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>
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            <pb pagenum="185" xlink:href="015/01/204.jpg"/>
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              <s id="id003219">Propoſitio centeſima ſeptuageſima.</s>
            </p>
            <p type="main">
              <s id="id003220">Coniugationes cuiuſuis numeri breuiter inuenire.</s>
            </p>
            <p type="main">
              <s id="id003221">Sint gratia exempli
                <expan abbr="decẽ">decem</expan>
              homines, & patet quod poſſent eſſe ſin
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                <arrow.to.target n="marg592"/>
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              guli, & hoc
                <expan abbr="decẽ">decem</expan>
              modis, quia ſunt
                <expan abbr="decẽ">decem</expan>
              , ut Petrus & Ioannes: item,
                <lb/>
              poſſunt eſſe omnes ſimul, & hoc uno modo tantum, & poſſunt eſſe
                <lb/>
              duo, & hoc poteſt uariari
                <expan abbr="q̃">qua</expan>
              draginta quinque modis: & poſſunt eſſe
                <lb/>
              octo, & manifeſtum eſt, quod
                <expan abbr="totidẽ">totidem</expan>
              modis uariantur, ſcilicet qua­
                <lb/>
              draginta quinque, nam cum erunt octo, duo
                <expan abbr="quirelinquũtur">qui relinquuntur</expan>
              , uariari
                <lb/>
              poſſunt 45 modis, ergo & illi octo ad
                <expan abbr="unguẽ">unguem</expan>
              totidem modis. </s>
              <s id="id003222">Et ſi­
                <lb/>
              militer tres quot modis uariantur tot modis
                <expan abbr="ſeptẽ">ſeptem</expan>
              , & quot modis
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              quatuor tot ſex: quinque autem quia ſunt dimidium decem, pluribus
                <lb/>
              modis uariantur. </s>
              <s id="id003223">Et ideò pro ordine huius detrahes
                <expan abbr="unũ">unum</expan>
              , ut ſi ſint
                <lb/>
              undecim uiri pones decem, ſi decem pones
                <expan abbr="nouẽ">nouem</expan>
              , & colliges natu­
                <lb/>
              ralem seriem numerorum, ut infrà uides uno ſemper termino defi­
                <lb/>
              ciente: & ex priore ordine, ubi uidebis ſemper
                <expan abbr="etiã">etiam</expan>
              duplicari nume­
                <lb/>
              ros: ut 3. 6. in de ſub 6. 10. & 20 àlatere, & ſub 20 35. & à latere 70 du­
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              plum 35, & ſub
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                <figure id="id.015.01.204.1.jpg" xlink:href="015/01/204/1.jpg" number="199"/>
              70 126, & à late­
                <lb/>
              re 252, & hoc pro
                <lb/>
              cognitione q̊d
                <lb/>
              rectè ſis opera­
                <lb/>
              tus. </s>
              <s id="id003224">Secundò a­
                <lb/>
              nimaduertes
                <expan abbr="ſe­quẽtes">ſe­
                  <lb/>
                quentes</expan>
              ordines
                <lb/>
              fieri ex recta li­
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              nea priorum, ue
                <lb/>
              lut ſextus ordo eſt 7. 28. 84. 210. 462. ita incipiendo in primo ordi­
                <lb/>
              ne à 7, & tendendo ad dextram, inuenies illos eoſdem numeros ad
                <lb/>
              unguem, & ita in ſeptimo ordine 8. 36. 120. 330. à ſiniſtra inuento 8
                <lb/>
              in primo ordine, & procedendo ad dextram, inuenies 36. 120. &
                <lb/>
              330. Tertium eſt quod numeri ultimi à medio ſunt ijdem, ut 462 &
                <lb/>
              462. 330 & 330. 165 & 165. 55 & 55. 11 & 11. Et ſeorſum, ut dixi, rema­
                <lb/>
              net 1. Oportet igitur colligere numeros angulares, ut à latere ui­
                <lb/>
              des, & fit 2047 numerus coniugationum, tot enim modis poſſunt
                <lb/>
              uariari. </s>
              <s id="id003225">Et ſi eſſent decem tantum, ut ab initio propoſui, primus or­
                <lb/>
              do finitur ad 10, ſecundus ad 45, tertius ad 120, quartus ad 210, quin
                <lb/>
              tus ad 252, ſextus redit ad 210, ſeptimus ad 120, octauus ad 45, no­
                <lb/>
              nus ad 10, decimus ad 1. Et ita colligeretur ſumma ex extremis nu­
                <lb/>
              meris angularibus 1023. Et tot erunt coniugationes. </s>
              <s id="id003226">Hic uides quia
                <lb/>
              numerus 10 eſt par, et quod adempta monade, relinquitur 9, qui eſt
                <lb/>
              impar quòd medius qui pertinet ad quintum ordinem eſt </s>
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          </chap>
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      </text>
    </archimedes>
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