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

Table of handwritten notes

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        <div xml:id="echoid-div165" type="section" level="1" n="110">
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            <s xml:id="echoid-s1588" xml:space="preserve">
              <pb o="61" file="0081" n="81" rhead="LIBER I."/>
            conſtructione, oſtenderemus, vt ſupra, tria latera, ΓΑ, Λ Η; </s>
            <s xml:id="echoid-s1589" xml:space="preserve">AD,
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            HO; </s>
            <s xml:id="echoid-s1590" xml:space="preserve">AB, HP; </s>
            <s xml:id="echoid-s1591" xml:space="preserve">eſſe ad inuicem ſuperpoſita, vnde ſi, Λ Η, æquidi-
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            ſtat plano, NOP, etiam neceſſe eſſe concluderetur, Λ Η, ſeu, ΓΑ,
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            in ea conſtitutam, æquidiſtare plano, NOP, vel ipſi, VST, ſeu,
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            ΓΑ, ipſi, CDB, quod erat oſtendendum.</s>
            <s xml:id="echoid-s1592" xml:space="preserve"/>
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        <div xml:id="echoid-div167" type="section" level="1" n="111">
          <head xml:id="echoid-head122" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s1593" xml:space="preserve">_E_X boc Lemmate colligitur ſimilium ſolidorum, iuxta Euclidis de-
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            finitionem, latera bomologa quœcunque, vel (duabus in ambitu
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            quibuſcumque figuris ſimilibus aſſumptis) iacere in plano ſimilium di-
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            ctarum figurarum, aut illis œquidiſtare, vel œqualiter eiſdem inclinari;
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            </s>
            <s xml:id="echoid-s1594" xml:space="preserve">Vt in figura Lemmatis 4. </s>
            <s xml:id="echoid-s1595" xml:space="preserve">ex. </s>
            <s xml:id="echoid-s1596" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1597" xml:space="preserve">CD, GL, (aſſumptis ſimilibus figuris,
              <lb/>
            HCD, OGL,) iacent in earum plano, BA, IF, autem vel ambo illi
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            œquidiſtant, vel eiſdem ſunt œqualiter inclinata, namiunctis, AC, A
              <lb/>
              <note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">_Lemma 4._</note>
            H, FG, FO, niſi bœc ſint lateradictorum ſolidorum, fiunt anguli, BA
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            H, IFO, BAC, IFG, œquales, & </s>
            <s xml:id="echoid-s1598" xml:space="preserve">triangula, ACH, FGO, ſimilia,
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            nam pyramides, ABCH, FIGO, ſunt inter ſe ſimiles, ipſa verò trian-
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              <note position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">_Lemma 1._</note>
            gula, ACH, FGO, œquè ad eandem partem inclinantur ipſis, HCD,
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            OGL, cum etiam, ACHD, FGLO, pyramides ſint ſimiles ex eodem
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            Lemmate 4. </s>
            <s xml:id="echoid-s1599" xml:space="preserve">vnde vel, AB, FI, œquidiſtant baſibus, CHD, GOL, vel
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            ſunt eiſdem œqualiter inclinata, idem de cœteris bomologis quibuſcum-
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            que lateribus, quibuslibet ſimilibus figuris in ambitu aſſumptis compa-
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            ratis, pariter intelligendum erit.</s>
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        <div xml:id="echoid-div169" type="section" level="1" n="112">
          <head xml:id="echoid-head123" xml:space="preserve">LEMMA VI.</head>
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            <s xml:id="echoid-s1601" xml:space="preserve">SI in ſimilibus ſolidis iuxta Euclidem ducantur plana duabus qui-
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            buſcumque ſimilibus figuris in eorum ambitu aſſumptis paralle-
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            la, quæ vt eorum baſes accipiantur; </s>
            <s xml:id="echoid-s1602" xml:space="preserve">diuidant autem ducta plana eo-
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            rum altitudines, reſpectu dictarum baſium captas, ſimiliter ad ean-
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            dem partem, quęcumque latera homologa ab eiſdem ſecabuntur, ſi-
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            militer ad eandem partem diuidentur.</s>
            <s xml:id="echoid-s1603" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s1604" xml:space="preserve">Sint in ſimilibus ſolidis iuxta Euclidis definition. </s>
            <s xml:id="echoid-s1605" xml:space="preserve">9. </s>
            <s xml:id="echoid-s1606" xml:space="preserve">Vndec. </s>
            <s xml:id="echoid-s1607" xml:space="preserve">Elem.
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            </s>
            <s xml:id="echoid-s1608" xml:space="preserve">aſſumptę in ambitu duæ ſimiles figurę tanquam baſes, ex. </s>
            <s xml:id="echoid-s1609" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1610" xml:space="preserve">trian-
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            gula ſimilia, ADB, MKN, ſint verò de ambitu etiam deſcripta
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            triangula ſimilia, AHI, MSQ; </s>
            <s xml:id="echoid-s1611" xml:space="preserve">AHD, MSK; </s>
            <s xml:id="echoid-s1612" xml:space="preserve">&</s>
            <s xml:id="echoid-s1613" xml:space="preserve">, IHD, QS
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            K; </s>
            <s xml:id="echoid-s1614" xml:space="preserve">quibus etiam adiungantur latera bomologa, IF, QP, ad verti-
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            ces, F, P, reſpectu dictarum baſium captos, pertingentia, reliquis
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            dimiſſis figuris eorum ambitum complentibus, ne nimia fieret Sche-
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            matis confuſio, ſint autem à verticibus, F, P, demiſſæ altitudines
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            reſpectu baſium, ADB, MKN, ipſę, FC, PO, planis baſium </s>
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