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

Table of handwritten notes

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        <div xml:id="echoid-div169" type="section" level="1" n="112">
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            <s xml:id="echoid-s1633" xml:space="preserve">
              <pb o="63" file="0083" n="83" rhead="LIBER I."/>
            L, ad, RT, vel vt, GΠ, ad, RZ, ſunt enim & </s>
            <s xml:id="echoid-s1634" xml:space="preserve">ipſæ, GL, RT,
              <lb/>
            ſimiliter ad eandem partem ſectę in punctis, Π, Z, nam ſimiliter ſe-
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            cantur ac, FC, PO, in punctis, Λ, Γ, ergo etiam reliqua, I Π, ad,
              <lb/>
            QZ, erit vt tota, GΠ, ad totam, RZ, ideſt vt, FC, ad, PO. </s>
            <s xml:id="echoid-s1635" xml:space="preserve">Eo-
              <lb/>
            dem modo oſtendemus, ΠH, ad, ZS, eſſe vt, FC, ad, PO, er-
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            go, IΠ, ad, QZ, erit vt, ΠH, ad, ZS, & </s>
            <s xml:id="echoid-s1636" xml:space="preserve">permutando, IΠ, ad,
              <lb/>
            ΠH, erit vt, QZ, ad, ZS, ſunt ergo latera homologa, IH, QS,
              <lb/>
            ſimiliter ad eandem partem ſecta à præfatis planis, quod eodem mo-
              <lb/>
            do de quibuſcumq; </s>
            <s xml:id="echoid-s1637" xml:space="preserve">homologis lateribus, quæ contingat dictis planis
              <lb/>
            ſecari, pariter oſtendemus, hoc verò demonſtrare propoſitum fuit.</s>
            <s xml:id="echoid-s1638" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div171" type="section" level="1" n="113">
          <head xml:id="echoid-head124" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1639" xml:space="preserve">_E_X boc autem Lemmate inſuper habetur nedum latera bomologa ſi-
              <lb/>
            milium ſolidorum, ſed etiam, ſi illa producantur vſq; </s>
            <s xml:id="echoid-s1640" xml:space="preserve">ad oppoſita
              <lb/>
            tangentia plana, eorum reſidua, vel ipſa tota, eſſe vt eorum dictas al-
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            titudines.</s>
            <s xml:id="echoid-s1641" xml:space="preserve"/>
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        <div xml:id="echoid-div172" type="section" level="1" n="114">
          <head xml:id="echoid-head125" xml:space="preserve">THEOREMA XXVI. PROPOS. XXIX.</head>
          <p>
            <s xml:id="echoid-s1642" xml:space="preserve">SI in duobus ſimilibus ſolidis iuxta defin. </s>
            <s xml:id="echoid-s1643" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1644" xml:space="preserve">vndec. </s>
            <s xml:id="echoid-s1645" xml:space="preserve">Elem.
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            </s>
            <s xml:id="echoid-s1646" xml:space="preserve">accipiantur, ac in eorumdem ambitu, duæ quæcumq; </s>
            <s xml:id="echoid-s1647" xml:space="preserve">
              <lb/>
            ſimiles figurę planę tanquam baſes, quibus parallela ducan-
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            tur quæcumq; </s>
            <s xml:id="echoid-s1648" xml:space="preserve">plana eadem ſecantia, necnon corum altitu-
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            dines, reſpectu dictarum baſium aſſumptas, ſimiliter ad ean-
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            dem partem diuidentia. </s>
            <s xml:id="echoid-s1649" xml:space="preserve">Productæ ijſdem in ſolidis figuræ
              <lb/>
            ſimiles erunt iuxta definitionem 10. </s>
            <s xml:id="echoid-s1650" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s1651" xml:space="preserve">omnium ho-
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            mologæ duabus quibuſdam regulis æquidiſtabunt.</s>
            <s xml:id="echoid-s1652" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1653" xml:space="preserve">Sint ſimilia ſolida iuxta defin. </s>
            <s xml:id="echoid-s1654" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">vndec. </s>
            <s xml:id="echoid-s1656" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1657" xml:space="preserve">ipſa, AEFSOGo,
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            Tl & </s>
            <s xml:id="echoid-s1658" xml:space="preserve">p f8s, in eorum autem ambitu capiantur ſimiles quæcumque
              <lb/>
            figurę planę, OGFS, f8 & </s>
            <s xml:id="echoid-s1659" xml:space="preserve">p, quibus parallela ducantur duo quę-
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            cumque plana eadem ſecantia, necnon & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">altitudines reſpectu dicta-
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            rum baſium aſſumptas ſimiliter ad eandem partem diuidentia, ac in
              <lb/>
            ipſis ſolidis figuras, LHMP, YVZd, producentia. </s>
            <s xml:id="echoid-s1661" xml:space="preserve">Dico has eſſe
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            ſimiles figuras planas icxta defin. </s>
            <s xml:id="echoid-s1662" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1663" xml:space="preserve">huius, omniumque ſic produ-
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            ctarum in dictis ſolidis homologas duabus quibuſdam regulis, vtex.
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            </s>
            <s xml:id="echoid-s1664" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1665" xml:space="preserve">ipſis, OS, fp, æquidiſtare. </s>
            <s xml:id="echoid-s1666" xml:space="preserve">Igitur figurarum ambientium dicta
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            ſolida duæ aliæ ſimiles quæcumq; </s>
            <s xml:id="echoid-s1667" xml:space="preserve">capiantur cum baſibus concurren-
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            tes, vt ex. </s>
            <s xml:id="echoid-s1668" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">oOS, sfp, ſimilia triangula, ducantur autem pręfa-
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            tis baſibus oppoſita tangentia plana, AC, TR, ſecantia </s>
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