Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

List of thumbnails

< >
561
561 (541) 		562
562 (542)
563
563 (543) 		564
564
565
565 		566
566
567
567 		568
568
569
569
< >
page |< < (543) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1252" type="section" level="1" n="757">
          <pb o="543" file="0563" n="563" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1254" type="section" level="1" n="758">
          <head xml:id="echoid-head791" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s14306" xml:space="preserve">PEr hanc ſuppletur prior parti prop. </s>
            <s xml:id="echoid-s14307" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14308" xml:space="preserve">poſterior verò oſtendetur
              <lb/>
            vt ibi, mutatis conſuetis nominibus &</s>
            <s xml:id="echoid-s14309" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14310" xml:space="preserve">ſicut etiam prop. </s>
            <s xml:id="echoid-s14311" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s14312" xml:space="preserve">Conſimili autem methodo adhibita in præſenti prop. </s>
            <s xml:id="echoid-s14313" xml:space="preserve">oſtendemus
              <lb/>
            quad. </s>
            <s xml:id="echoid-s14314" xml:space="preserve">ſolidum, GE, ad quadratum ſolidum, HMEF, in ſuperiori fig. </s>
            <s xml:id="echoid-s14315" xml:space="preserve">
              <lb/>
            (hoc eſt in figura p.</s>
            <s xml:id="echoid-s14316" xml:space="preserve">3.</s>
            <s xml:id="echoid-s14317" xml:space="preserve">lib.</s>
            <s xml:id="echoid-s14318" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14319" xml:space="preserve">quadratum ſolidum, SF, ad quadratum
              <lb/>
            ſolidum, HDFG,) eſſe vt rectangulum ſolidum ſub, QM, MR, ad
              <lb/>
            rectangulum ſolidum ſub trapezijs, PQET, SRET, hoc eſt vt re-
              <lb/>
            ctangulum, QER, ad rectangulum ſub, QE, ST, vna cum rectan-
              <lb/>
            gulo ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s14320" xml:space="preserve">PS, & </s>
            <s xml:id="echoid-s14321" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s14322" xml:space="preserve">TM, & </s>
            <s xml:id="echoid-s14323" xml:space="preserve">ſub, TM, ideſt viſo ſche-
              <lb/>
            mate p.</s>
            <s xml:id="echoid-s14324" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14325" xml:space="preserve">vt rectangulum, OEN, ad rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s14326" xml:space="preserve">NM,
              <lb/>
              <note position="right" xlink:label="note-0563-01" xlink:href="note-0563-01a" xml:space="preserve">18. huius.</note>
            vna cum rectangulo ſub compoſita ex {1/2}. </s>
            <s xml:id="echoid-s14327" xml:space="preserve">NO, & </s>
            <s xml:id="echoid-s14328" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s14329" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s14330" xml:space="preserve">ſub, M
              <lb/>
            E; </s>
            <s xml:id="echoid-s14331" xml:space="preserve">poſterior pars autem eiuſdem prop.</s>
            <s xml:id="echoid-s14332" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14333" xml:space="preserve">deducetur vt ibidem, mu-
              <lb/>
            tatis nominibus &</s>
            <s xml:id="echoid-s14334" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14335" xml:space="preserve">Sicut & </s>
            <s xml:id="echoid-s14336" xml:space="preserve">omnes prop. </s>
            <s xml:id="echoid-s14337" xml:space="preserve">à 4. </s>
            <s xml:id="echoid-s14338" xml:space="preserve">vſque ad 20. </s>
            <s xml:id="echoid-s14339" xml:space="preserve">incluſi-
              <lb/>
            uè, cum earum Corollarijs. </s>
            <s xml:id="echoid-s14340" xml:space="preserve">In prop. </s>
            <s xml:id="echoid-s14341" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14342" xml:space="preserve">verò patebit quadratum ſo-
              <lb/>
            lidum, OP, viſa illius figura æquari rectangulo ſolido ſub, O
              <lb/>
            LS, OVCS, figuris, regula, DC, etenim ex ibi demonſtratis liquidò
              <lb/>
            apparet hæc eſſe ſolida æqualiter analoga iuxta dictam reguiam,
              <lb/>
            ex quo de inde reliqua concludentur mutatis nominibus &</s>
            <s xml:id="echoid-s14343" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14344" xml:space="preserve">ſicuti
              <lb/>
            & </s>
            <s xml:id="echoid-s14345" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s14346" xml:space="preserve">In prop: </s>
            <s xml:id="echoid-s14347" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14348" xml:space="preserve">figura ſic eſt corrigenda, debet enim, EC, hinc
              <lb/>
            inde produci, vt incidat aſymptotis, OY, OP, verſus eam productis,
              <lb/>
            in, S, I, quælitterę deſunt, cæterum prop. </s>
            <s xml:id="echoid-s14349" xml:space="preserve">oſtendetur vt ibidem mu-
              <lb/>
            tatis &</s>
            <s xml:id="echoid-s14350" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14351" xml:space="preserve">ſimul cum Corollarijs, necnon prop. </s>
            <s xml:id="echoid-s14352" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14353" xml:space="preserve">24. </s>
            <s xml:id="echoid-s14354" xml:space="preserve">25. </s>
            <s xml:id="echoid-s14355" xml:space="preserve">26. </s>
            <s xml:id="echoid-s14356" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14357" xml:space="preserve">28.
