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

Table of contents

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[121.] THEOREMA XXX. PROPOS. XXXIII.
Page: 95 (75)
[122.] THEOREMA XXXI. PROPOS. XXXIV.
Page: 96 (76)
[123.] COROLLARIVM.
Page: 97 (77)
[124.] THEOREMA XXXII. PROPOS. XXXV.
Page: 97 (77)
[125.] COROLLARIVM.
Page: 98 (78)
[126.] THEOREMA XXXIII. PROPOS. XXXVI.
Page: 98 (78)
[127.] THEOREMA XXXIV. PROPOS. XXXVII.
Page: 99 (79)
[128.] COROLLARIVM.
Page: 101 (81)
[129.] THEOREMA XXXV. PROPOS. XXXVIII.
Page: 101 (81)
[130.] THEOREMA XXXVI. PROPOS. XXXIX.
Page: 103 (83)
[131.] THEOREMA XXXVII. PROPOS. XL.
Page: 103 (83)
[132.] SCHOLIVM.
Page: 104 (84)
[133.] THEOREMA XXXVIII. PROPOS. XLI.
Page: 105 (85)
[134.] THEOREMA XXXIX PROPOS. XLII.
Page: 105 (85)
[135.] THEOREMA XL. PROPOS. XLIII.
Page: 105 (85)
[136.] THEOREMA XLI. PROPOS. XLIV.
Page: 106 (86)
[137.] THEOREMA XLII. PROPOS. XLV.
Page: 107 (87)
[138.] THEOREMA XLIII. PROPOS. XLVI.
Page: 107 (87)
[139.] THEOREMA XLIV. PROPOS. XLVII.
Page: 108 (88)
[140.] COROLLARIVM.
Page: 109 (89)
[141.] SCHOLIVM.
Page: 109 (89)
[142.] LEMMA.
Page: 110 (90)
[143.] COROLLARIVM.
Page: 112 (92)
[144.] THEOREMA XLV. PROPOS. XLVIII.
Page: 112 (92)
[145.] COROLLARIVM.
Page: 113 (93)
[146.] THEOREMA XLVI. PROPOS. XLIX.
Page: 114 (94)
[147.] THEOREMA XLVII. PROPOS. L:
Page: 115 (95)
[148.] COROLLARIVM I.
Page: 117 (97)
[149.] COROLLARIVM II.
Page: 117 (97)
[150.] SCHOLIVM.
Page: 118 (98)
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              <pb o="161" file="0181" n="181" rhead="LIBER II."/>
            CEG, veltrianguli, CAE, ex quo patet tripla etiam eſſe rectangulo-
              <lb/>
            rum bis ſub triangulis, AEC, CEG, (ſunt enim omnia quadrata, AG,
              <lb/>
            æqualia omnibus quadratis triangulorum, AEC, CEG, & </s>
            <s xml:id="echoid-s3808" xml:space="preserve">rectangulis
              <lb/>
              <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">_D. Corol._
                <lb/>
              _23. huius._</note>
            bis ſub eiſdem triangulis) ita apparebit quadrata maximarum abſciſſa-
              <lb/>
            rum, C G, tripla eſſe quadratorum omnium abſciſſarum, bel quadrato-
              <lb/>
            rum reſiduarum omnium abſciſſarum, CG, & </s>
            <s xml:id="echoid-s3809" xml:space="preserve">tripla etiam eſſe rectan-
              <lb/>
            gulorum fub dictis omnibus abſciſſis, reſiduiſque bis ſumptis, ſexcupla
              <lb/>
            berò eorundem rectangulorum ſemel ſumptorum, ſunt autem maximæ
              <lb/>
            abſciſſarum, abſciſſæ, & </s>
            <s xml:id="echoid-s3810" xml:space="preserve">reſiduærecti tranſitus ſi angulus, EGC, ſitre-
              <lb/>
              <note position="right" xlink:label="note-0181-02" xlink:href="note-0181-02a" xml:space="preserve">_Ex diff._
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              _huius._</note>
            ctus, vel eiuſdem obliquitranſitus, ſi ille non ſit angulus rectus.</s>
            <s xml:id="echoid-s3811" xml:space="preserve"/>
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        <div xml:id="echoid-div406" type="section" level="1" n="248">
          <head xml:id="echoid-head263" xml:space="preserve">THEOREMA XXV. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s3812" xml:space="preserve">SI in duobus parallelogrammis ſumptis duobus lateribus
              <lb/>
            pro baſibus, & </s>
            <s xml:id="echoid-s3813" xml:space="preserve">regulis, ipſa parallelogramma fuerint in
              <lb/>
            eadem altitudine ſumpta reſpectu dictarum baſium; </s>
            <s xml:id="echoid-s3814" xml:space="preserve">in ei-
              <lb/>
            ſdem autem baſibus, & </s>
            <s xml:id="echoid-s3815" xml:space="preserve">altitudine fuerint aliæ duæ planæ fi-
              <lb/>
            guræ ita ſe habentes, vt ſi ducatur vtcunque parallela dictis
              <lb/>
            baſibus (quæ in directum ſint conſtitutæ) recta linea, eiu-
              <lb/>
            ſdem portiones dictis parallelogrammis, & </s>
            <s xml:id="echoid-s3816" xml:space="preserve">figuris interce-
              <lb/>
            ptæ, vel abeiſdem deſcriptę planæ figuræ ſint proportiona-
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            les, homologis exiſtentibus, quæ ſunt in parallelogrammis,
              <lb/>
            & </s>
            <s xml:id="echoid-s3817" xml:space="preserve">pariter quę ſunt in figuris, in ijſdem baſibus, & </s>
            <s xml:id="echoid-s3818" xml:space="preserve">altitudine
              <lb/>
            cum illis conſtitutis, dictorum parallelogrammorum, ac fi-
              <lb/>
            gurarum omnes lineæ, ſi lineæ, vel omnes figurę planę ſimi-
              <lb/>
            les, ſi iſtæ comparentur (fimiles in quam exiſtentibus, quæ
              <lb/>
            ſunt in vnaquaque figura) erunt proportionales.</s>
            <s xml:id="echoid-s3819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3820" xml:space="preserve">Sint parallelogramma, AE,
              <lb/>
              <figure xlink:label="fig-0181-01" xlink:href="fig-0181-01a" number="104">
                <image file="0181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0181-01"/>
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            ED, in baſibus, CE, EF, in
              <lb/>
            directum iacentibus, & </s>
            <s xml:id="echoid-s3821" xml:space="preserve">in eadem
              <lb/>
            altitudine reſpectu dictarum ba-
              <lb/>
            ſium conſtituta, AE, ED, ſit
              <lb/>
            autem regula, CE, vel, EF, & </s>
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            in eiuſdem tanquam in baſibus,
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            & </s>
            <s xml:id="echoid-s3823" xml:space="preserve">eadem altitudine cum paral.
              <lb/>
            </s>
            <s xml:id="echoid-s3824" xml:space="preserve">lelogrammis, AE, ED, ſint fi-
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            guræ, BCE, BEF, eiuſmodi, vt ſi duxerimus vtcunqueipſi, CF,
              <lb/>
            parallelam, vt, MQ, cuius portiones interceptę </s>
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