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

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          <p>
            <s xml:id="echoid-s14137" xml:space="preserve">
              <pb o="540" file="0560" n="560" rhead="GEOMETRI Æ"/>
            cta, TX, ſecante curuam, MH, in, I, regula, OH, oſtendemus
              <lb/>
            quadratum ſolidum, PH, viſa dicta figura, ad quadratum ſo-
              <lb/>
            lidum, ABHM, eſſe vt, ON, ad compoſitam ex, NR, & </s>
            <s xml:id="echoid-s14138" xml:space="preserve">@. </s>
            <s xml:id="echoid-s14139" xml:space="preserve">RO.</s>
            <s xml:id="echoid-s14140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14141" xml:space="preserve">Extendantur .</s>
            <s xml:id="echoid-s14142" xml:space="preserve">n. </s>
            <s xml:id="echoid-s14143" xml:space="preserve">HO, VR, verſus, OR, & </s>
            <s xml:id="echoid-s14144" xml:space="preserve">fiant, OC, RA, ſingulæ
              <lb/>
            æquales ipſi, ON, &</s>
            <s xml:id="echoid-s14145" xml:space="preserve">, DO, BR, capiantur ſingulæ æquales ipſi, RN
              <lb/>
            & </s>
            <s xml:id="echoid-s14146" xml:space="preserve">iungantur, AC, BD, CB, quas extenſſa indefinitè, TX, ſecet in, F’
              <lb/>
            P, E. </s>
            <s xml:id="echoid-s14147" xml:space="preserve">Etunt ergo, AO, BO, AD, parallelogramma. </s>
            <s xml:id="echoid-s14148" xml:space="preserve">Cum verò, CO’
              <lb/>
            æquetur, ON, & </s>
            <s xml:id="echoid-s14149" xml:space="preserve">DO, ipſi, RN, erit, CD, æqualis, OR .</s>
            <s xml:id="echoid-s14150" xml:space="preserve">i. </s>
            <s xml:id="echoid-s14151" xml:space="preserve">ipſi, DB,
              <lb/>
            vnde etiam, EP, ipſi, PB, hoc eſt ipſi, RX, & </s>
            <s xml:id="echoid-s14152" xml:space="preserve">tota, EX, toti, NX, & </s>
            <s xml:id="echoid-s14153" xml:space="preserve">
              <lb/>
            reliqua, FE, reliquæ, OX, æqualis erit. </s>
            <s xml:id="echoid-s14154" xml:space="preserve">Quoniam vero quadratum,
              <lb/>
              <figure xlink:label="fig-0560-01" xlink:href="fig-0560-01a" number="367">
                <image file="0560-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0560-01"/>
              </figure>
            OH, ad quadratum, XI, eſt
              <lb/>
            vt, ON, ad, NX, hoc eſt, FX,
              <lb/>
            ad, XE, hoc eſt quadratum,
              <lb/>
            FX, vel quadratum, CO, ad
              <lb/>
            rectangulum, FXE, ideo per-
              <lb/>
            mutando quadratum, HO,
              <lb/>
            ad quadratum, OC, erit vt
              <lb/>
            quadratum, IX, ad rectangu-
              <lb/>
            lum, FXE, ex quo conclude-
              <lb/>
            mus, vt in ſuperioribus rectangulum ſolidum ſub, AO, & </s>
            <s xml:id="echoid-s14155" xml:space="preserve">trapezio,
              <lb/>
            BCOR, eſſe proportionaliter analogum quadrato ſolido, RMHO.
              <lb/>
            </s>
            <s xml:id="echoid-s14156" xml:space="preserve">Similiter oſtendemus quadrata ſolida, AO, OV, eſſe proportionali-
              <lb/>
            ter analoga, & </s>
            <s xml:id="echoid-s14157" xml:space="preserve">conſequenter prædictis duobus ſolidis eſſe propor-
              <lb/>
            tionalia colligemus, vnde permutando quadratum ſolidum, VO,
              <lb/>
            ad quadratum ſolidum, MORH, ſeu (conſpecta figura prop. </s>
            <s xml:id="echoid-s14158" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14159" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14160" xml:space="preserve">
              <lb/>
            4.) </s>
            <s xml:id="echoid-s14161" xml:space="preserve">quadratum ſolidum, PH, ad quadratum ſolidum fruſti, ABHM,
              <lb/>
            erit vt quadratum ſolidum, AO, ad rectangulum ſolidum ſub, AO,
              <lb/>
              <note position="left" xlink:label="note-0560-01" xlink:href="note-0560-01a" xml:space="preserve">Cor. 1. 13.
                <lb/>
              huius 20.
