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="id002559">
ad d b æqualem b, multo maior eſt ex communi animi ſententia e f
<lb/>
b d
<expan abbr="quã">quam</expan>
f b d, quia e continet f, & quantum eſt d inſuper: cum ergo
<lb/>
b cum d moueat a in proportione b d ad a & f cum d mouebit a in
<lb/>
<lb/>
locius, quàm dupla proportione, uerùm dupla comparatione ad
<lb/>
proportionem b d ad a, non autem duplicata ſed dupla, ut dixi, quę
<lb/>
erit maior quàm dupla per
exceſſus. </s>
<lb/>
ter homo, erit dupla ad illam duplam, ueluti addendo æqualem d b
<lb/>
f e, adeò ut ſi proportio d b f e eſſet quintupla, mouerent illi duo in
<lb/>
proportione decupla. </s>
<s id="id002561">Sed annexo baculo aut lima aut ſerra annu­
<lb/>
lo h, ita ut circunuolui poſsit h æquabit uires non ſolum d b f e ſed
<lb/>
multorum hominum. </s>
<s id="id002562">igitur multo plus aget homo ambabus ma­
<lb/>
<lb/>
unius manus, & hoc incrementum eſt non ſolum magnæ
<lb/>
utilitatis, ſed ualde
<expan abbr="accõmodatum">accommodatum</expan>
in actionibus artificum
<lb/>
operum grauiorum. </s>
<s id="id002563">Et huiuſmodi conduplicatio eſt ratio
<lb/>
limæ quam ſurdam uocamus.</s>
</p>
<p type="margin">
<s id="id002564">
<margin.target id="marg499"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
37.</s>
</p>
<p type="margin">
<s id="id002565">
<margin.target id="marg500"/>
P
<emph type="italics"/>
er
<emph.end type="italics"/>
2.</s>
</p>
<p type="main">
</p>
<p type="main">
<s id="id002567">Si lineę datę alia linea adiungatur, ab extremitatibus autem pri­
<lb/>
oris lineę duæ rectæ in unum punctum concurrant proportionem
<lb/>
<lb/>
punctus concurſus à puncto extremo lineæ adiectæ diſtans per li­
<lb/>
neam mediam. </s>
<s id="id002568">Quòd ſi ab extremo alicuius lineæ æqualis mediæ
<lb/>
ſeu peripheria circuli cuius ſemidiameter ſit media linea duæ lineæ
<lb/>
ad prædicta puncta producantur, ipſę erunt in proportione medię
<lb/>
<lb/>
<arrow.to.target n="marg501"/>
</s>
</p>
<p type="margin">
<s id="id002569">
<margin.target id="marg501"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
m.</s>
</p>
<p type="main">
<s id="id002570">Hęc propoſitio eſt admirabilis: & etiam deſcripſi, ut multa ſecre­
<lb/>
ta Dialecticæ potius
<expan abbr="aperirent̃">aperirentur</expan>
quam quod huic propoſito
<expan abbr="multũ">multum</expan>
<lb/>
congrueret. </s>
<s id="id002571">Ideò potius ſcholij cauſa poſita eſt quam ipſius tracta­
<lb/>
tionis: ut
<expan abbr="modũ">modum</expan>
demonſtrandi magis quam id, q̊d
<expan abbr="demonſtrat̃">demonſtratur</expan>
, re­
<lb/>
ſpicere oporteat. </s>
<s id="id002572">
<expan abbr="Conſtituat̃">Conſtituatur</expan>
ergo (per uiam problematis) linea a b
<lb/>
<lb/>
ut g ad c, eritque g media inter a f & f b, quod licet ſolum ſupponatur
<lb/>
ab Appollonio,
<expan abbr="tamẽ">tamen</expan>
facilè demonſtratur & à Commandino adie­
<lb/>
cta eſt
<expan abbr="demõ">demon</expan>
ſtratio. </s>
<s id="id002573">Concurrant ergo ex a & b duę lineę in aliquod </s>
</p>
<p type="main">
<s id="id002574">
<arrow.to.target n="marg502"/>
<lb/>
punctum, putat h ut ſit a h ad h b uelut c ad d, dico quod ſi ducat
<lb/>
h f quod ipſa erit æqualis g, ducatur b l æquidiſtans a h, & quia
<lb/>
<arrow.to.target n="marg503"/>
<lb/>
ex ſuppoſito a h ad h b, ut g ad b f, erit b h ad h a, ut b f ad g, & quia
<lb/>
trianguli a h f & b l f ſunt ſimiles erit proportio a h ad b l, ueluti a f
<lb/>
<arrow.to.target n="marg504"/>
<lb/>
ad fb, igitur per ęquam proportionem b e h ad b l, ut a f ad g, ſed ut
<lb/>
<arrow.to.target n="marg505"/>
<lb/>
a f ad g ita g ad b f ex ſuppoſito: & ut a f ad g, it a h a ad h b, ex ſuppo </s>
</p>
</chap>
</body>
</text>
</archimedes>