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

Page concordance

< >
Scan Original
291 105
292 106
293 107
294 108
295 109
296 110
297 111
298 112
299 113
300 114
301 115
302 116
303 117
304 118
305 119
306 120
307 121
308 122
309 123
310 124
311 125
312 126
313 127
314 128
315 129
316 130
317 131
318 132
319 123
320 134
< >
page |< < (114) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div866" type="section" level="1" n="347">
          <p>
            <s xml:id="echoid-s8344" xml:space="preserve">
              <pb o="114" file="0300" n="300" rhead=""/>
            abſcindens A B F, cuius baſis ſit A E F, & </s>
            <s xml:id="echoid-s8345" xml:space="preserve">Canon rectus A B F. </s>
            <s xml:id="echoid-s8346" xml:space="preserve">Dico
              <lb/>
            hanc ſolidam portionem _MINIMAM_ eſſe earum, quæ à quocunque alio
              <lb/>
            plano per eandem A F ducto ex dato ſolido abſcindi poſſunt.</s>
            <s xml:id="echoid-s8347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8348" xml:space="preserve">Diuidatur A F bifariam in G, & </s>
            <s xml:id="echoid-s8349" xml:space="preserve">per G in plano per axem A B C de-
              <lb/>
            ſcribatur in prima figura (exhibente Conum) Hyperbole G H I,
              <note symbol="a" position="left" xlink:label="note-0300-01" xlink:href="note-0300-01a" xml:space="preserve">4. ſec.
                <lb/>
              Conic.</note>
            aſymptoti ſint B A, B C; </s>
            <s xml:id="echoid-s8350" xml:space="preserve">in ſecunda verò (quodcunque aliorum ſolidorum
              <lb/>
            repræſentante) deſciibatur coni-ſectio G H I ſimilis, & </s>
            <s xml:id="echoid-s8351" xml:space="preserve">concentrica
              <note symbol="b" position="left" xlink:label="note-0300-02" xlink:href="note-0300-02a" xml:space="preserve">5. 6. 7.
                <lb/>
              primi h.</note>
            ctioni A B C, quæ in vtraque figura omnino continget rectam A F in G,
              <lb/>
            (nam ſi alia eſſet contingens per G ſectionem G H I, ipſa producta ad
              <lb/>
            vtranque partem exteriori ſectioni A B C occurreret, ac bifariam ſecare-
              <lb/>
            tur in G: </s>
            <s xml:id="echoid-s8352" xml:space="preserve">vnde duæ applicate per G in ſectione A B C ſe mutuò
              <note symbol="c" position="left" xlink:label="note-0300-03" xlink:href="note-0300-03a" xml:space="preserve">Coroll.
                <lb/>
              45. h.</note>
            ſecarent, quod eſſet contra 26. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">ſec. </s>
            <s xml:id="echoid-s8354" xml:space="preserve">Conic.</s>
            <s xml:id="echoid-s8355" xml:space="preserve">, quæ vnicuique coni-ſectioni
              <lb/>
            inſeruit, licet de ſola Ellipſi, vel Circulo agat, ſed hoc idem, & </s>
            <s xml:id="echoid-s8356" xml:space="preserve">pro angulo
              <lb/>
            ſimul, aliter patet, ex primo Coroll. </s>
            <s xml:id="echoid-s8357" xml:space="preserve">68. </s>
            <s xml:id="echoid-s8358" xml:space="preserve">h.) </s>
            <s xml:id="echoid-s8359" xml:space="preserve">& </s>
            <s xml:id="echoid-s8360" xml:space="preserve">concipiatur circa commu-
              <lb/>
            nem axim B D H ſectio G H I in gyrum conuersá: </s>
            <s xml:id="echoid-s8361" xml:space="preserve">patet hanc deſcribere
              <lb/>
            ſolidum G H I ſimile, & </s>
            <s xml:id="echoid-s8362" xml:space="preserve">concentricum exteriori A B C; </s>
            <s xml:id="echoid-s8363" xml:space="preserve">& </s>
            <s xml:id="echoid-s8364" xml:space="preserve">cum recta A F
              <lb/>
            contingat ſectionem G H I in G, & </s>
            <s xml:id="echoid-s8365" xml:space="preserve">per A F ductum ſit planum A E F ipſi
              <lb/>
            plano per axem G H I perpendiculare, hoc ipſum continget
              <note symbol="d" position="left" xlink:label="note-0300-04" xlink:href="note-0300-04a" xml:space="preserve">55. h.</note>
            ſolidi ſuperficiem in puncto G.</s>
            <s xml:id="echoid-s8366" xml:space="preserve"/>
          </p>
          <figure number="243">
            <image file="0300-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0300-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s8367" xml:space="preserve">Ponatur primò punctum G eſſe extra axis verticem H, & </s>
            <s xml:id="echoid-s8368" xml:space="preserve">per G intelli-
              <lb/>
            gatur duci planum G L I ad axem erectum, quod in ſolido G H I circulum
              <lb/>
            efficiet centrum habentem in axe, vt in D, & </s>
            <s xml:id="echoid-s8369" xml:space="preserve">cuius communis ſectio
              <note symbol="e" position="left" xlink:label="note-0300-05" xlink:href="note-0300-05a" xml:space="preserve">4. primi
                <lb/>
              Conic. &
                <lb/>
              12. Arch.
                <lb/>
              de Co-
                <lb/>
              noid. &c.</note>
            plano per axem erit diameter G D I, cum alio autem plano A E F erit recta
              <lb/>
            E G, quæ cum ſit communis ſectio duorum planorum ad planum A B C
              <lb/>
            erectorum, erit ad idem planum recta, ac ideo cum diametro G D I
              <note symbol="f" position="left" xlink:label="note-0300-06" xlink:href="note-0300-06a" xml:space="preserve">19. vnd.
                <lb/>
              Elem.</note>
            ctum conſtituet angulum E G I, ſiue ipſa E G in puncto tantùm G circu-
              <lb/>
            lum continget.</s>
            <s xml:id="echoid-s8370" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8371" xml:space="preserve">Iam intelligatur per A F aliud planum duci ad planum per axem A B C
              <lb/>
            non erectum (ſed tale quod de exteriori ſolido aliam terminatam ſectionem
              <lb/>
            abſcindat) cuius communis ſectio cum circuli plano diuerſa erit à linea G E
              <lb/>
            (planum enim nunc ductum conuenit cum plano A E F per rectam tantùm
              <lb/>
            A F.) </s>
            <s xml:id="echoid-s8372" xml:space="preserve">Sit ipſa G L. </s>
            <s xml:id="echoid-s8373" xml:space="preserve">Et quoniam G E rectos facit angulos cum G I, ipſa.</s>
            <s xml:id="echoid-s8374" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum