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

Table of contents

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[191.] COROLLARIVM.
Page: 144 (124)
[192.] THEOREMA XII. PROPOS. XII.
Page: 144 (124)
[193.] COROLLARIVM.
Page: 145 (125)
[194.] THEOREMA XIII. PROPOS. XIII.
Page: 145 (125)
[195.] COROLLARIVM.
Page: 146 (126)
[196.] THEOREMA XIV. PROPOS. XIV.
Page: 146 (126)
[197.] COROLLARIVM.
Page: 147 (127)
[198.] THEOREMA XV. PROPOS. XV.
Page: 147 (127)
[199.] A. DEMONSTRATIONIS SECTIO I.
Page: 148 (128)
[200.] B. SECTIO SECVNDA.
Page: 149 (129)
[201.] C. SECTIO III.
Page: 149 (129)
[202.] D. SECTIO IV.
Page: 150 (130)
[203.] E. SECTIO V. ET VLTIMA.
Page: 150 (130)
[204.] COROLLARIVM I.
Page: 151 (131)
[205.] COROLLARIVM II.
Page: 151 (131)
[206.] THEOREMA XVI. PROPOS. XVI.
Page: 151 (131)
[207.] SCHOLIV M.
Page: 152 (132)
[208.] THEOREMA XVII. PROPOS. XVII.
Page: 153 (133)
[209.] A. DEMONSTRATIONIS SECTIO I.
Page: 153 (133)
[210.] B. SECTIO II.
Page: 157 (137)
[211.] D. SECTIO IV.
Page: 160 (140)
[212.] E. SECTIO V.
Page: 161 (141)
[213.] F. SECTIO VI.
Page: 163 (143)
[214.] G. SECTIO VII.
Page: 164 (144)
[215.] H. SECTIO VIII. ET VLTIMA.
Page: 164 (144)
[216.] COROLLARIVM I.
Page: 165 (145)
[217.] COROLLARIVM II.
Page: 165 (145)
[218.] THE OREMA XVIII. PROPOS. XVIII.
Page: 165 (145)
[219.] THE OREMA XIX. PROPOS. XIX.
Page: 166 (146)
[220.] COROLLARIVM I.
Page: 167 (147)
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            trìangulorum in eadem baſi, & </s>
            <s xml:id="echoid-s4176" xml:space="preserve">altitudine cum parallelogrammis conſti-
              <lb/>
            tutorum ſunt omnium quadratorum dictorum parallelogrammorum ſub-
              <lb/>
              <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">24. huius.</note>
            tripla, ſumpto communi latere pro regula, vt probatum eſt.</s>
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        <div xml:id="echoid-div425" type="section" level="1" n="258">
          <head xml:id="echoid-head273" xml:space="preserve">THEOREMA XXX. PROPOS. XXX.</head>
          <p>
            <s xml:id="echoid-s4178" xml:space="preserve">SI intra parallelogrammum agatur à puncto baſis lateri-
              <lb/>
            bus oppoſitis parallela, & </s>
            <s xml:id="echoid-s4179" xml:space="preserve">conſtitutorum hinc parallelo-
              <lb/>
            grammorum vnius ducatur diameter: </s>
            <s xml:id="echoid-s4180" xml:space="preserve">Rectangula ſub factis
              <lb/>
            parallelogrammis ad rectangula ſub trapezio, & </s>
            <s xml:id="echoid-s4181" xml:space="preserve">triangulo in
              <lb/>
            toto parallelogrammo per dictam diametrum conſtitutis, re-
              <lb/>
            gula baſi, habebunt eandem rationem, quam baſis paralle-
              <lb/>
            logrammi, in quo non ducitur diameter ad compoſitam ex,
              <lb/>
            {1/2}, eiuſdem, &</s>
            <s xml:id="echoid-s4182" xml:space="preserve">, {1/6}, baſis alterius: </s>
            <s xml:id="echoid-s4183" xml:space="preserve">Rectangula verò ſub toto
              <lb/>
            parallelogrammo, & </s>
            <s xml:id="echoid-s4184" xml:space="preserve">ſub eo, in quo ducitur diameter, ad re-
              <lb/>
            ctangula ſub dicto trapezio, & </s>
            <s xml:id="echoid-s4185" xml:space="preserve">ſub triangulo, qui eſt trape-
              <lb/>
            zijportio, erunt vt baſis totius parallelogrammi ad compoſi-
              <lb/>
