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

Table of contents

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[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
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            <s xml:id="echoid-s7617" xml:space="preserve">Quoniam ergo, OF, eſt diſtantia parallelarum axi ductarum à
              <lb/>
            punctis, BF, abſcindatur à, BF, recta, FE, æqualis diſtantiæ, F
              <lb/>
            O, inſuper intelligatur adhuc ipſa, CD, ducta vtcunque parallela
              <lb/>
            rectæ, BF, terminans in puncta, CD, curuæ parabolæ, & </s>
            <s xml:id="echoid-s7618" xml:space="preserve">cum
              <lb/>
            ſit, VG, diſtantia parallelarumaxi, quæ à punctis, CD, ducun-
              <lb/>
            tur, abſcindatur ab ipſa, CD, verſus, D, ipſa, DZ, æqualis di-
              <lb/>
            ſtantiæ, VG; </s>
            <s xml:id="echoid-s7619" xml:space="preserve">ſic ductis in portione, BCDF, omnibus lineis, regu-
              <lb/>
            la, BF, in earundem ſingulis intell gantur ſumptæ diſtantiæ, ſicut
              <lb/>
            acceptæ ſuerunt, EF, ZD, quarum extrema puncta ſint in curua
              <lb/>
            parabolica, FDCB, ſint autem in huius curuæ ea parte, in qua
              <lb/>
            ſunt puncta, DF, patet ergo ſi fumamus punctum, S, verticem
              <lb/>
            portionis, BSF, quod dictarum omnium linearum extrema puncta
              <lb/>
            erunt in curua parabolica, quæ incipit a vertice, S, & </s>
            <s xml:id="echoid-s7620" xml:space="preserve">deſinit in, F;
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            </s>
            <s xml:id="echoid-s7621" xml:space="preserve">
              <figure xlink:label="fig-0336-01" xlink:href="fig-0336-01a" number="226">
                <image file="0336-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0336-01"/>
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            per alia ergo extrema puncta earundem
              <lb/>
            diſtantiarum intelligatur ducta linea, S
              <lb/>
            ZE. </s>
            <s xml:id="echoid-s7622" xml:space="preserve">Dico figuram, SFE, compre-
              <lb/>
            henſam recta, EF, curua parabolica,
              <lb/>
            SDF, & </s>
            <s xml:id="echoid-s7623" xml:space="preserve">linea, SZE, eſſe huiuſmo-
              <lb/>
            di, quod, ſi duxerimus intra ipſam vt-
              <lb/>
            cunq; </s>
            <s xml:id="echoid-s7624" xml:space="preserve">ipſi, BF, parallelam, quæ pro-
              <lb/>
            ducatur vſq; </s>
            <s xml:id="echoid-s7625" xml:space="preserve">ad curuam parabolicam,
              <lb/>
            huius portio manens in figura, SEF, erit diſtantia parallelarum
              <lb/>
            axi, quæ ducuntur ab extremis punctis ab eadem producta in curua
              <lb/>
            parabolica ſignatis. </s>
            <s xml:id="echoid-s7626" xml:space="preserve">Intelligatur ergo ducta vtcunque, DZ, ipſi, B
              <lb/>
            F, parallela, & </s>
            <s xml:id="echoid-s7627" xml:space="preserve">producta vſq; </s>
            <s xml:id="echoid-s7628" xml:space="preserve">ad curuam parabolicam incidens illi
              <lb/>
            in puncto, C, quoniam ergo, CD, eſt vna earum, quæ dicuntur
              <lb/>
            omnes lineæ figurę, BSF, portio eiuſdem manens intra figuram,
              <lb/>
            SEF, erit diſtantia parallelarum axi, quę ab eiuſdem extremis pun-
              <lb/>
            ctis ductæ intelliguntur, & </s>
            <s xml:id="echoid-s7629" xml:space="preserve">hoc per conſtructionem patet, quoniam
              <lb/>
            abipſa, CD, abſciſſa eſt, DZ, quę terminat in lineam, SZE, æ-
              <lb/>
            qualis dictę diſtantię, ergo figura, SEF, deſcripta eſt, qualem pro-
              <lb/>
            blema poſtulabat; </s>
            <s xml:id="echoid-s7630" xml:space="preserve">quę vocetur figura diſtantiarum portionis, ſiue pa-
              <lb/>
            rabolę, BSF.</s>
            <s xml:id="echoid-s7631" xml:space="preserve"/>
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        <div xml:id="echoid-div757" type="section" level="1" n="446">
          <head xml:id="echoid-head466" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s7632" xml:space="preserve">_Q_Via verò oſtenſum eſt, BF, ad diſtantiam parallelarum axià, B,
              <lb/>
            F, ductarum, eſſe vt, CD, ad diſtantiam parallelarum axi à
              <lb/>
            punctis, C, D, ductarum, ſunt autem, EF, ZD, æquales dictis diſtan-
              <lb/>
            tijs, ideò erit, BF, ad, FE, vt, CD, ad, DZ, & </s>
            <s xml:id="echoid-s7633" xml:space="preserve">ſic erit quælibet du-
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            cta in portione, BSF, parallelaipſi, BF, adeiuſdem partemincluſam@
              <lb/>
            figura, SEF, vt, BF, ad, FE.</s>
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