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="id002345">Quarta regula propoſita quantitate ab uno in continua propor
<lb/>
tione, ſi uis ſcire cuius naturæ ſit detracto uno conſidera, an poſsit
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diuidi per duo, eſt quadratum medietatis, & ita procedes diuiden­
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do uſque ad numerum primum, qui uel eſt 2, & erit ex genere quad
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<s id="id002346">uel 3, & erit ex genere quadratorum cuborum, & ſimiliter ſi
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ſit 9, erit ex genere quadratorum cubi cubi. </s>
<s id="id002347">Et ſi proueniat alius nu
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merus primus, ut 5. 7. 11. 13. erit quadratum relati illius ordinis. </s>
<s id="id002348">Et ſi
<lb/>
non poteſt diuidi numerus quantitatum per 2 uide, ſi poſsit diuidi
<lb/>
per 3, tunc erit cubus illius quantitatis, & ſi illa quantitas, quæ pro­
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uenit ex diuiſione: fuerit 3, uel potuerit diuidi per 3, erit cubus, uel
<lb/>
cubus cubi, & ita deinceps. </s>
<s id="id002349">Si uerò ſit alius numerus primus, ut 5.
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7. 11. erit cubus relati. </s>
<s id="id002350">Et ita ſi
<expan abbr="">non</expan>
poſsit diuidi per 2, nec per 3, erit ex
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genere relati. </s>
<s id="id002351">Et tunc ſi poſsit diuidi per alium numerum, ut 35, erit
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relatum ex eo genere. </s>
<s id="id002352">Vtpotè trigeſima quinta quantitas eſt rela­
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tum ſecundum relati primi, ſeu relatum primum relati ſecundi.
<lb/>
</s>
<s id="id002353">Nam quoties quantitas poteſt diuidi per duos numeros, dicetur
<lb/>
ſub utro que uiciſsim, ut duodecima poteſt diuidi per 4 & 3, ideò di­
<lb/>
<s id="id002355">cub. </s>
<s id="id002356">& per 2 & 6, & dicetur
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<lb/>
proportionis, ad quam omnia referri debent.</s>
</p>
<p type="main">
<s id="id002357">Quinta regula ex præcedenti pendet, & eſt, quod denomina­
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tiones, & proportiones uiciſsim commutantur: uelut 256 eſt quad
<lb/>
<lb/>
mini ipſo computato, & inter quad quad, & quod uiſi duo, ergo
<lb/>
<lb/>
duplicatæ non conſtituunt quad: nam 64 continet duas duplas
<lb/>
<lb/>
</p>
<p type="main">
<s id="id002358">Sexta regula ſimiliter ex dictis pendet, & eſt, quòd gratia exem­
<lb/>
pli relatum primum comparatum ad primum terminum eſt ſexta
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quantitas, cum autem comparatur ad rem, iam præſupponit pro­
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portionem. </s>
<s id="id002359">Exemplum relatum primum proportionis 21/20 eſt 4084101/3200000
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& eſt aliquanto maior ſexquiquarta, & ſi colligas terminos 100.
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105. 110 1/4 115 61/80 121 861/1600 127 19681/32000. Tu uides quòd ſunt ſex termini in
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utra que computando primum, ſed in 21/20 ſunt duo termini, & in qua­
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duo & ultimus ſcilicet ſextus fit ex relato ipſo. </s>
<s id="id002360">Ergo ultra propor­
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tionem ſunt tantum quatuor termini.</s>
</p>
<p type="main">
<s id="id002361">Septima regula ad effugiendum omnes errores tu ſcis, quòd
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