Cardano, Girolamo, De subtilitate, 1663

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    <archimedes>
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          <chap>
            <p type="main">
              <s id="s.011044">
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              A D ad latus A B. </s>
              <s id="s.011045">Atque ita etiam ratio
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              ſubtenſæ quatuor lateribus & duobus, &
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              ſubtenſæ ſex lateribus ac tribus, tum alia­
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              rum cum latere reſpiciente ſubtenſas. </s>
              <s id="s.011046">Mul­
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              tiplex igitur ratio in figuris æquilateris cir­
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              culis inſcriptis, & quæ ex his compo­
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              nuntur.
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              </s>
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            <p type="margin">
              <s id="s.011047">
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              Ratio gene­
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              ralis
                <expan abbr="omniũ">omnium</expan>
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              figurarum
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              æqualia ha­
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              bentium la­
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              tera circulo
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              inſcripta­
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              rum.</s>
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            <p type="margin">
              <s id="s.011048">
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              Laterum
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              heptagoni
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              ratio.</s>
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              <s id="s.011049">Sed nulla melius, quam heptagoni cir­
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              culo inſcripti, & æquilateri. </s>
              <s id="s.011050">Si igitur he­
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              ptagonus deſcriptus ABCDEFG, & duo­
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              bus lateribus ſubtenſa AF & B F ſubtenſa
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              A B, & AF, cumque vt demonſtratum eſt,
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              angulus F B A duplus ſit angulo A F B, &
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              arcus BCDEF duplus eiſdem rationibus ar­
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              cui AGF, erit angulus BAF duplus angulo
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              ABF, quare ex demonſtrata proportione
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              BA, & BF ad AF vt AF ad AB: itémque per
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                <expan abbr="eandẽ">eandem</expan>
              AB & AF, ad BF vt BF ad AF. </s>
              <s id="s.011051">Refle­
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              xa igitur hæc bis proportio vocabitur. </s>
              <s id="s.011052">Po­
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              namus igitur A B nouem, poſita igitur AF
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              ſexdecim & BF viginti, ſi propoſitio viginti
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              nouem ad ſexdecim eſſet qualis ſexdecim ad
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                <expan abbr="nouẽ">nouem</expan>
              haberemus latera trigoni ABF. </s>
              <s id="s.011053">Sed
                <expan abbr="cũ">cum</expan>
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              maior ſit proportio vigintinouem ad ſexde­
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              cim, quàm ſexdecim ad nouem, ponemus
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              AF ſexdecim, ac rem habebis prope A B
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              200. A F 359. BF 448. vel per Alizam
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              regulam poſita AF. 1. erit BF. </s>
              <s id="s.011054">R Mut. </s>
              <s id="s.011055">7/54 in
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              2 1/3 ( m 1/3. ex prima æſtimatione. </s>
              <s id="s.011056">Quibus
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              habitis, ſi ducatur ex B linea per centrum,
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              & vbi cadit in circuli periferia linea ad F
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                <figure id="id.016.01.246.1.jpg" xlink:href="016/01/246/1.jpg" number="104"/>
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              & ad A, habebis quadrilaterum cum duo­
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              bus dimetientibus, cuius duo latera, & di­
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              metientium vna erit cognita. </s>
              <s id="s.011057">Duos inſu­
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              per trigonos orthogonios, quorum baſis
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              erit diameter circuli: vnde poſita reliqua
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              dimetientium re, cùm dimetientibus re­
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              ctangulum æquale ſit rectangulis duobus
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              quæ fiunt ex lateribus quadranguli inuicem
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              oppoſitis per demonſtrata à Ptolomæo, erit
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              ex his, quæ docuimus in Arte magna,
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              compoſitis minoribus capitulis ratio dia­
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              metri circuli ad A B latus heptagoni co­
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              gnita. </s>
              <s id="s.011058">Ex his igitur conſtat methodi reſo­
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              lutoriæ, cuius toties Galenus meminit, ex­
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              quiſitiſſimum, cui non par eſt in medica
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              arte exemplum. </s>
              <s id="s.011059">Propoſitum in circulo co­
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              gnitæ diametri heptagonum deſcribere: fa­
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              ctum iam ſupponamus, & ſit ſuprà deſ­
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              criptus: oportet igitur ſcire, qualiter de­
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              ducta diametro deducenda ſit AB. </s>
              <s id="s.011060">Vt ve­
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              rò hoc ſciamus, ratio A B ad diametrum
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              excogitanda eſt: vt verò hæc habeatur, ra­
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              tio ad A F, & F B quærenda erit: vt
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              hanc habeas, excogitata eſt rurſus angu­
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              lorum proportio, quæ ſola eſt manifeſta.
