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

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            <s xml:id="echoid-s6432" xml:space="preserve">
              <pb o="257" file="0277" n="277" rhead="LIBER III."/>
            ibi oſtenſum eſt, ſumpta regula, DP, omnia quadrata portionis, D
              <lb/>
            EP, ad omnia quadrata parallelogrammi, FP, eſſe vt compoſita ex
              <lb/>
            ſexta parte, EB, & </s>
            <s xml:id="echoid-s6433" xml:space="preserve">dimidia, BR, ad ipſam, BR, oſtenſum etiam
              <lb/>
            eſt ſolidum ſimilare genitum ex portione, DEP, ad ſolidum ſibi ſi-
              <lb/>
            milare genitum ex parallelogrammo, FP, eſſe vt compoſita ex ſex-
              <lb/>
            ta parte, EB, & </s>
            <s xml:id="echoid-s6434" xml:space="preserve">dimidia, BR, adipſam, BR. </s>
            <s xml:id="echoid-s6435" xml:space="preserve">Cum verò oſten-
              <lb/>
            ſum eſt omnia quadrata portionis, EDP, ad omnia quadrata trian-
              <lb/>
            guli, DEP, eſſe vt compoſita ex dimidia totius, ER, & </s>
            <s xml:id="echoid-s6436" xml:space="preserve">ipſa, BR,
              <lb/>
            ad eandem, BR; </s>
            <s xml:id="echoid-s6437" xml:space="preserve">pariter oſtenſum eſt ſolidum ſimilare genitum ex
              <lb/>
            portione, EDP, ad ſibi ſimilare genitum ex triangulo, DEP, iux-
              <lb/>
            ta eaſdem regulas eſſe, vt compoſita ex dimidia totius, ER, & </s>
            <s xml:id="echoid-s6438" xml:space="preserve">ipſa,
              <lb/>
            BR, ad eandem, BR.</s>
            <s xml:id="echoid-s6439" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6440" xml:space="preserve">Cum verò in Corollario eiuſdem Theorem. </s>
            <s xml:id="echoid-s6441" xml:space="preserve">collectum eſt, omnia
              <lb/>
            quadrata parallelogrammi, FP, eſſe ſexquialtera omnium quadra-
              <lb/>
            torum portionis, DEP, (ſi, DP, per centrum, A, tranſeat) hæc
              <lb/>
            verò eſſe dupla omnium quadratorum trianguli, DEP; </s>
            <s xml:id="echoid-s6442" xml:space="preserve">patet, quod
              <lb/>
            etiam ſolidum ſimilare genitum ex parallelogrammo, FP, ſexquial-
              <lb/>
            terum erit ſolidi ſibi ſimilaris geniti ex portione, DEP, iuxta ean-
              <lb/>
            dem regulam, DP, hoc verò erit duplum ſolidi ſibi ſimilaris geniti
              <lb/>
            ex triangulo, DEP, iuxta eandem regulam, DP.</s>
            <s xml:id="echoid-s6443" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div616" type="section" level="1" n="358">
          <head xml:id="echoid-head375" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6444" xml:space="preserve">_Q_Voniam verò ſolida ad inuicem ſimilaria genita ex duabus figuris
              <lb/>
              <note position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">_A. Def. @_
                <lb/>
              _lib. 1._</note>
            planis, iuxta datas regulas, totuplicia ſunt, quotuplices ſunt fi-
              <lb/>
            guræ ſimiles, quæ dicuntur, omnes figuræ ſimiles duarum genitri-
              <lb/>
            cium figurarum, cum eiſdem regulis aſſu
              <unsure/>
            mpta, iuxta quas dicta ſolida
              <lb/>
            ſimilaria genita dicuntur, figurarum autem variationes nullo dato nu-
              <lb/>
            mero clauduntur, ideò nec horum ſimilarium ſolidorum variationes vl-
              <lb/>
            lo dato coarctantur numero, vnde euidentiſſimè apparet banc demon.
              <lb/>
            </s>
            <s xml:id="echoid-s6445" xml:space="preserve">ſtrandi methodum, ipſamque demonſtrationem, infinitè (vt ita dicam)
              <lb/>
            locupletem eſſe; </s>
            <s xml:id="echoid-s6446" xml:space="preserve">vt igitur ad parttcularia ſolida ſimi aria deſcendamus,
              <lb/>
            expendendæ ſunt ipſæ figuræ, quæ dicuntur (omnes figuræ ſimiles, &</s>
            <s xml:id="echoid-s6447" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s6448" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">_34. Lib. 2._</note>
            patet igitur ex alibi à me o
              <unsure/>
            ſtenſis, ſi figuræ aſſumptæ ſint omnes figuræ ſi-
              <lb/>
            miles parall@logrammi, quod tunc i
              <unsure/>
            ſtæ erunt omnia plana cylindrici; </s>
            <s xml:id="echoid-s6449" xml:space="preserve">ſi
              <lb/>
            verò illæ ſint omnes figuræ ſimiles trianguli (intellige in parallelogram-
              <lb/>
            mo, & </s>
            <s xml:id="echoid-s6450" xml:space="preserve">triangulo vnum laterum pro regula) illæ erunt omnia plana Co-
              <lb/>
              <note position="right" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">_34. Lib. 2._</note>
            nici; </s>
            <s xml:id="echoid-s6451" xml:space="preserve">& </s>
            <s xml:id="echoid-s6452" xml:space="preserve">ſi parallelogrammum ſit rectangulum, & </s>
            <s xml:id="echoid-s6453" xml:space="preserve">figuræ eidem erectæ
              <lb/>
            erit cylindricus rectus, ſcalenus autem niſi ſit rectangulum, vel figuræ
              <lb/>
            non eidem erecta; </s>
            <s xml:id="echoid-s6454" xml:space="preserve">ex quo babes, qualeſcunque figuras intellexeris eſſe
              <lb/>
            eas, quæ dicuntur omnes figuræ ſimiles parallelogrammi, FP, regula,
              <lb/>
            DP, veltrianguli, EDP, regula eadem, ſolidum genitum ex </s>
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