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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              1. P
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              ropoſ.
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              10. E
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              lem.
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              P
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              er
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              11.
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              ter
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              tij
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              E
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              lement.
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              E
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              x
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              10.
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              diff.
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              <s id="id002843">tertij
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              E
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              lem.
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              P
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              er
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              1.
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              deci­
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              mi
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              E
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              lem.
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              </s>
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            <p type="main">
              <s id="id002845">Propoſitio centeſima ſexageſima.</s>
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            <p type="main">
              <s id="id002846">Propoſita linea tribus que in ea ſignis punctum inuenire, ex que
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              ductæ tres lineæ ad ſigna ſint in proportionibus datis.
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              </s>
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              <s id="id002847">
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              C
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              o
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              ^{m}.</s>
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            <p type="main">
              <s id="id002848">Sit data linea a b c in qua puncta dicta & datæ tres lineę d e f, uo­
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              lo inuenire punctum, puta g ex quo ductæ tres
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              lineæ ad a b c puncta ſint in proportione a g ad </s>
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            <p type="main">
              <s id="id002849">
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              g b, ut d ad e & g b ad g c, ut e ad f. </s>
              <s id="id002850">Per pręceden
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                <figure id="id.015.01.181.1.jpg" xlink:href="015/01/181/1.jpg" number="191"/>
                <lb/>
              tia inuenio circulum ex cuius peripheria omni­
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              bus ex punctis ductæ lineæ ad a b ſint in pro­
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              portione d ad e, & per idem circulum ex cuius
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              peripheria quælibet lineæ ductæ ad b c puncta
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              ſint in proportione c ad f, ſi igitur iſti duo circu­
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              li ſe ſecabunt in aliquo puncto puta g: liquet
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              quod lineæ ductæ ex g ad a b c, erunt in propor
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              tione d e f.
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                <arrow.to.target n="marg554"/>
              </s>
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              <s id="id002851">
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              P
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              er
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              154.</s>
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              <s id="id002852">
                <margin.target id="marg554"/>
              C
                <emph type="italics"/>
              or
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              ^{m}_{m}.</s>
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            <p type="main">
              <s id="id002853">Ex quo liquet quod ſi uoluero ducere ad tria puncta data, tres
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              lineas in continua proportione data d ad e, ſubijciam tertiam uel in
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              terponam, ſi uoluero mediam. </s>
              <s id="id002854">Et ſi uellem, ut eſſet a g ad g b dupli­
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              cata ei quæ eſt g b ad b c, & uellem quòd proportio d ad a d f data
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              eſſet, oporteret inuenire duas medias proportione inter d & f, in de
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              operari cum una earum per modum propoſitum. </s>
              <s id="id002855">Differt corrola­
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              rium hoc à propoſitione in hoc, quod in propoſitione non quæri­
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              mus niſi proportionem g a ad g b & g b ad b c, non g a ad g c, neque
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              comparationem proportionum: at in corrolario quærimus tres
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              proportiones g a g b & g c, & comparationem proportionum in­
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              ter ſe, ſcilicet æqualitatem.</s>
            </p>
            <p type="main">
              <s id="id002856">Propoſitio centeſima ſexageſima prima.</s>
            </p>
            <p type="main">
              <s id="id002857">Si fuerint duo trianguli quorum baſes in eadem linea ſint con­
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              ſtituti & æquales & ad unum punctum terminati, & latus unum
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              commune inter reliqua quantita­
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                <figure id="id.015.01.181.2.jpg" xlink:href="015/01/181/2.jpg" number="192"/>
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              te medium, neceſſe eſt angulum à
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              maioribus lineis contentum mi­
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              norem eſſe.</s>
            </p>
            <p type="main">
              <s id="id002858">Sint duo trianguli a b c, a c d, </s>
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            <p type="main">
              <s id="id002859">
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              quales proponuntur, & ſit a d ma­
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                <arrow.to.target n="marg556"/>
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              ior a b dico angulum d a c eſſe mi­
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              norem. </s>
              <s id="id002860">Si non fiat angulus d a c æ­
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              qualis ex alia parte, & oportet ſi non ſit minor ut uel cadat a d ſu­
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                <arrow.to.target n="marg557"/>
                <lb/>
              per a b & ducta a d ad ęqualitatem cadet infra b, ducta ergo d c erit
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              trigonus a d c maior a b c, quod eſſe non poteſt cum ſint æquales. </s>
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          </chap>
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