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              </s>
              <s id="s.011061">Inde ea habita quærendum, quòd hæc
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              proportio inter latera decernat. </s>
              <s id="s.011062">Atque hæc
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              bis reflexa proportio dicitur. </s>
              <s id="s.011063">Hanc cùm
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              ex reflexis ſimplicibus conſtet, diuiſam
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              demonſtrare oportet. </s>
              <s id="s.011064">Atque hic eſt finis
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              reſolutoriæ methodi. </s>
              <s id="s.011065">Ab hoc igitur fine,
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              compoſita methodus, quam præpoſuimus
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              in laterum heptagoni demonſtratione, ini­
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              tium ſumit. </s>
              <s id="s.011066">Sed & in his quandoque error
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              contingit, ſi quis non diligenter omninò
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              aduertat. </s>
              <s id="s.011067">Cuius rei exemplum eſt: ſit cir­
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              culus A B C, in eo diameter B C, cui
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                <figure id="id.016.01.246.2.jpg" xlink:href="016/01/246/2.jpg" number="105"/>
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              ſupereſt ad perpendiculum D A: ex A in­
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              quam videtur deduci poſſe linea aliqua ſe­
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              cans BC, vt A E F, ita vt ſit CE ad EA,
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              vt AE ad EF, quia CB poteſt quantumuis
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              augeri, quod tamen fieri non poteſt: etſi
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              fieri poſſet, Aliza regula non indiguiſſe­
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              mus: quia poſita BC, 10. AE puta 6. fieret
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                <expan abbr="cõfeſtim">confeſtim</expan>
              ED cognita, ideoque & EC & EB,
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              & quia proportio C E ad E A, eſt velut
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              EF ad EB, ex demonſtratis ab Euclide in
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              3. Elementorum, fieret, vt aggregato pri­
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              mæ, & quartæ quantitatis, tum tertia co­
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              gnitis, vt quantitates cognoſcerentur. </s>
              <s id="s.011068">Igi­
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              tur cubi, & alicuius numeri æqualis, de­
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              cem rebus notum eſt capitulum. </s>
              <s id="s.011069">Diſſolu­
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              tio paralogiſmi eſt, quia iam AD eſt me­
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              dia inter partes C D & BD, vt notum eſt
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              per ſe, & ſemper creſcit proportio A E ad
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              EF, magis quam CE ad E A, igitur pro­
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              portio CE ad E A minor eſt proportione
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              AE ad EF. </s>
              <s id="s.011070">Vbicunque tamen punctus aſ­
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              ſumatur in circunferentia A B ſemper de­
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              duci poterit, quia proportio partis CB ter­
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              minatæ ad deductam ex puncto illo ad per­
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              pendiculum eſt maior, quam deductæ ad
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              ad perpendiculum AD reſiduum, cui ſem­
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              per eſt æquale, & prior proportio minùs
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              augetur quam poſterior, igitur quandoque
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              peruenient ad æqualitatem. </s>
              <s id="s.011071">In vniuerſum
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              igitur paralogiſmi fiunt, vel cum aſſumitur
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              aliquid in
                <expan abbr="cõſtructione">conſtructione</expan>
              problematis, quo
                <expan abbr="nõ">non</expan>
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              vtimur in demonſtratione, vel cum vtimur
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              principio non vero, ſed veriſimili, vel cum
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              aſſumimus non demonſtrata pro demonſtra­
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              tis, vel pro medio, quod medium non eſt.
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              </s>
              <s id="s.011072">Omnia autem hæc magis contingunt in
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              remotis à ſenſu, vt corporibus, & diuerſi </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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