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 ...

List of thumbnails

< >
111
111
112
112
113
113
114
114
115
115
116
116
117
117
118
118
119
119
120
120
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001797">
                <pb pagenum="99" xlink:href="015/01/118.jpg"/>
              quomodolibet, ut ſe ſecent in e, erunt anguli d c a, & d b a æquales,
                <lb/>
                <arrow.to.target n="marg369"/>
                <lb/>
              quia in ead́em portione circuli a d, & anguli a d e ęquales, quia con
                <lb/>
              tra ſe poſiti. </s>
              <s id="id001798">igitur trianguli a b e, & c d e ſimiles, & proportio d c ad
                <lb/>
                <arrow.to.target n="marg370"/>
                <lb/>
              a b, ut c e ad b e, c d autem fuit 5 a b 4, igitur ſi b e ponatur 4 pos c e
                <lb/>
              erit 5 pos. </s>
              <s id="id001799">Per eaſdem, & eodem modo a d ad b c ut d e ad e c. igitur
                <lb/>
              poſita c e 5 pos erit e d 10 pos, tota igitur d b 14 pos. </s>
              <s id="id001800">Et quoniam ea­
                <lb/>
                <arrow.to.target n="marg371"/>
                <lb/>
              dem proportio a e ad e b per eadem, & e b fuit 4 pos: igitur a e eſt 8
                <lb/>
              pos, quare a e 13. poſt productum igitur ex a c in d b, eſt 182 quad.
                <lb/>
              </s>
              <s id="id001801">& hoc æquatur productis a b in c d, quod eſt 20, & b c in a d quod
                <lb/>
              eſt 18, totum igitur eſt 38, igitur res eſt <02> 19/91. Quare notę erunt lineæ
                <lb/>
              b e, e d, a e, & e c, ſed ſufficit, ut cognita ſit a c, uel b d. </s>
              <s id="id001802">Per regulam
                <lb/>
              enim triangulorum erunt notæ areæ a b c, & a d e, quare tota ſuper­
                <lb/>
              ficies a b c d. </s>
              <s id="id001803">Et eſt inuentum Scipionis Ferri Bononienſis de quo
                <lb/>
              aliâs. </s>
              <s id="id001804">Poteſt etiam inuenta a c uel b d haberi ſuperficies facilius
                <lb/>
              per catheros.</s>
            </p>
            <p type="margin">
              <s id="id001805">
                <margin.target id="marg364"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              _{m}.</s>
            </p>
            <p type="margin">
              <s id="id001806">
                <margin.target id="marg365"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              52. E
                <emph type="italics"/>
              le
                <lb/>
              ment.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001807">
                <margin.target id="marg366"/>
              I
                <emph type="italics"/>
              n
                <emph.end type="italics"/>
              16.
                <emph type="italics"/>
              de
                <emph.end type="italics"/>
                <lb/>
              S
                <emph type="italics"/>
              ubtil.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001808">
                <margin.target id="marg367"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              3.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001809">
                <margin.target id="marg368"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              23.
                <emph type="italics"/>
              ſex
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001810">
                <margin.target id="marg369"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              21.
                <emph type="italics"/>
              ter
                <lb/>
              tij
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001811">
                <margin.target id="marg370"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001812">
                <margin.target id="marg371"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              32.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001813">Sit modo obtuſi angulus a b c, & nota latera ſingula, & angu­
                <lb/>
              lus a b c, & producantur latera ad perpendicu­
                <lb/>
                <figure id="id.015.01.118.1.jpg" xlink:href="015/01/118/1.jpg" number="112"/>
                <lb/>
              lum, ut ſint d & e recti, & quia anguli ad a ſunt
                <lb/>
              æquales, erunt anguli e b a, & d e a ſemper æ­
                <lb/>
                <arrow.to.target n="marg372"/>
                <lb/>
              quales. </s>
              <s id="id001814">Et hoc idem contingit in acuti angulis
                <lb/>
              triangulis intus, & eſt utile mechanicum: &
                <lb/>
              quia a b c notus eſt, & d notus, erunt anguli tri
                <lb/>
              goni d b c noti: & ſi fuerit angulus a notus,
                <expan abbr="erũt">erunt</expan>
              anguli d a c & e a b
                <lb/>
              noti, & ideo anguli e b a, & d c a: & ſemper notum, quod fit ex b a
                <lb/>
              in a d, uel c a in a e, ſunt enim ęqualia inter ſe: etiam notæ ad & a c,
                <lb/>
              quoniam duplum horum eſt exceſſus quadrati b c ſuper quadrata
                <lb/>
              a b, & a c. </s>
              <s id="id001815">Quod uerò propositurà Monteregio de cognitione an­
                <lb/>
              gulorum in triangulis non eſt intelligendum, ut uerba ſignificant,
                <lb/>
                <arrow.to.target n="marg373"/>
                <lb/>
              ſed ſolum de cognitione quoad uſum tabularum.</s>
            </p>
            <p type="margin">
              <s id="id001816">
                <margin.target id="marg372"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              32.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001817">
                <margin.target id="marg373"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              12.
                <emph type="italics"/>
              ſe­
                <lb/>
              cundi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id001818">Et iterum ponamus, quòd proportio a c c b ad a b ſit qualis a b
                <lb/>
              ad a c, dico quòd angulus c duplus eſt angulo b. </s>
              <s id="id001819">Si non ducatur c d
                <lb/>
                <figure id="id.015.01.118.2.jpg" xlink:href="015/01/118/2.jpg" number="113"/>
                <lb/>
              faciens angulum d c b duplum b, erit igitur pro­
                <lb/>
              portio d c c b ad d b, ut d b ad d c. </s>
              <s id="id001820">Maior eſt
                <expan abbr="autẽ">autem</expan>
                <lb/>
              d c, quàm a c, aut æqualis, aut minor, ſi æqualis,
                <lb/>
              igitur maior proportio d c c b ad b d quàm b a,
                <lb/>
              igitur maior proportio b d ad d c quam b a ad a c
                <lb/>
              ad a c & æquales ſunt igitur b d maior d a pars toto, quod eſſe non
                <lb/>
              poteſt. </s>
              <s id="id001821">Si uerò d c ponatur maior a c, magis ex hoc ſequitur b d ma­
                <lb/>
              iorem eſſe b a. </s>
              <s id="id001822">Quod ſi minor ſit d c quàm a c. </s>
              <s id="id001823">Ex demonſtratio­
                <lb/>
              ne ipſius reflexæ proportionis patet hoc contingere non poſſe.
                <lb/>
              </s>
              <s id="id001824">Et ſimiliter patet conuerſas in reliquis etiam ueras eſſe, non ſolum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>