            tam ex, {1/2}, baſis parallelogrammi, in quo non ducitur diame-
              <lb/>
            ter, & </s>
            <s xml:id="echoid-s4186" xml:space="preserve">ex, {1/3}, baſis alterius.</s>
            <s xml:id="echoid-s4187" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s4188" xml:space="preserve">Sit ergo parallelogrammum, AF, in baſi, DF, quæ ſit regula,
              <lb/>
            intra quam ſumptum ſit punctum, E, & </s>
            <s xml:id="echoid-s4189" xml:space="preserve">per, E, ipſis, AD, CF,
              <lb/>
            acta parallela, BE, ducatur autem in alterutro parallelogrammo-
              <lb/>
            rum, AE, EC, vtin, EC, diameter, EC. </s>
            <s xml:id="echoid-s4190" xml:space="preserve">Dico ergo rectangula
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                <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0191-01"/>
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            ſub, AE, EC, ad rectangula ſub tra-
              <lb/>
            pezio, ADEC, & </s>
            <s xml:id="echoid-s4191" xml:space="preserve">triangulo, CEF,
              <lb/>
            eſſe vt, DE, ad compoſitam ex, {1/2}, D
              <lb/>
            E, &</s>
            <s xml:id="echoid-s4192" xml:space="preserve">, {1/6}, EF. </s>
            <s xml:id="echoid-s4193" xml:space="preserve">Rectangula enim ſub
              <lb/>
              <note position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">Per A.
                <lb/>
              Coroll.
                <lb/>
              @3. huius.</note>
            trapezio, ADEC, diuiſo per lineam,
              <lb/>
            BE, & </s>
            <s xml:id="echoid-s4194" xml:space="preserve">ſub triangulo, CEF, indiui-
              <lb/>
            ſo, æquantur rectangulis ſub, AE, & </s>
            <s xml:id="echoid-s4195" xml:space="preserve">
              <lb/>
            triangulo, CEF, vel triangulo, BE
              <lb/>
            C, & </s>
            <s xml:id="echoid-s4196" xml:space="preserve">rectangulis ſub triangulo, BE
              <lb/>
            C, & </s>
            <s xml:id="echoid-s4197" xml:space="preserve">triangulo, CEF, nunc patet
              <lb/>
            rectangula ſub, AE, EC, ad rectan-
              <lb/>
              <note position="right" xlink:label="note-0191-03" xlink:href="note-0191-03a" xml:space="preserve">Corol. 1.
                <lb/>
              26. huius.</note>
            gula ſub, AE, & </s>
            <s xml:id="echoid-s4198" xml:space="preserve">triangulo, BCE, eſſe vt, BF, ad triangulum, ſt
              <lb/>
            EC, .</s>
            <s xml:id="echoid-s4199" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4200" xml:space="preserve">dupla .</s>
            <s xml:id="echoid-s4201" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4202" xml:space="preserve">vt, DE, ad, {1/2}, DE, quod ſerua.</s>
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          <p>
            <s xml:id="echoid-s4204" xml:space="preserve">Item rectangula ſub, AE, EC, ad omnia quadrata, BF, ſunt vt
              <lb/>
            rectangulum, DEF, ad quadratum, EF, .</s>
            <s xml:id="echoid-s4205" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4206" xml:space="preserve">vt, DE, ad, EF, om-
              <lb/>
              <note position="right" xlink:label="note-0191-04" xlink:href="note-0191-04a" xml:space="preserve">14. huius.</note>
            nia verò quadrata, BF, ſunt ſexcupla rectangulorum ſub </s>
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