              <lb/>
            </s>
            <s xml:id="echoid-s14358" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14359" xml:space="preserve">& </s>
            <s xml:id="echoid-s14360" xml:space="preserve">29. </s>
            <s xml:id="echoid-s14361" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14362" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14363" xml:space="preserve">30. </s>
            <s xml:id="echoid-s14364" xml:space="preserve">autem patet ex dictis. </s>
            <s xml:id="echoid-s14365" xml:space="preserve">His deniq; </s>
            <s xml:id="echoid-s14366" xml:space="preserve">
              <lb/>
            reſtauratis, acſequenti ſcholio modificato, iuxta quod dictum fuit
              <lb/>
              <note position="right" xlink:label="note-0563-02" xlink:href="note-0563-02a" xml:space="preserve">22. huius.
                <lb/>
              Annot.22.
                <lb/>
              & 26. hu-
                <lb/>
              ius.</note>
            in examine lib. </s>
            <s xml:id="echoid-s14367" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14368" xml:space="preserve">& </s>
            <s xml:id="echoid-s14369" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14370" xml:space="preserve">ſequentia Corollaria vſq; </s>
            <s xml:id="echoid-s14371" xml:space="preserve">ad finem eiuſdem l.
              <lb/>
            </s>
            <s xml:id="echoid-s14372" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14373" xml:space="preserve">per quadratorum ſolidorum prædemonſtrata, ſimiliter, vt in præ-
              <lb/>
            fatis libris, colligentur, hæc autem pro reſtauratione lib.</s>
            <s xml:id="echoid-s14374" xml:space="preserve">5. </s>
            <s xml:id="echoid-s14375" xml:space="preserve">dicta
              <lb/>
            ſint ſatis.</s>
            <s xml:id="echoid-s14376" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14377" xml:space="preserve">Quoad lib.</s>
            <s xml:id="echoid-s14378" xml:space="preserve">6. </s>
            <s xml:id="echoid-s14379" xml:space="preserve">verò patet in eo traditas demonſtrationes, quæ ex
              <lb/>
            methodo indiuiſibilium dependebant, ibidẽ fuiſſe reſtauratas. </s>
            <s xml:id="echoid-s14380" xml:space="preserve">Illæ
              <lb/>
            autem propoſitiones, in quibus adhibentur aliquando nomina om-
              <lb/>
            nium quadratorum talium, vel talium figurarum, adhuc ſubſiſtent,
              <lb/>
            ſi illis nomina quadratorum ſolidorum earundem figurarum ſub-
              <lb/>
            ſtituamus, hac.</s>
            <s xml:id="echoid-s14381" xml:space="preserve">n. </s>
            <s xml:id="echoid-s14382" xml:space="preserve">ſola mutatione facta, cætera omnia manent in
              <lb/>
            ſuo robore, vt in eo libro innuitur in ſcholio prop. </s>
            <s xml:id="echoid-s14383" xml:space="preserve">20. </s>
            <s xml:id="echoid-s14384" xml:space="preserve">ac ſuperius
              <lb/>
            ſæpè ſæpius repetitum fuit.</s>
            <s xml:id="echoid-s14385" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1256" type="section" level="1" n="759">
          <head xml:id="echoid-head792" style="it" xml:space="preserve">Finis Septimi Libri.</head>
        </div>
      </text>
    </echo>
Impressum