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

Table of handwritten notes

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          <p>
            <s xml:id="echoid-s12879" xml:space="preserve">Manifeſla eſt ſimiliter hæc Prop. </s>
            <s xml:id="echoid-s12880" xml:space="preserve">cum enim ſecto quolibet cy-
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              <note position="left" xlink:label="note-0524-01" xlink:href="note-0524-01a" xml:space="preserve">Corol.12.
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              lib. 1.</note>
            lindrico plano æquidiſtanter baſi, producatur in eo figura æqualis
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            ipſi baſi, propterea vt baſis ad baſim, ſic erit figura ad ſiguram ab
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            eodem plano baſibus æquidiſtante etcumq; </s>
            <s xml:id="echoid-s12881" xml:space="preserve">productam, ergo hi
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            cylindrici erunt figurę proportionaliter analogæ, iuxta ipſas baſes,
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              <note position="left" xlink:label="note-0524-02" xlink:href="note-0524-02a" xml:space="preserve">3.huius.</note>
            ergo cylindrici æquè alti erunt inter ſe vt baſes.</s>
            <s xml:id="echoid-s12882" xml:space="preserve"/>
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        <div xml:id="echoid-div1164" type="section" level="1" n="696">
          <head xml:id="echoid-head729" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s12883" xml:space="preserve">HOc demonſtrato haud difficile erit ſtylo veteri oſtendere cy-
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            lindricos exiſtentes in eadem baſi eſſe inter ſe vt altitudines,
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            vel vt latera æqualiter baſibus inclinata.</s>
            <s xml:id="echoid-s12884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12885" xml:space="preserve">Similiter eoſdem habere inter ſe rationem compoſitam ex ra-
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            tione baſium, & </s>
            <s xml:id="echoid-s12886" xml:space="preserve">altitudinum, vel laterum æqualiter baſibus incli-
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            natorum. </s>
            <s xml:id="echoid-s12887" xml:space="preserve">Et eos qui habent baſes altitudinibus, vel lateribus æ-
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            qualiter baſibus inclinatis, reciprocas æquales eſſe; </s>
            <s xml:id="echoid-s12888" xml:space="preserve">Vel æquales,
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            baſes haberet altitudinibus, ſeu lateribus æqualiter baſibus incli-
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            natis, reciprocas atq; </s>
            <s xml:id="echoid-s12889" xml:space="preserve">ſimiles cylindricos eſſe in tripla ratione late-
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            rum hom ologorum. </s>
            <s xml:id="echoid-s12890" xml:space="preserve">Sufficiet namq; </s>
            <s xml:id="echoid-s12891" xml:space="preserve">nos methodum imitari, qua
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            dem onſtrata Prop. </s>
            <s xml:id="echoid-s12892" xml:space="preserve">9. </s>
            <s xml:id="echoid-s12893" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12894" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12895" xml:space="preserve">poſtmodum reliquæ vſq; </s>
            <s xml:id="echoid-s12896" xml:space="preserve">ad Prop. </s>
            <s xml:id="echoid-s12897" xml:space="preserve">14.
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            </s>
            <s xml:id="echoid-s12898" xml:space="preserve">oſtenſæ fuerunt, probando circa cylindricos, quod ibi circa omnia
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            quadrata datorum parallelogram. </s>
            <s xml:id="echoid-s12899" xml:space="preserve">oſtendebatur. </s>
            <s xml:id="echoid-s12900" xml:space="preserve">Hæc autem pro
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            cylindricis poſtea collecta ſunt in eodem lib. </s>
            <s xml:id="echoid-s12901" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12902" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s12903" xml:space="preserve">34. </s>
            <s xml:id="echoid-s12904" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s12905" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12906" xml:space="preserve">
              <lb/>
            generali a ſec. </s>
            <s xml:id="echoid-s12907" xml:space="preserve">B. </s>
            <s xml:id="echoid-s12908" xml:space="preserve">vſq; </s>
            <s xml:id="echoid-s12909" xml:space="preserve">ad ſec. </s>
            <s xml:id="echoid-s12910" xml:space="preserve">G. </s>
            <s xml:id="echoid-s12911" xml:space="preserve">quæ quidem animaduertere opus
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            erat.</s>
            <s xml:id="echoid-s12912" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12913" xml:space="preserve">In Prop. </s>
            <s xml:id="echoid-s12914" xml:space="preserve">15. </s>
            <s xml:id="echoid-s12915" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s12916" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12917" xml:space="preserve">hæc ſupplenda videntur. </s>
            <s xml:id="echoid-s12918" xml:space="preserve">In Sec. </s>
            <s xml:id="echoid-s12919" xml:space="preserve">A.
