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

Table of contents

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[221.] COROLLARIVM II.
Page: 167 (147)
[222.] LEMMA.
Page: 168 (148)
[223.] THE OREMA XX. PROPOS. XX.
Page: 168 (148)
[224.] COROLLARIVM.
Page: 169 (149)
[225.] THE OREMA XXI. PROPOS. XXI.
Page: 169 (149)
[226.] COROLLARIVM.
Page: 170 (150)
[227.] THE OREMA XXII. PROPOS. XXII.
Page: 170 (150)
[228.] A. COROLLARII SECTIO I.
Page: 174 (154)
[229.] B. SECTIO II.
Page: 174 (154)
[230.] C. SECTIO III.
Page: 174 (154)
[231.] D. SECTIO IV.
Page: 174 (154)
[232.] E. SECTIO V.
Page: 175 (155)
[233.] F. SECTIO VI.
Page: 175 (155)
[234.] THEOR EMA XXIII. PROPOS. XXIII.
Page: 175 (155)
[235.] A. COROLLARII SECTIO I.
Page: 176 (156)
[236.] B. SECTIO II.
Page: 177 (157)
[237.] C. SECTIO III.
Page: 177 (157)
[238.] D. SECTIO IV.
Page: 177 (157)
[239.] E. SECTIO V.
Page: 177 (157)
[240.] F. SECTIO VI.
Page: 177 (157)
[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
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            quoties, BD, ſecta eſſe ſupponitur, exceptis tamen extremis, vt ex.
              <lb/>
            </s>
            <s xml:id="echoid-s3688" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ipſa, CI, in qua parte, CI, quæin recta, CI, feparari debuiſ-
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            ſent per lineas, AEC, AFI, in puncta, C, I, partibus, BE, FD,
              <lb/>
            reſpondentia degenerauerunt. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Dico quæcunque demonſtrantur in
              <lb/>
            linea, BD, circa quadrata, vel rectangula, illi, vel illius partibus ap-
              <lb/>
            plicata, verificari de omnibus quadratis totius figurę, BADC, ſiue
              <lb/>
            partium eiuſdem figuræ per dictas lineas conſtitutarum, ſiue de re-
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            ctangulis ſub eiuſdem partibus. </s>
            <s xml:id="echoid-s3691" xml:space="preserve">Vtex gr. </s>
            <s xml:id="echoid-s3692" xml:space="preserve">quia in 3. </s>
            <s xml:id="echoid-s3693" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">Vide D.
                <lb/>
              Defin. 8.
                <lb/>
              huius.</note>
            Elem. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">oſtenditur rectangulum ſub, BD, DF, æquari rectangulo
              <lb/>
            ſub, BFD, cum quadrato, FD, ſic dico verum eſſe rectangula ſub
              <lb/>
              <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a" number="101">
                <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0176-01"/>
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            figura, ABCD, & </s>
            <s xml:id="echoid-s3698" xml:space="preserve">figura, ADI, æquari re-
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            ctangulis ſub figuris, ABIF, ADIF, cum om-
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            nibus quadratis figuræ, ADIF, ſi enim aliam
              <lb/>
            vtcunque duxerimus regulæ, BD, parallelam,
              <lb/>
            vt, HO, ſecantem lineas, AC, in, M, &</s>
            <s xml:id="echoid-s3699" xml:space="preserve">, A
              <lb/>
            I, in, N, verum eſſe comperiemus rectangulum,
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            HON, æquari rectangulo, HNO, cum qua-
              <lb/>
            drato, NO, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">idem in cęteris regulę, BD, pa-
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            rallelis in figura, ABCD, ductis reperiemus,
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            ergo verum erit rectangula illa ſimul collecta, ideſt rectangula ſub fi-
              <lb/>
              <note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            gura, ABID, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">figura, ADI, æquari rectangulis ſub figuris, AB
              <lb/>
            I, ADI, cum omnibus quadratis, ADI, quod 3. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">lib.
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            </s>
            <s xml:id="echoid-s3705" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3706" xml:space="preserve">reſpondet.</s>
            <s xml:id="echoid-s3707" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3708" xml:space="preserve">Similiter ſi ſupponamus, BF, bifariam ſecari in, E, cui adiunga-
              <lb/>
            tur, FD, ſuppoſuerimus etiam lineam, AC, bifariam ſecare quam-
              <lb/>
            libet omnium linearum figuræ, ABI, regula, BD, ſupradictarum,
              <lb/>
            quarum ſingulis aditur, quę in directum manetin figura, ADI, ve-
              <lb/>
            luti Propoſ. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">oſtenditur rectangulum, BDF, cum quadrato, FE,
              <lb/>
            æquari quadrato, ED, ita hic ad modum ſuperioris oſtendemus re-
              <lb/>
            ctangula ſub figura, ABID, &</s>
            <s xml:id="echoid-s3711" xml:space="preserve">, ADI, cum omnibus quadratis fi-
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            guræ, ACI, æquari omnibus quadratis figuræ, ACD, quod re-
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            ſpondet Prop. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Conſimiliter reliqua demonſtrabimus,
              <lb/>
            vnde iuxta I. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Secundi Elem. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">colligemus.</s>
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          <head xml:id="echoid-head250" xml:space="preserve">A. COROLLARII SECTIO I.</head>
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            <s xml:id="echoid-s3719" xml:space="preserve">_R_Ectangula ſub figura indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ſub diuiſa, ACD, per
              <lb/>
            lineam, AI, æquari rectangulis ſub indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">ſub
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            partibus diuiſæ, quæ ſunt, ACI, AID.</s>
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