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="id002377">
tus eſt ordo, & facere tot numeros ſequentes; quotus eſt ordo, &
<lb/>
<lb/>
demus o, & fiet 20, nec alium quęremus numerum. </s>
<s id="id002378">Sed quia cubi­
<lb/>
ca eſt ſecundo loco, habebit prima nota 00, & fiet 300, & ſecundum
<lb/>
<lb/>
& 00 ſecundo, & o tertio, & ita habebimus 4000. 600. 40. ſed quia
<lb/>
in tabula non eſt 4 ultimum, addemus ſimilem primo ſemper. </s>
<s id="id002379">In
<lb/>
relato primo, ergo habebimus 50000. 1000. 1000. 50. & in cubo
<lb/>
quadrati 600000. 150000. 20000. 1500. 60. Manifeſtum eſt, quòd
<lb/>
his uice uerſa aſſumpſimus 15 & 6 ſimiles prioribus addendo ſem­
<lb/>
per ut dixi o minus, donec ad unam peruenerit. </s>
<s id="id002380">Et ita in relato ſe­
<lb/>
cundo 7000000. 2100000. 350000. 35000. 2100. 70. & ita deinceps.</s>
</p>
<p type="margin">
<s id="id002381">
<margin.target id="marg464"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002382">Propoſitio centeſima trigeſima nona.</s>
</p>
<p type="main">
<s id="id002383">Radices omnes à propoſitis numeris extrahere.
<lb/>
<arrow.to.target n="marg465"/>
</s>
</p>
<p type="margin">
<s id="id002384">
<margin.target id="marg465"/>
C
<emph type="italics"/>
o
<emph.end type="italics"/>
^{m}.</s>
</p>
<p type="main">
<s id="id002385">Propoſitis quibuſuis numeris utpotè 916132832, uolo detrahere
<lb/>
<02> relatam primam, primum habebo in tabula deſcripta relata pri­
<lb/>
ma numerorum ſimplicium uſque ad 10 uelut in exemplo. </s>
<s id="id002386">Dein de
<lb/>
<lb/>
ſubſcribam pun­
<lb/>
ctum ſub prima
<lb/>
nota à dextra, &
<lb/>
quia eſt quarta in
<lb/>
ordine hoc, ſeu quinta denominatio ſecun­
<lb/>
dum noſtrum, omittam quatuor notas in­
<lb/>
ter medias, & ſubſcribam punctum aliud,
<lb/>
& ita facerem ſi eſſent plures quàm decem
<lb/>
<expan abbr="pũctum">punctum</expan>
primum
<lb/>
à ſiniſtra 9161, cuius quęro <02> relatam pri­
<lb/>
mam in tabula, quam inuenio eſſe 6, nam
<lb/>
7776 eius relatum primum eſt
<lb/>
<lb/>
detraho igitur 7776, ex numero
<lb/>
propoſitio relinquitur. </s>
<s id="id002387">Dein de
<lb/>
póno 6 & quadratum eius, & cub. </s>
<lb/>
quadrati, quia, ut dixi, eſt quarta denominatio a­
<lb/>
pud illum, & è regione numeros præcedentes in­
<lb/>
uentos relati primi ex præcedenti propoſitione: & duco ſingulos
<lb/>
cum ſuis collateralibus, ut uides etiam in figura, et cum ultimo pro­
<lb/>
ducto, ſcilicet 64800000 diuido 138532832 exit 2, huius accipio o­
<lb/>
mnes numeros ad relatum primum uſque ut uides, & pono minores
<lb/>
è regione maiorum, utpotè 2 è regione 1296 & 50000, & 4 è </s>
</p>
</chap>
</body>
</text>
</archimedes>