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 ...

Page concordance

< >
Scan Original
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id002559">
                <pb pagenum="145" xlink:href="015/01/164.jpg"/>
              ad d b æqualem b, multo maior eſt ex communi animi ſententia e f
                <lb/>
              b d
                <expan abbr="quã">quam</expan>
              f b d, quia e continet f, & quantum eſt d inſuper: cum ergo
                <lb/>
              b cum d moueat a in proportione b d ad a & f cum d mouebit a in
                <lb/>
              proportione eadem qua b d, ergo per uiam additionis duplo ue­
                <lb/>
              locius, quàm dupla proportione, uerùm dupla comparatione ad
                <lb/>
              proportionem b d ad a, non autem duplicata ſed dupla, ut dixi, quę
                <lb/>
              erit maior quàm dupla per
                <expan abbr="additionẽ">additionem</expan>
              exceſſus. </s>
              <s id="id002560">Ergo ſi addatur al­
                <lb/>
              ter homo, erit dupla ad illam duplam, ueluti addendo æqualem d b
                <lb/>
              f e, adeò ut ſi proportio d b f e eſſet quintupla, mouerent illi duo in
                <lb/>
              proportione decupla. </s>
              <s id="id002561">Sed annexo baculo aut lima aut ſerra annu­
                <lb/>
              lo h, ita ut circunuolui poſsit h æquabit uires non ſolum d b f e ſed
                <lb/>
              multorum hominum. </s>
              <s id="id002562">igitur multo plus aget homo ambabus ma­
                <lb/>
              nibus radendo aut ſecando cum g, quàm quadrupla proportione
                <lb/>
              unius manus, & hoc incrementum eſt non ſolum magnæ
                <lb/>
              utilitatis, ſed ualde
                <expan abbr="accõmodatum">accommodatum</expan>
              in actionibus artificum
                <lb/>
              operum grauiorum. </s>
              <s id="id002563">Et huiuſmodi conduplicatio eſt ratio
                <lb/>
              limæ quam ſurdam uocamus.</s>
            </p>
            <p type="margin">
              <s id="id002564">
                <margin.target id="marg499"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              37.</s>
            </p>
            <p type="margin">
              <s id="id002565">
                <margin.target id="marg500"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2.</s>
            </p>
            <figure id="id.015.01.164.1.jpg" xlink:href="015/01/164/1.jpg" number="170"/>
            <p type="main">
              <s id="id002566">Propoſitio centeſima quadrageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id002567">Si lineę datę alia linea adiungatur, ab extremitatibus autem pri­
                <lb/>
              oris lineę duæ rectæ in unum punctum concurrant proportionem
                <lb/>
              habentes quam media inter totam & adiectam, ad adiectam erit
                <lb/>
              punctus concurſus à puncto extremo lineæ adiectæ diſtans per li­
                <lb/>
              neam mediam. </s>
              <s id="id002568">Quòd ſi ab extremo alicuius lineæ æqualis mediæ
                <lb/>
              ſeu peripheria circuli cuius ſemidiameter ſit media linea duæ lineæ
                <lb/>
              ad prædicta puncta producantur, ipſę erunt in proportione medię
                <lb/>
              ad adiectam.
                <lb/>
                <arrow.to.target n="marg501"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002569">
                <margin.target id="marg501"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="main">
              <s id="id002570">Hęc propoſitio eſt admirabilis: & etiam deſcripſi, ut multa ſecre­
                <lb/>
              ta Dialecticæ potius
                <expan abbr="aperirent̃">aperirentur</expan>
              quam quod huic propoſito
                <expan abbr="multũ">multum</expan>
                <lb/>
              congrueret. </s>
              <s id="id002571">Ideò potius ſcholij cauſa poſita eſt quam ipſius tracta­
                <lb/>
              tionis: ut
                <expan abbr="modũ">modum</expan>
              demonſtrandi magis quam id, q̊d
                <expan abbr="demonſtrat̃">demonſtratur</expan>
              , re­
                <lb/>
              ſpicere oporteat. </s>
              <s id="id002572">
                <expan abbr="Conſtituat̃">Conſtituatur</expan>
              ergo (per uiam problematis) linea a b
                <lb/>
              & proportio c ad d, & fiat d e ad c, ut c ad d, & a b ad e ut b f ad d, &
                <lb/>
              ut g ad c, eritque g media inter a f & f b, quod licet ſolum ſupponatur
                <lb/>
              ab Appollonio,
                <expan abbr="tamẽ">tamen</expan>
              facilè demonſtratur & à Commandino adie­
                <lb/>
              cta eſt
                <expan abbr="demõ">demon</expan>
              ſtratio. </s>
              <s id="id002573">Concurrant ergo ex a & b duę lineę in aliquod </s>
            </p>
            <p type="main">
              <s id="id002574">
                <arrow.to.target n="marg502"/>
                <lb/>
              punctum, putat h ut ſit a h ad h b uelut c ad d, dico quod ſi ducat
                <lb/>
              h f quod ipſa erit æqualis g, ducatur b l æquidiſtans a h, & quia
                <lb/>
                <arrow.to.target n="marg503"/>
                <lb/>
              ex ſuppoſito a h ad h b, ut g ad b f, erit b h ad h a, ut b f ad g, & quia
                <lb/>
              trianguli a h f & b l f ſunt ſimiles erit proportio a h ad b l, ueluti a f
                <lb/>
                <arrow.to.target n="marg504"/>
                <lb/>
              ad fb, igitur per ęquam proportionem b e h ad b l, ut a f ad g, ſed ut
                <lb/>
                <arrow.to.target n="marg505"/>
                <lb/>
              a f ad g ita g ad b f ex ſuppoſito: & ut a f ad g, it a h a ad h b, ex ſuppo </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum