Biancani, Giuseppe, Aristotelis loca mathematica, 1615

List of thumbnails

< >
191
191 		192
192
193
193 		194
194
195
195 		196
196
197
197 		198
198
199
199 		200
200
< >
page |< < of 355 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.005256">
                <pb pagenum="15" xlink:href="009/01/299.jpg"/>
              extrinſeca rei, de qua demonſtratur; quinimò ſubiectum ipſius ſunt. </s>
              <s id="s.005257">Quia
                <lb/>
              verò facta conſtructione, ſtatim perſpicuè apparet ortum eſſe triangulum,
                <lb/>
              æquilaterum, non eſt illi curę probare illud eſſe triangulum, ſed quia an ſit
                <lb/>
              æquilaterum ignoratur, idcircò totus demonſtrationis diſcurſus verſatur in
                <lb/>
              demonſtranda trium illarum linearum æqualitate.</s>
            </p>
            <p type="main">
              <s id="s.005258">Quem
                <expan abbr="quidẽ">quidem</expan>
              diſcurſum continere cauſam, quamuis per ſe pateat, vt mox
                <lb/>
              apparebit, non deeſt
                <expan abbr="tamẽ">tamen</expan>
              Procli authoritas adeò clara, vt magnopere mi­
                <lb/>
              rer Piccolomineum Procli ſtudioſum, eam non vidiſſe: Proclus enim in
                <expan abbr="cõ-men">conm
                  <lb/>
                men</expan>
              . huius demonſtrationis hæc habet; quando autem per deſcriptionem
                <lb/>
              circulorum, quod conſtructum eſt triangulum æquilaterum eſſe oſtenditur,
                <lb/>
              à cauſa apprehenſio fit; ſimilitudinem. </s>
              <s id="s.005259">n. </s>
              <s id="s.005260">& æqualitatem circulorum cauſam
                <lb/>
              dicimus eſſe æqualitatis laterum illius trianguli. </s>
              <s id="s.005261">Quibus verbis non ſolum
                <lb/>
              authoritas, ſed ratio etiam optima, cur hæc ſit demonſtratio à cauſa, con­
                <lb/>
              tinetur, quia nimirum oſtendit cauſam æqualitatis laterum eſſe, quia ſint
                <lb/>
              ſemidiametri æqualium circulorum. </s>
              <s id="s.005262">Quæ argumentatio procedit à defini­
                <lb/>
              tione ſubiecti, quod eſt circulus: quamuis non tota, ſed tantum quatenus
                <lb/>
              neceſſaria eſt, afferatur, ideſt definitio ſemidiametrorum, quod ad demon­
                <lb/>
              ſtrandum ſufficit, vt benè notat Zabarella, loquens de hac ipſa demonſtra­
                <lb/>
              tione; cùm igitur medium ſit definitio ſubiecti, patet eam eſſe perfectam
                <lb/>
              demonſtrationem, in qua paſſionis oſtenſæ allata eſt propria, & adæquata
                <lb/>
              cauſa, quæ eſt natura circuli. </s>
              <s id="s.005263">
                <expan abbr="ſicq́">ſicque</expan>
              ; Euclides optimè demonſtraujt ex con­
                <lb/>
              ſtructione, quàm præceperat, gigni triangulum æquilaterum. </s>
              <s id="s.005264">Subiectum
                <lb/>
              igitur eſt il a circulorum, ac linearum configuratio, medium definitio cir­
                <lb/>
              culi, paſſio triangulum
                <expan abbr="æquilaterũ">æquilaterum</expan>
              . </s>
              <s id="s.005265">ex qua
                <expan abbr="demõſtratione">demonſtratione</expan>
              erui poteſt etiam
                <lb/>
              definitio paſſionis cauſalis, ideſt, eſſe triangulum æquilaterum ex tali
                <expan abbr="cõſtru-ctione">conſtru­
                  <lb/>
                ctione</expan>
              ortum. </s>
              <s id="s.005266">Quare huic nihil deeſt ad perfectam
                <expan abbr="demonſtrationẽ">demonſtrationem</expan>
              . </s>
              <s id="s.005267">ex qui­
                <lb/>
              bus videas, quàm immeritò nonnulli eam impugnent, putantes eam eſſe per
                <lb/>
              extranea; cauſa erroris fuit, quia exiſtimarunt abſolutè demonſtrari
                <expan abbr="triã-gulum">trian­
                  <lb/>
                gulum</expan>
              illud eſſe æquilaterum. </s>
              <s id="s.005268">verùm decepti ſunt, quia in hoc, & in omni­
                <lb/>
              bus alijs problematis, demonſtratur talem conſtructionem parere triangu­
                <lb/>
              lum, vel
                <expan abbr="quadratũ">quadratum</expan>
              , vel quid aliud, vt patet Euclidem, vel obiter
                <expan abbr="inſpiciẽti">inſpicienti</expan>
              .</s>
            </p>
            <p type="main">
              <s id="s.005269">Placet adhuc alteram à formali cauſa procedentem expendere. </s>
              <s id="s.005270">ea eſt 46.
                <lb/>
              primi elem. </s>
              <s id="s.005271">quæ ſimiliter problema eſt, quo docet Euclides, qua ratione ſu­
                <lb/>
              pra data recta linea quadratum deſcribatur. </s>
              <s id="s.005272">tradit igitur quandam linea­
                <lb/>
              rum conſtructionem, ex qua poſtea demonſtrat ortum eſſe quadratum, ita
                <lb/>
              vt conſtructio illa ſit loco ſubiecti, de qua demonſtratvr eſſe quadratum. </s>
              <s id="s.005273">non
                <lb/>
              igitur intendit, vt nonnulli falsò putant,
                <expan abbr="demõſtrare">demonſtrare</expan>
              abſolutè illud eſſe qua­
                <lb/>
              dratum, ſed ex tali conſtructione ortum eſſe quadratum duo autem ſunt de
                <lb/>
              eſſentia quadrati, primum habere quatuor latera æqualia, ſecundum habe­
                <lb/>
              re quatuor angulos rectos, vt ex definitione conſtat. </s>
              <s id="s.005274">Neutrum autem ſine
                <lb/>
              altero ſufficit,
                <expan abbr="nã">nam</expan>
              & Rhombus quatuor latera æqualia habet, & Altera par­
                <lb/>
              te longius habet quatuor angulos rectos, neutrum tamen quadratum eſt. </s>
              <s id="s.005275">ſi
                <lb/>
              verò
                <expan abbr="vtrunq;">vtrunque</expan>
              ſimul cuipiam figuræ competat, illam neceſſariò quadratum
                <lb/>
              eſſe efficient. </s>
              <s id="s.005276">Probat igitur Euclid. vtraq, euidenter ineſſe illi figuræ ex vi
                <lb/>
              illius conſtructionis, & ideò illi quadrati definitionem competere. </s>
              <s id="s.005277">Quare
                <lb/>
              hęc erit potiſſima demonſtratio, cùm cauſam afferat
                <expan abbr="intrinſecã">intrinſecam</expan>
              , </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum