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="id002543">
                <pb pagenum="144" xlink:href="015/01/163.jpg"/>
              una eſt ſuperflua, quia ut dixi, una ſequitur ad aliam. </s>
              <s id="id002544">Ex hoc pa­
                <lb/>
              tet cur Diocles aſſumpſerit lineam unam, quæ eſt a c, quæ ſe ha­
                <lb/>
              bet ad a d, & d b, ut uiciſsim a d, & d b ad additas, quod eſt pri­
                <lb/>
              mum demonſtratum. </s>
              <s id="id002545">Sic enim omittit primum quod proponit Ar
                <lb/>
              chimedes, & aſſumit quod proximum eſt: & ideò Archimedes non
                <lb/>
              probat, nec præſupponit, quod à Diocle probatur, ſcilicet datum
                <lb/>
              eſſe punctum d in linea a b, ſed ſolum in linea g f, ideò cogitur pro­
                <lb/>
              bare ſecundum quod demonſtratur ab Eutocio, & à nobis demon
                <lb/>
              ſtratum eſt ſuprà. </s>
              <s id="id002546">Archimedes
                <expan abbr="aũt">aut</expan>
              aſſumit
                <expan abbr="lineã">lineam</expan>
              extra circulum,
                <expan abbr="quã">quam</expan>
                <lb/>
              uocat b f, quæ eſt æqualis b c medietati: aliam aſſumit quam uocat
                <lb/>
              b h, cuius proportio ad b d eſt ſicut quadrati ad a d quadratum a b.
                <lb/>
              </s>
              <s id="id002547">Conſtat ergo quod proportio g d ad d f eſt data. </s>
              <s id="id002548">Et ſimiliter f g ad
                <lb/>
              g d, & eſt 1 præ proportione data. </s>
              <s id="id002549">Vnde notandum quod datum
                <lb/>
              dicitur, ſimpliciter cognitum alio modo, dicitur datum poſitione,
                <lb/>
              quod eſt certum & tale, uelut ſi quis dicat, diuide 10 in duos nume­
                <lb/>
              ros quadratos: hoc non eſt datum, poteſt enim diuidi pluribus mo
                <lb/>
              dis. </s>
              <s id="id002550">At ſi dicas ut una pars ſit alterius
                <expan abbr="quadratũ">quadratum</expan>
              , iſtud antequàm ſci
                <lb/>
              untur partes, dicitur datum poſitione. </s>
              <s id="id002551">Ergo datum poſitione eſt du
                <lb/>
              plex, uel ut ratio nota ſit, non autem quantitas, ut ſi dicam a b eſt du
                <lb/>
              pla ad b c, utra que dicitur nota poſitione, quo­
                <lb/>
              niam neſcio quanta ſit a b. </s>
              <s id="id002552">Vel ſi quantitas eſt
                <lb/>
                <figure id="id.015.01.163.1.jpg" xlink:href="015/01/163/1.jpg" number="168"/>
                <lb/>
              nota proportio ignota ſit, ut ſi a c ſit 10, & ſit,
                <lb/>
              ut b c ſit <02> relata, a b erit punctus b, & proportio a b ad b c data po
                <lb/>
              ſitione, non tamen nota. </s>
              <s id="id002553">Et ſi dicas igitur omnia, quæ habent deter
                <lb/>
              minationem erunt data poſitione? </s>
              <s id="id002554">Dico quod non, quia oportet,
                <lb/>
              ut illa determinatio comprehendatur ſub una ratione, eaque ſaltem
                <lb/>
              generaliter cognita.</s>
            </p>
            <p type="main">
              <s id="id002555">Propoſitio centeſima quinquageſima tertia.</s>
            </p>
            <p type="main">
              <s id="id002556">Vim quan cun que manus multiplicare.
                <lb/>
                <arrow.to.target n="marg498"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002557">
                <margin.target id="marg498"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id002558">Cum enim radimus aut trahimus manifeſtum eſt, </s>
            </p>
            <p type="main">
              <s id="id002559">
                <arrow.to.target n="marg499"/>
                <lb/>
              quod ambabus manibus uis conduplicatur, & ma­
                <lb/>
                <figure id="id.015.01.163.2.jpg" xlink:href="015/01/163/2.jpg" number="169"/>
                <lb/>
              ior redditur, quanta eſt proportio totius ad exceſ­
                <lb/>
              ſum: uelut ſit a quod mouetur ab una manu uiribus
                <lb/>
              ut b, quæ ſunt exceſſus b d ſupra a, cum ergo propor
                <lb/>
              tio c b d ad a ſit compoſita ex proportionibus c &
                <lb/>
              b d ad a manifeſtum eſt, quod erit producta ex pro­
                <lb/>
              portione c b d ad b d, & b d ad a, ſed e b d eſt dupla
                <lb/>
              ad b d, quia e eſt æqualis, c igitur proportio c b d ad
                <lb/>
                <arrow.to.target n="marg500"/>
                <lb/>
              a eſt maior multo quàm duorum exceſſuum, qui mo
                <lb/>
              uerent in proportione dupla: uelut ſi adderemus f </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum