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

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          <p>
            <s xml:id="echoid-s13892" xml:space="preserve">
              <pb o="535" file="0555" n="555" rhead="LI R VII."/>
            ſimiliter in Cor. </s>
            <s xml:id="echoid-s13893" xml:space="preserve">colligemus quadratum ſolidum, AFVT, ad quad
              <lb/>
            ſolidum, AGVS, eſſe vt quadratum, FT, ad quadratum, GS, ſubau-
              <lb/>
            di tamen in illius ſchemate ſecundas diametros, FT, GS, eſſe in eadẽ
              <lb/>
            recta linea. </s>
            <s xml:id="echoid-s13894" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13895" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13896" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13897" xml:space="preserve">demonſtrantur, vt ibi, Prop. </s>
            <s xml:id="echoid-s13898" xml:space="preserve">verò
              <lb/>
            12. </s>
            <s xml:id="echoid-s13899" xml:space="preserve">ſimiliter, ſolita tantum nominum mutatione facta. </s>
            <s xml:id="echoid-s13900" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s13901" xml:space="preserve">13.
              <lb/>
            </s>
            <s xml:id="echoid-s13902" xml:space="preserve">oſtendetur quoque mutatis nominibus, & </s>
            <s xml:id="echoid-s13903" xml:space="preserve">c in qua aduerte pag. </s>
            <s xml:id="echoid-s13904" xml:space="preserve">27. </s>
            <s xml:id="echoid-s13905" xml:space="preserve">
              <lb/>
            lin. </s>
            <s xml:id="echoid-s13906" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13907" xml:space="preserve">ſuperfluè dici in, EF, quadratum, EI, detractum à rectan-
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            gulo ſub, IE, EF, relinquere rectangulum ſub, EI, IF, vt concluda-
              <lb/>
            tur detractis omnibus quadratis ſemiportionis, OCD, à rectangu-
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            lis ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s13908" xml:space="preserve">ſemiportione, OCD, relinqui re-
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            ctangula ſub, OCD, DCV, hoc enim conſtat ex C. </s>
            <s xml:id="echoid-s13909" xml:space="preserve">23. </s>
            <s xml:id="echoid-s13910" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13911" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13912" xml:space="preserve">vt ci-
              <lb/>
            tatur in margine, illud tamen ad maiorem declarationem appoſi-
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            tum erat. </s>
            <s xml:id="echoid-s13913" xml:space="preserve">Corollarium eiuſdem pariter declarabitur mutatis, &</s>
            <s xml:id="echoid-s13914" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13915" xml:space="preserve">
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s13916" xml:space="preserve">14. </s>
            <s xml:id="echoid-s13917" xml:space="preserve">ſimiliter probabitur, cum Cor. </s>
            <s xml:id="echoid-s13918" xml:space="preserve">mutatis nominibus, &</s>
            <s xml:id="echoid-s13919" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13920" xml:space="preserve">
              <lb/>
            Sic etiam Prop. </s>
            <s xml:id="echoid-s13921" xml:space="preserve">15. </s>
            <s xml:id="echoid-s13922" xml:space="preserve">16. </s>
            <s xml:id="echoid-s13923" xml:space="preserve">17. </s>
            <s xml:id="echoid-s13924" xml:space="preserve">18. </s>
            <s xml:id="echoid-s13925" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13926" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13927" xml:space="preserve">21. </s>
            <s xml:id="echoid-s13928" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13929" xml:space="preserve">in qua patebit
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            rectangula ſub, ASB, AHTFB, æquari rectangulis ſub triangulis,
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            ABD, AVD, cum ſint ſolida æqualiter analoga, & </s>
            <s xml:id="echoid-s13930" xml:space="preserve">hoc in figura
              <lb/>
            circuli, in figura autem ellipſis dicta ſolida oſtendentur eſſe propor-
              <lb/>
            tion aliter analoga, ac inter ſe vt coniugatarum diametrorum qua-
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            drata. </s>
            <s xml:id="echoid-s13931" xml:space="preserve">Sic etiam Prop. </s>
            <s xml:id="echoid-s13932" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13933" xml:space="preserve">23. </s>
            <s xml:id="echoid-s13934" xml:space="preserve">24. </s>
            <s xml:id="echoid-s13935" xml:space="preserve">25. </s>
            <s xml:id="echoid-s13936" xml:space="preserve">26. </s>
            <s xml:id="echoid-s13937" xml:space="preserve">in qua ſchema ante-
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            cedentis reponendum eſt. </s>
            <s xml:id="echoid-s13938" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s13939" xml:space="preserve">27. </s>
            <s xml:id="echoid-s13940" xml:space="preserve">28. </s>
            <s xml:id="echoid-s13941" xml:space="preserve">29. </s>
            <s xml:id="echoid-s13942" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13943" xml:space="preserve">31. </s>
            <s xml:id="echoid-s13944" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13945" xml:space="preserve">
              <lb/>
            Prop. </s>
            <s xml:id="echoid-s13946" xml:space="preserve">32. </s>
            <s xml:id="echoid-s13947" xml:space="preserve">cum Cor. </s>
            <s xml:id="echoid-s13948" xml:space="preserve">ac tandem Prop. </s>
            <s xml:id="echoid-s13949" xml:space="preserve">33. </s>
            <s xml:id="echoid-s13950" xml:space="preserve">pariter cum Cor.</s>
            <s xml:id="echoid-s13951" xml:space="preserve"/>
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        <div xml:id="echoid-div1237" type="section" level="1" n="747">
          <head xml:id="echoid-head780" xml:space="preserve">THEOREMA XXII. PROPOS. XXII.</head>
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            <s xml:id="echoid-s13952" xml:space="preserve">EXpoſitis duabus quibuſcumq; </s>
            <s xml:id="echoid-s13953" xml:space="preserve">figuris planis, & </s>
            <s xml:id="echoid-s13954" xml:space="preserve">in ea-
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            rum vnaquaq; </s>
            <s xml:id="echoid-s13955" xml:space="preserve">ſumpta vtcumq; </s>
            <s xml:id="echoid-s13956" xml:space="preserve">regula, vt quadrata
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            ſolida earundem figurarum iuxta dictas regulas, ita erunt
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            ſolida quæcumq; </s>
            <s xml:id="echoid-s13957" xml:space="preserve">ad inuicem ſimilaria ex eiſdem genita fi-
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            guris, iuxta eaſdem regulas.</s>
            <s xml:id="echoid-s13958" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13959" xml:space="preserve">Sint duæ quæcumq; </s>
            <s xml:id="echoid-s13960" xml:space="preserve">figuræ planæ, ABC, DEF, in qnibus duæ
              <lb/>
            vtcumq; </s>
            <s xml:id="echoid-s13961" xml:space="preserve">ſint ſumptæ, BC, EF, rectælineæ. </s>
            <s xml:id="echoid-s13962" xml:space="preserve">Dico igitur vt qua-
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            dratum ſolidum figuræ, ABC, ad quadratum ſolidum figuræ, DE
              <lb/>
            F, regulis iam dictis ita eſſe quodcunq; </s>
            <s xml:id="echoid-s13963" xml:space="preserve">ſolidum ſimilare genitum
              <lb/>
            ex, ABC, ad ſibi ſimilare genitum ex, DEF, iuxta eaſdem regulas.
              <lb/>
            </s>
            <s xml:id="echoid-s13964" xml:space="preserve">Ducatur in altera figurarum, vt in, DEF, vtcumq; </s>
            <s xml:id="echoid-s13965" xml:space="preserve">regulæ, EF, pa-
              <lb/>
              <note position="right" xlink:label="note-0555-01" xlink:href="note-0555-01a" xml:space="preserve">15. 1. 2.</note>
            rallela, HM. </s>
            <s xml:id="echoid-s13966" xml:space="preserve">Igitur quadratum, EF, ad quadratum, HM, habet
              <lb/>
            duplicatam rationem eius, quam habet, EF, ad, HM, ſed etiam
              <lb/>
              <note position="right" xlink:label="note-0555-02" xlink:href="note-0555-02a" xml:space="preserve">15. l. 2.</note>
            alia quælibet figura plana deſcripta ab, EF, ad ſibi ſimilem </s>
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