Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of Notes

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            <s xml:id="echoid-s7465" xml:space="preserve">
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            28. </s>
            <s xml:id="echoid-s7466" xml:space="preserve">in quibus eorum centra non ſunt in B D axe reuolutionis Ellipſis, prout
              <lb/>
            ſunt in reliquis, ducatur per centrum F diameter I L eidem axi B D æqui-
              <lb/>
            diſtans, & </s>
            <s xml:id="echoid-s7467" xml:space="preserve">concipiatur, tum circulum, tum Ellipſim conuerti eadem arte,
              <lb/>
            qua ſuperiùs vſi ſumus, non abſimili ratiocinatione, atque ope 56. </s>
            <s xml:id="echoid-s7468" xml:space="preserve">huius,
              <lb/>
            oſtendetur incluſam Sphæram Sphæroides contingere, vel in vnico puncto,
              <lb/>
            vt euenit in 21. </s>
            <s xml:id="echoid-s7469" xml:space="preserve">22. </s>
            <s xml:id="echoid-s7470" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7471" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7472" xml:space="preserve">27. </s>
            <s xml:id="echoid-s7473" xml:space="preserve">ac 28. </s>
            <s xml:id="echoid-s7474" xml:space="preserve">vel in duobus tantùm, vt in 24. </s>
            <s xml:id="echoid-s7475" xml:space="preserve">& </s>
            <s xml:id="echoid-s7476" xml:space="preserve">25.
              <lb/>
            </s>
            <s xml:id="echoid-s7477" xml:space="preserve">vel ad integram circuli peripheriam, vt in 19. </s>
            <s xml:id="echoid-s7478" xml:space="preserve">& </s>
            <s xml:id="echoid-s7479" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7480" xml:space="preserve">ideoque omnes rectas,
              <lb/>
            quæ à centro F ad puncta Sphæricæ ſuperficiei ducuntur, æquales eſſe ijs,
              <lb/>
            quæ ad prædicta contactuum puncta, vel ad peripherias ducuntur, ac pro-
              <lb/>
            pterea, quæ ad circumſcriptam Sphæroidis ſuperſiciem, præter ad eadem
              <lb/>
            puncta, vel peripherias ducentur, maiores erunt. </s>
            <s xml:id="echoid-s7481" xml:space="preserve">Vnde ipſæ eductæ, à
              <lb/>
            dato puncto F ad reperta contactuum puncta, vel ad peripherias ſuper dati
              <lb/>
            Sphæroidis ſuperficiem erunt _MINIMAE_. </s>
            <s xml:id="echoid-s7482" xml:space="preserve">Quod vltimò faciendum erat.</s>
            <s xml:id="echoid-s7483" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div774" type="section" level="1" n="305">
          <head xml:id="echoid-head314" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s7484" xml:space="preserve">Iraberis fortaſſe, ac non immeritò, proximas haſce quinque
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            propoſitiones circa planas portiones verſantes, & </s>
            <s xml:id="echoid-s7485" xml:space="preserve">immediatè
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            poſt quadrageſimam quintam huius aptè apponendas, locum
              <lb/>
            hunc inter ſolida ſortitas fuiſſe: </s>
            <s xml:id="echoid-s7486" xml:space="preserve">ſed inuitam, vel fortuitam
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            potiùs huius tranſmisſionis cauſam, hic tibi enarrare ſuperuacaneum
              <lb/>
            puto. </s>
            <s xml:id="echoid-s7487" xml:space="preserve">His itaque vtaris prout ſuo loco inſertis; </s>
            <s xml:id="echoid-s7488" xml:space="preserve">nulla namque ipſarum
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            indiget aliqua præcedentium vſque ad num. </s>
            <s xml:id="echoid-s7489" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7490" xml:space="preserve">incluſiuè, licet ſola quin-
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            quageſima prima nonnullarum ſequentium notionem aſſumat.</s>
            <s xml:id="echoid-s7491" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div775" type="section" level="1" n="306">
          <head xml:id="echoid-head315" xml:space="preserve">THEOR. XXXVIII. PROP. LXIII.</head>
          <p>
            <s xml:id="echoid-s7492" xml:space="preserve">Æquales portiones eiuſdem coni - ſectionis, vel circuli, ſi
              <lb/>
            fuerint de eadem Parabola habebunt intercepta diametrorum
              <lb/>
              <note position="left" xlink:label="note-0268-01" xlink:href="note-0268-01a" xml:space="preserve">Conuer-
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              ſum Pro-
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              p. 40. h.</note>
            ſegmenta inter ſe æqualia. </s>
            <s xml:id="echoid-s7493" xml:space="preserve">Si de eadem Hyperbola, vel Ellipſi,
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            vel circulo, prædicta diametrorum ſegmenta erunt proprijs ſe-
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            mi- diametris proportionalia.</s>
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            <s xml:id="echoid-s7495" xml:space="preserve">SInt, in quacunque harum figurarum, duæ portiones A B C, D E F inter
              <lb/>
            ſe æquales, quæ in ſectione Ellipſis tertiæ figuræ ſint primò minores ſe-
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            mi- Ellipſi, & </s>
            <s xml:id="echoid-s7496" xml:space="preserve">harum omnium ſegmenta diametrorum ſint B G, E H, tùm
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            in Parabola primæ figuræ, tùm in reliquis, quarum centrum ſit O. </s>
            <s xml:id="echoid-s7497" xml:space="preserve">Dico,
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            in prima, ſegmenta E H, B G inter ſe æqualia eſſe, in reliquis verò, eſſe vt
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            H E ad E O, ita G B ad B O.</s>
            <s xml:id="echoid-s7498" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7499" xml:space="preserve">Ex altera diametrorum, vtputa ex E H, ſecetur, in prima figura, E I
              <lb/>
            æqualis ſegmento B G; </s>
            <s xml:id="echoid-s7500" xml:space="preserve">& </s>
            <s xml:id="echoid-s7501" xml:space="preserve">in reliquis, fiat O E ad E I, vt O B ad B G, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s7502" xml:space="preserve">in omnibus ordinatim applicetur per I ipſi diametro E I recta L I M, </s>
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