                <lb/>
              l. 2.</note>
            & </s>
            <s xml:id="echoid-s14162" xml:space="preserve">trapezio, BCOR .</s>
            <s xml:id="echoid-s14163" xml:space="preserve">i. </s>
            <s xml:id="echoid-s14164" xml:space="preserve">vt, AO, ad, BCOR .</s>
            <s xml:id="echoid-s14165" xml:space="preserve">i. </s>
            <s xml:id="echoid-s14166" xml:space="preserve">vt, CO, ad compoſi-
              <lb/>
            tam ex, OD, & </s>
            <s xml:id="echoid-s14167" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s14168" xml:space="preserve">DC, .</s>
            <s xml:id="echoid-s14169" xml:space="preserve">i. </s>
            <s xml:id="echoid-s14170" xml:space="preserve">vt, ON, ad compoſitam ex, NR, & </s>
            <s xml:id="echoid-s14171" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s14172" xml:space="preserve">R
              <lb/>
            O, quod &</s>
            <s xml:id="echoid-s14173" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14174" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1248" type="section" level="1" n="754">
          <head xml:id="echoid-head787" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s14175" xml:space="preserve">PEr hanc ſimiliter ſuppletur prop. </s>
            <s xml:id="echoid-s14176" xml:space="preserve">23. </s>
            <s xml:id="echoid-s14177" xml:space="preserve">poſterior .</s>
            <s xml:id="echoid-s14178" xml:space="preserve">n. </s>
            <s xml:id="echoid-s14179" xml:space="preserve">pars, cum
              <lb/>
            Cor. </s>
            <s xml:id="echoid-s14180" xml:space="preserve">deducetur vt ibi, mutatis nominibus &</s>
            <s xml:id="echoid-s14181" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14182" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14183" xml:space="preserve">24. </s>
            <s xml:id="echoid-s14184" xml:space="preserve">reſtau-
              <lb/>
            ratione non indiget, ſicut etiam p. </s>
            <s xml:id="echoid-s14185" xml:space="preserve">25. </s>
            <s xml:id="echoid-s14186" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14187" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s14188" xml:space="preserve">26. </s>
            <s xml:id="echoid-s14189" xml:space="preserve">oſtende-
              <lb/>
            tur etiam vt ibi, mutatis, &</s>
            <s xml:id="echoid-s14190" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14191" xml:space="preserve">ſicut & </s>
            <s xml:id="echoid-s14192" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14193" xml:space="preserve">27. </s>
            <s xml:id="echoid-s14194" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14195" xml:space="preserve">ſimiliter p.
              <lb/>
            </s>
            <s xml:id="echoid-s14196" xml:space="preserve">28. </s>
            <s xml:id="echoid-s14197" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14198" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14199" xml:space="preserve">29. </s>
            <s xml:id="echoid-s14200" xml:space="preserve">cum Corollarijs, p. </s>
            <s xml:id="echoid-s14201" xml:space="preserve">30. </s>
            <s xml:id="echoid-s14202" xml:space="preserve">cum Corollarijs, p. </s>
            <s xml:id="echoid-s14203" xml:space="preserve">
              <lb/>
            31. </s>
            <s xml:id="echoid-s14204" xml:space="preserve">32. </s>
            <s xml:id="echoid-s14205" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14206" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14207" xml:space="preserve">33. </s>
            <s xml:id="echoid-s14208" xml:space="preserve">34. </s>
            <s xml:id="echoid-s14209" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14210" xml:space="preserve">35. </s>
            <s xml:id="echoid-s14211" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s14212" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14213" xml:space="preserve">36. </s>
            <s xml:id="echoid-s14214" xml:space="preserve">37. </s>
            <s xml:id="echoid-s14215" xml:space="preserve">38. </s>
            <s xml:id="echoid-s14216" xml:space="preserve">39. </s>
            <s xml:id="echoid-s14217" xml:space="preserve">40. </s>
            <s xml:id="echoid-s14218" xml:space="preserve">
              <lb/>
            cum Cor. </s>
            <s xml:id="echoid-s14219" xml:space="preserve">41. </s>
            <s xml:id="echoid-s14220" xml:space="preserve">42. </s>
            <s xml:id="echoid-s14221" xml:space="preserve">43. </s>
            <s xml:id="echoid-s14222" xml:space="preserve">44. </s>
            <s xml:id="echoid-s14223" xml:space="preserve">45. </s>
            <s xml:id="echoid-s14224" xml:space="preserve">p. </s>
            <s xml:id="echoid-s14225" xml:space="preserve">46. </s>
            <s xml:id="echoid-s14226" xml:space="preserve">autem eſt nobis reſtauranda.</s>
            <s xml:id="echoid-s14227" xml:space="preserve"/>
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