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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              L
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              emmate
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              rop.
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              159.</s>
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              diff
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              er præce­
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              dentem.
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            <p type="head">
              <s id="id002885">SCHOLIVM.</s>
            </p>
            <p type="main">
              <s id="id002886">Ratio autem quòd omnis angulus contactus indiuiduus ſit, ſeu
                <lb/>
              duorum circulorum, ſeu circuli cum recta eſt, quoniam cum fuerint
                <lb/>
              duæ rationes contrariæ, & una perpetuò minuitur, alia manet ne­
                <lb/>
              ceſſe eſt, ut tandem, quæ minuitur, ſuperetur ab ea quæ manet: cum
                <lb/>
              ergo circuli curuitas maneat, & angulus tendat in punctum perpe­
                <lb/>
              tua diminutione neceſſe eſt, ut curuitas circuli impediat diuiſio­
                <lb/>
              nem rectè: ſed hoc habet duplicem obicem. </s>
              <s id="id002887">Primum, quia nullus
                <lb/>
              angulus ex circumferentia & recta poſſet diuidi: hoc autem falſum
                <lb/>
              eſt manifeſtè, cum ſolus ille qui fit ex contactu lineæ, quæ non di­
                <lb/>
              uidit circulum, diuidi non poſsit. </s>
              <s id="id002888">Secundò, quod angulus conta­
                <lb/>
              ctus duorum circulorum ſe exterius tangentium multo minus
                <lb/>
              poſſet diuidi angulo contactus interioris duorum circulorum,
                <lb/>
              quod tamen falſum eſt: & hoc animaduertit Campanus noſter, uir
                <lb/>
              acutus. </s>
              <s id="id002889">Dico ergo quòd in his qui ſe tangunt exterius, non fit diui­
                <lb/>
              ſio niſi ſemel: & quamuis inclinentur mutuò, tamen in concurſu
                <lb/>
              non aptantur, ut cum obuiat rectæ aut cauæ parti circuli quia ne­
                <lb/>
              ceſſe eſt, ut accedat, in alio autem diſcedat: indicio eſt quod circu­
                <lb/>
              los ſe exterius tangentes, in puncto facilè deſcribes, interius uix fie­
                <lb/>
              ri poteſt, ſed uidentur coniuncti
                <lb/>
                <figure id="id.015.01.183.1.jpg" xlink:href="015/01/183/1.jpg" number="194"/>
                <lb/>
              per longum interuallum. </s>
              <s id="id002890">Ad aliud
                <lb/>
              dico, quòd ille angulus ex recta &
                <lb/>
              peripheria conuexa circuli propter
                <lb/>
              diſceſſum ſeruat maiorem inclina­
                <lb/>
              tionem in quocunque puncto, quàm
                <lb/>
              ſit acceſſus conuexæ partis exterio­
                <lb/>
              ris circuli.</s>
            </p>
            <p type="main">
              <s id="id002891">Propoſitio centeſima ſexageſima
                <lb/>
              ſecunda.</s>
            </p>
            <p type="main">
              <s id="id002892">Proportionem duorum orbium
                <lb/>
              quorum diametrorum
                <expan abbr="cõuexæ">conuexæ</expan>
              par
                <lb/>
              tis, & concauæ proportiones datæ
                <lb/>
              ſint, inueſtigare.</s>
            </p>
            <p type="main">
              <s id="id002893">Sint duo orbes a b c d & e f g h,
                <lb/>
                <arrow.to.target n="marg569"/>
                <lb/>
              & ſit proportio a d ad b c, data & e
                <lb/>
              h ad f g, data & rurſus a d ad e h, di­
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              co orbis proportionem a b c d ad
                <lb/>
                <expan abbr="orbẽ">orbem</expan>
              e f g h eſſe
                <expan abbr="datã">datam</expan>
              . </s>
              <s id="id002894">Quia. n. </s>
              <s id="id002895">propor
                <lb/>
              tio a d ſphærę ad b c eſt ueluti ad di
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              metientis ad b c
                <expan abbr="dimetientẽ">dimetientem</expan>
              triplicata, ideò
                <expan abbr="cũ">cum</expan>
              nota ſit a d ad b c di
                <lb/>
                <arrow.to.target n="marg570"/>
                <lb/>
                <expan abbr="metientiũ">metientium</expan>
              , erit nota
                <expan abbr="etiã">etiam</expan>
              a d ſphæræ ad b c
                <expan abbr="ſphęrã">ſphęram</expan>
              . </s>
              <s id="id002896">quare orbis ad ad
                <lb/>
                <expan abbr="ſphęrã">ſphęram</expan>
              b c. nota eſt
                <expan abbr="etiã">etiam</expan>
              proportio b c
                <expan abbr="dimetiẽtis">dimetientis</expan>
              ad a d & ad a d e h & </s>
            </p>
          </chap>
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