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

Table of contents

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[321.] E. SECTIO V.
Page: 236 (216)
[322.] F. SECTIO VI.
Page: 236 (216)
[323.] THEOREMA XI. PROPOS. XII.
Page: 236 (216)
[324.] THEOREMA XII. PROPOS. XIII.
Page: 237 (217)
[325.] COROLLARIVM.
Page: 239 (219)
[326.] THEOREMA XIII. PROPOS. XIV.
Page: 239 (219)
[327.] COROLLARIVM.
Page: 242 (222)
[328.] THEOREMA XIV. PROPOS. XV.
Page: 242 (222)
[329.] ALITER.
Page: 244 (224)
[330.] THEOREMA XV. PROPOS. XVI.
Page: 244 (224)
[331.] THEOREMA XVI. PROPOS. XVII.
Page: 247 (227)
[332.] COROLLARIVM I.
Page: 248 (228)
[333.] COROLLARIVM II.
Page: 249 (229)
[334.] THEOREMA XVII. PROPOS. XVIII.
Page: 249 (229)
[335.] COROLLARIVM.
Page: 251 (231)
[336.] THEOREMA XVIII. PROPOS. XIX.
Page: 251 (231)
[337.] COROLLARIVM.
Page: 252 (232)
[338.] THEOREMA XIX. PROPOS. XX.
Page: 252 (232)
[339.] COROLLARIVM.
Page: 254 (234)
[340.] THEOREMA XX. PROPOS. XXI.
Page: 254 (234)
[341.] COROLLARIVM.
Page: 256 (236)
[342.] THEOREMA XXI. PROPOS. XXII.
Page: 257 (237)
[343.] THEOREMA XXII. PROPOS. XXIII.
Page: 261 (241)
[344.] THEOREMA XXIII. PROPOS. XXIV.
Page: 262 (242)
[345.] THEOREMA XXIV. PROPOS. XXV.
Page: 264 (244)
[346.] THEOREMA XXV. PROPOS. XXVI.
Page: 265 (245)
[347.] THEOREMA XXVI. PROPOS. XXVII.
Page: 267 (247)
[348.] THEOREMA XXVII. PROPOS. XXVIII.
Page: 268 (248)
[349.] THEOREMA XXVIII. PROPOS. XXIX.
Page: 269 (249)
[350.] THEOREMA XXIX. PROPOS. XXX.
Page: 271 (251)
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          <head xml:id="echoid-head457" xml:space="preserve">SCHOLIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7476" xml:space="preserve">_D_Eſiderari fortè tamen videtur, quod oſtendamus has varietates
              <lb/>
            parabolis contingere poſſe, nec eaſdem eſſe, exempligratia, vt
              <lb/>
            circulos, quibus tantum contingit ſe habere, vt diametrorum quadra-
              <lb/>
            ta, nec alia ijſdem accidit variatio, propterea ſubſequens Theorema,
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            ſubijciemus.</s>
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          <head xml:id="echoid-head458" xml:space="preserve">THEOREMA XIX. PROPOS. XX.</head>
          <p>
            <s xml:id="echoid-s7478" xml:space="preserve">DAto quocunq; </s>
            <s xml:id="echoid-s7479" xml:space="preserve">parallelogrammo, circa eiuſdem duo
              <lb/>
            latera angulum continentia ſemiparabola deſcribi
              <lb/>
            poteſt, cuius alterum eorundem laterum ſit baſis, alterum
              <lb/>
            axis, vel diameter integræ parabolæ, ad quem dicta baſis
              <lb/>
            ordinatim applicatur.</s>
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            <s xml:id="echoid-s7481" xml:space="preserve">Sit parallelogrammum quodcunque, AD, cuius ſumantur vt-
              <lb/>
            cunque duo latera, AC, CD, circa angulum, ACD. </s>
            <s xml:id="echoid-s7482" xml:space="preserve">Dico cir-
              <lb/>
            ca, AC, CD, ſemiparabolam de@cribi poſſe, ita vt alterum ipſo-
              <lb/>
            rum, AC, CD, ſit baſis dictæ ſemiparabolæ, alterum ſit axis, vel
              <lb/>
              <figure xlink:label="fig-0330-01" xlink:href="fig-0330-01a" number="221">
                <image file="0330-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0330-01"/>
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            diameter integræ parabolæ; </s>
            <s xml:id="echoid-s7483" xml:space="preserve">Eſto
              <lb/>
            quod velimus, CD, eſſe baſim, &</s>
            <s xml:id="echoid-s7484" xml:space="preserve">,
              <lb/>
            CA, axim, vel diametrum inte-
              <lb/>
            græ parabolæ; </s>
            <s xml:id="echoid-s7485" xml:space="preserve">applicetur ergo ad,
              <lb/>
            AC, rectangulum æquale quadra-
              <lb/>
            to, CD, quod latitudinem faciat
              <lb/>
            ipſam, XA, erit ergo quadratum,
              <lb/>
            CD, æquale rectangulo ſub, CA,
              <lb/>
            AX, &</s>
            <s xml:id="echoid-s7486" xml:space="preserve">, AX, erit linea, iuxta
              <lb/>
            quam poſſunt, quæ à curua para-
              <lb/>
            bolæ tranſeunte per puncta, D, A,
              <lb/>
              <note position="left" xlink:label="note-0330-01" xlink:href="note-0330-01a" xml:space="preserve">Schol.40.
                <lb/>
              lib.1.</note>
            vertice, A, ad axim, vel diametrum, AC, ordinatim applicari
              <lb/>
            poſſunt; </s>
            <s xml:id="echoid-s7487" xml:space="preserve">erit ergo quædam ſemiparabola, cuius curua tranſibit per
              <lb/>
            puncta, AD, in baſi, CD, exiſtente, AC, axi, vel diametro in-
              <lb/>
            tegræ parabolæ, ſit autem dicta ſemiparabola, ACD, quod oſten-
              <lb/>
            dere opus erat.</s>
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