="main">
</p>
<p type="main">
<lb/>
<lb/>
<arrow.to.target n="marg481"/>
</s>
</p>
<p type="margin">
<s id="id002478">
<margin.target id="marg481"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002479">Sit linea a b diuiſa in c uolo eius
<lb/>
<lb/>
</p>
<p type="main">
<s id="id002480">
<arrow.to.target n="marg482"/>
<lb/>
tum eſt, ſtatuo mediam c d inter a e &
<lb/>
<arrow.to.target n="marg483"/>
<lb/>
c b quæ ſit c d, & facio ut c d ad c a ita
<lb/>
c a ad a e, & ut d c ad c b ita c b ad b f, quia ergo d e media eſt inter
<lb/>
<arrow.to.target n="marg484"/>
<lb/>
a c & c b, & ut ea ad a cita d c a c b ad c f erunt omnes in continua
<lb/>
<arrow.to.target n="marg485"/>
<lb/>
proportione, quare proportio e c ad c a ut c f ad b f & e c ad ea ut
<lb/>
c f ad c b quod eſt propoſitum.</s>
</p>
<p type="margin">
<s id="id002481">
<margin.target id="marg482"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
13.
<emph type="italics"/>
ſex
<lb/>
ti
<emph.end type="italics"/>
E
<emph type="italics"/>
lem.
<emph.end type="italics"/>
</s>
</p>
<p type="margin">
<s id="id002482">
<margin.target id="marg483"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
11.
<emph type="italics"/>
ſex
<lb/>
ti
<emph.end type="italics"/>
E
<emph type="italics"/>
lement.
<emph.end type="italics"/>
</s>
</p>
<p type="margin">
<s id="id002483">
<margin.target id="marg484"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
11.
<lb/>
<emph type="italics"/>
quinti
<emph.end type="italics"/>
E
<emph type="italics"/>
lem.
<emph.end type="italics"/>
</s>
</p>
<p type="margin">
<s id="id002484">
<margin.target id="marg485"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
18.
<lb/>
<emph type="italics"/>
quinti
<emph.end type="italics"/>
E
<emph type="italics"/>
lem.
<emph.end type="italics"/>
</s>
</p>
<p type="main">
</p>
<p type="main">
<s id="id002486">Propoſitis tribus lineis primam ſic diuidere, ut adiectis duabus
<lb/>
alijs lineis ſecundum rationem mutuam ſingularum ſingulis ag­
<lb/>
<lb/>
<lb/>
<arrow.to.target n="marg486"/>
</s>
</p>
<p type="margin">
<s id="id002487">
<margin.target id="marg486"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
m.</s>
</p>
<p type="main">
<s id="id002488">Sit a, b, c, d, propoſitæ lineę,
<lb/>
<lb/>
uolo diuidere a b ita in e ut
<lb/>
ſumpta ſecundum proportio­
<lb/>
nem alicuius quantitatis, puta
<lb/>
<lb/>
e b ſic g a ad a e ut ſit propor­
<lb/>
<s id="id002489">Sint ergo
<lb/>
omnia
<expan abbr="cõſtituta">conſtituta</expan>
& ſit g rectan­
<lb/>
gulum ex a e in e b, cum ergo
<lb/>
g a contineat a e ut g continet e b, g autem continet e b ſecundum
<lb/>
a e, igitur g a continet a e ſecundum a c, ergo ex diffinitione qua­</s>
</p>
<p type="main">
<s id="id002490">
<arrow.to.target n="marg487"/>
<lb/>
drati a g eſt quadratum a e. </s>
<s id="id002491">Pari ratione b f eſt quadratum b e. </s>
<s id="id002492">pro­
<lb/>
portio igitur g e ad e f cum ſit ut c ad e ex ſuppoſito erit ut ipſi pro­
<lb/>
portioni addamus, & detrahamus ex duplo a b & dimidium reſi­
<lb/>
dui ducamus in ſe, & addamus aggregato quadrati a b cum ipſa </s>
</p>
</chap>
</body>
</text>
</archimedes>