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            </s>
            <s xml:id="echoid-s12920" xml:space="preserve">probatur figuram, KQM, ipſi, ABD, &</s>
            <s xml:id="echoid-s12921" xml:space="preserve">, ΠΤΩ, ipſi, φΣΛ, æqualem
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            eſſe ex Prop. </s>
            <s xml:id="echoid-s12922" xml:space="preserve">3. </s>
            <s xml:id="echoid-s12923" xml:space="preserve">eiuſdem, nempè ex methodo Indiuiſibilium, hoc
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            autem patebit etiam ex prop. </s>
            <s xml:id="echoid-s12924" xml:space="preserve">prima huius, ſunt enim dictæ figuræ
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            æqualiter analogæ. </s>
            <s xml:id="echoid-s12925" xml:space="preserve">In ſec. </s>
            <s xml:id="echoid-s12926" xml:space="preserve">B. </s>
            <s xml:id="echoid-s12927" xml:space="preserve">figuram, MZP, adæquari ipſi, KQ
              <lb/>
            M, &</s>
            <s xml:id="echoid-s12928" xml:space="preserve">, Ω℟&</s>
            <s xml:id="echoid-s12929" xml:space="preserve">, ipſi, ΠΤΩ, eodem modo deducetur ex prima huius. </s>
            <s xml:id="echoid-s12930" xml:space="preserve">
              <lb/>
            In ſec. </s>
            <s xml:id="echoid-s12931" xml:space="preserve">C. </s>
            <s xml:id="echoid-s12932" xml:space="preserve">probabitur vt, MP, ad, PO, ita eſſe figuram, MZP, ad, O
              <lb/>
            ZP, ex prop. </s>
            <s xml:id="echoid-s12933" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12934" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s12935" xml:space="preserve">In ſec. </s>
            <s xml:id="echoid-s12936" xml:space="preserve">D. </s>
            <s xml:id="echoid-s12937" xml:space="preserve">ſimiliter oſtendemus figuram, O
              <lb/>
            ZP, ad figuram, Ω℟&</s>
            <s xml:id="echoid-s12938" xml:space="preserve">, eſſe vt, ZP, ad, ℟&</s>
            <s xml:id="echoid-s12939" xml:space="preserve">, ſimiliter ex prop. </s>
            <s xml:id="echoid-s12940" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12941" xml:space="preserve">
              <lb/>
            huius. </s>
            <s xml:id="echoid-s12942" xml:space="preserve">Cętera verò abſq; </s>
            <s xml:id="echoid-s12943" xml:space="preserve">methodo indiuiſibilium ſubſiſtunt; </s>
            <s xml:id="echoid-s12944" xml:space="preserve">vt & </s>
            <s xml:id="echoid-s12945" xml:space="preserve">
              <lb/>
            Corollaria, & </s>
            <s xml:id="echoid-s12946" xml:space="preserve">prop. </s>
            <s xml:id="echoid-s12947" xml:space="preserve">16.</s>
            <s xml:id="echoid-s12948" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12949" xml:space="preserve">In Prop. </s>
            <s xml:id="echoid-s12950" xml:space="preserve">17. </s>
            <s xml:id="echoid-s12951" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s12952" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12953" xml:space="preserve">hæc pariter ſupplenda ſunt. </s>
            <s xml:id="echoid-s12954" xml:space="preserve">In ſec.
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            </s>
            <s xml:id="echoid-s12955" xml:space="preserve">A. </s>
            <s xml:id="echoid-s12956" xml:space="preserve">elicitur ex 3. </s>
            <s xml:id="echoid-s12957" xml:space="preserve">pariter lib. </s>
            <s xml:id="echoid-s12958" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12959" xml:space="preserve">ſolidum, HZ {00/ }, æquari ſolido, ABP
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            C, &</s>
            <s xml:id="echoid-s12960" xml:space="preserve">, ΣΓ2, ſolido, VΠ&</s>
            <s xml:id="echoid-s12961" xml:space="preserve">Ω, cum verò hæc ſolida ſint figuræ æqua-
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            liter analogæ vt eorum conditiones expendenti patebit, ideò quod
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            ibi ex 3. </s>
            <s xml:id="echoid-s12962" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s12963" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12964" xml:space="preserve">hic ex prima huius deducemus. </s>
            <s xml:id="echoid-s12965" xml:space="preserve">In ſec. </s>
            <s xml:id="echoid-s12966" xml:space="preserve">B. </s>
            <s xml:id="echoid-s12967" xml:space="preserve"/>
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