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

Table of handwritten notes

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            in, X, ducatur in plano, NOP, recta, QR, à puncto, Q, perpen-
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            dicularis ipſi, OP, & </s>
            <s xml:id="echoid-s1573" xml:space="preserve">iungatur, HR, triangulumque, HRQ, ſe-
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            cet duo triangula, VST, KST, in rectis, YX, ZX. </s>
            <s xml:id="echoid-s1574" xml:space="preserve">Quia ergo
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              <note position="left" xlink:label="note-0080-01" xlink:href="note-0080-01a" xml:space="preserve">16. Vnd.
                <lb/>
              Elem.</note>
            triangula, VST, NOP, ſunt parallela, erunt etiam ipſę, ZX, R
              <lb/>
            Q, parallelæ, ſed &</s>
            <s xml:id="echoid-s1575" xml:space="preserve">, ST, OP, ſunt parallelę, ergo anguli, ZXS,
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            RQO, erunt æquales, rectus ergo eſt etiam ipſe, ZXS, ſed etiam,
              <lb/>
              <note position="left" xlink:label="note-0080-02" xlink:href="note-0080-02a" xml:space="preserve">10.Vnd.
                <lb/>
              Elem.</note>
            SXH, rectus eſt, ergo, SX, eſt duabus, ZX, XH, perpendicula-
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            ris, & </s>
            <s xml:id="echoid-s1576" xml:space="preserve">ſubinde plano per ipſas tranſeunti, & </s>
            <s xml:id="echoid-s1577" xml:space="preserve">conſequenter, SXY, eſt
              <lb/>
              <note position="left" xlink:label="note-0080-03" xlink:href="note-0080-03a" xml:space="preserve">4.Vndec.
                <lb/>
              Elem.</note>
            rectus, vnde, HXZ, erit inclinatio planorum, HST, KST, &</s>
            <s xml:id="echoid-s1578" xml:space="preserve">, H
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            XY, inclinatio planorum, HST, SVT, hæc autem eſt æqualis in-
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            clinationi planorum, HOP, NOP, ex hypoteſi, ideſt angulo, H
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              <figure xlink:label="fig-0080-01" xlink:href="fig-0080-01a" number="42">
                <image file="0080-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0080-01"/>
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            QR, ideſt angulo, H
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            XZ, ergo angulus, H
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            XY, qui eſt totum, eſt
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            ęqualis augulo, HXZ,
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            eiuſdem parti, quod eſt
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            abſurdũ, ergo abſurdum
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            etiam eſt dicere trian-
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            gulum, VST, non æ-
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            quidiſtare ipſi, NOP,
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            æquidiſtat ergo, & </s>
            <s xml:id="echoid-s1579" xml:space="preserve">ip-
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            ſæ, VS, VT, ſunte-
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              <note position="left" xlink:label="note-0080-04" xlink:href="note-0080-04a" xml:space="preserve">16. Vnd.
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              Elem.</note>
            tiam parallelæ ipſis, N
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            O, NP, & </s>
            <s xml:id="echoid-s1580" xml:space="preserve">triangula,
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            VHS, ipſi, NHO, V
              <lb/>
            HT, ipſi, NHP, nec-
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            non, VST, ipſi, NOP, ſunt ſimilia, ergo pyramides, HVST,
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            HNOP, ſunt ſimiles, eſt autem pyramis, HVST, ſimilis, immo
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            & </s>
            <s xml:id="echoid-s1581" xml:space="preserve">ęqualis, ipſi, ACDB, ergo pyramides, ACDB, HNOP, in-
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            ter ſe ſimiles erunt, & </s>
            <s xml:id="echoid-s1582" xml:space="preserve">anguli, ACB, HVT, ACD, HVS, inter
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            ſe æquales, ergo, AC, HV, rectę lineę ſtantes in ſublimi, & </s>
            <s xml:id="echoid-s1583" xml:space="preserve">cum
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            ipſis, CD, CB, VS, VT, angulos æquales continentes (à quibus
              <lb/>
            etiam contenti anguli, DCB, SVT, ſunt ęquales) erunt ad plana
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              <note position="left" xlink:label="note-0080-05" xlink:href="note-0080-05a" xml:space="preserve">35. Vnd.
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              Elem.</note>
            triangulorum, CDB, NOP, æqualiter inclinata, & </s>
            <s xml:id="echoid-s1584" xml:space="preserve">ſunt ipſæ py-
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            ramides, ACDB, HNOP, ſimiles, vt propoſitum fuit demon-
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            ſtrare.</s>
            <s xml:id="echoid-s1585" xml:space="preserve"/>
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            <s xml:id="echoid-s1586" xml:space="preserve">Si verò rectæ lineæ angulos æquales cum ipſis, DA, AB, OH,
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            HP, continentes eſſent ipſæ, AT, Η Λ, quarum, Λ Η, eſſet paral-
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            lela plano, VST, probaremus etiam, TA, eſſe parallelam plano,
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            CDB, alioquin ſi cum ipſo producta concurreret, etiam, Λ Η, ex
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            ſupra oſtenſis, producta concurreret cum plano trianguli, VST. </s>
            <s xml:id="echoid-s1587" xml:space="preserve">Vel
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            præintellectis duabus iam datis, AC, HN, & </s>
            <s xml:id="echoid-s1588" xml:space="preserve">ſuppoſita </s>
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