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

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        <div xml:id="echoid-div413" type="section" level="1" n="251">
          <head xml:id="echoid-head266" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s3965" xml:space="preserve">_H_Abetur ſecundò cylindricos in eadem altitudine exiſtentes eſſe in-
              <lb/>
            terſe, vt baſes, quod de cæteris, veluti de ſupradictis, FE, GD
              <lb/>
            E, oſiendetur, quamuis aliter etiam id aliundè infra colligetur.</s>
            <s xml:id="echoid-s3966" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div414" type="section" level="1" n="252">
          <head xml:id="echoid-head267" xml:space="preserve">COROLLARIVM III.</head>
          <p style="it">
            <s xml:id="echoid-s3967" xml:space="preserve">_H_Abetur tertiò, ſi non ſint in ſupradictis duobus Theorematibus ex-
              <lb/>
            poſita duo parallelogramma, & </s>
            <s xml:id="echoid-s3968" xml:space="preserve">duæ figuræ, ſed vnum tantum,
              <lb/>
            & </s>
            <s xml:id="echoid-s3969" xml:space="preserve">vna figurain eadem baſi, & </s>
            <s xml:id="echoid-s3970" xml:space="preserve">altitudine cumipſo, cuius baſi poſita pro
              <lb/>
            regula, & </s>
            <s xml:id="echoid-s3971" xml:space="preserve">ſumpto vteunque puncto in vno laterum baſi inſi§tentium,
              <lb/>
            perque ipſum baſi ducta parallela, reperiatur eam, quæ intercipitur pa-
              <lb/>
            rallelogrammo ad eam, quæ intercibitur figura, vel figuras ſimiles ab
              <lb/>
            ipſis deſcriptas, tanquam homologis lineis, vel lateribus, eſſe vt vnam
              <lb/>
            ex maximis abſciſſarum lateris, in quo ſumptum eſt punctum, ad abſciſ-
              <lb/>
            ſam per ductam baſi &</s>
            <s xml:id="echoid-s3972" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3973" xml:space="preserve">quidiſtantem, vel vt iſtas adiuncta quadam recta,
              <lb/>
            linea, vel vt iſtarum figuras ſimiles ab ipſis tanquam lineis, vel lateri-
              <lb/>
            bus homologis deſcriptas, ita vt figuræ deſcriptæ &</s>
            <s xml:id="echoid-s3974" xml:space="preserve">a4; </s>
            <s xml:id="echoid-s3975" xml:space="preserve">ſingulis earum, quæ
              <lb/>
            dicuntur omnes lineæ parallelogrammi, & </s>
            <s xml:id="echoid-s3976" xml:space="preserve">dictæ figuræ, ſint ſimiles, vt
              <lb/>
            pariter, quæ deſcribuntur &</s>
            <s xml:id="echoid-s3977" xml:space="preserve">a4; </s>
            <s xml:id="echoid-s3978" xml:space="preserve">ſingulis earum, quæ dicuntur maximæ ab-
              <lb/>
            ſciſſarum, vel abſciſſæ dicti lateris, quod adbuc dictæ magnitudines col-
              <lb/>
            lectæ erunt proportionales: </s>
            <s xml:id="echoid-s3979" xml:space="preserve">Vt ex. </s>
            <s xml:id="echoid-s3980" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3981" xml:space="preserve">ſi in Theorematis antecedentis fi-
              <lb/>
            gura habeamus tantum parallelogrammum, BF, & </s>
            <s xml:id="echoid-s3982" xml:space="preserve">in eiuſdem baſi, E
              <lb/>
            F, & </s>
            <s xml:id="echoid-s3983" xml:space="preserve">eadem altitudine, figuram, BEF, & </s>
            <s xml:id="echoid-s3984" xml:space="preserve">ſumpto in vno laterum, B
              <lb/>
            E, DF, vtcunque puncto, O, & </s>
            <s xml:id="echoid-s3985" xml:space="preserve">per, O, ducta, OQ, parallela ipſi, E
              <lb/>
            F, reperiamus, QO, ad, OP, eſſe vt, EB, ad, BO, vel figuras ſimiles
              <lb/>
            deſcriptas ab, OQ, OP, tanquam lineis, vel lateribus homologis, vt
              <lb/>
            ex. </s>
            <s xml:id="echoid-s3986" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3987" xml:space="preserve">quadratum, QO, ad quadratum, OP, eſſe vt, EB, ad, BO, vel
              <lb/>
            vt, EB, adiuncta quadam linea ad, BO, adiuncta eadem, vel vt abiſtis
              <lb/>
            deſcriptas ſimiles figuras, dico collectas magnitudines, quæ comparan-
              <lb/>
            tur eſſe proportionales: </s>
            <s xml:id="echoid-s3988" xml:space="preserve">Nam ſi ipſi, BE, intelligatur applicatum pa-
              <lb/>
            rallelogrammum, AE, cuius baſis ſit, CE, in directum ipſi, EF, con-
              <lb/>
            ſtituta, &</s>
            <s xml:id="echoid-s3989" xml:space="preserve">, CE, &</s>
            <s xml:id="echoid-s3990" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3991" xml:space="preserve">qualis ipſi, EB, tunc omnes lineæ, AE, regula, C
              <lb/>
              <note position="left" xlink:label="note-0186-01" xlink:href="note-0186-01a" xml:space="preserve">_Corol. 2._
                <lb/>
              _19. huius._</note>
            E, ſunt &</s>
            <s xml:id="echoid-s3992" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3993" xml:space="preserve">quales maximis abſciſſarum, BE, vt probatum eſt, & </s>
            <s xml:id="echoid-s3994" xml:space="preserve">omnes
              <lb/>
            abſciſſæ &</s>
            <s xml:id="echoid-s3995" xml:space="preserve">ae;</s>
            <s xml:id="echoid-s3996" xml:space="preserve">quales omnibus lineis trianguli BCE, ſi ſit iuncta, BC, (quæ
              <lb/>
            ſecet, MO, in, X,) vnde vice earum, quæ dicuntur maximæ abſciſſa-
              <lb/>
            rum, vel abſciſſæ ipſius, BE, rectè ſumemus omnes lineas, AE, & </s>
            <s xml:id="echoid-s3997" xml:space="preserve">tri-
              <lb/>
            anguli, BCE, & </s>
            <s xml:id="echoid-s3998" xml:space="preserve">itareperiemus quadratum, QO, ad quadratum, OP,
              <lb/>
            ex. </s>
            <s xml:id="echoid-s3999" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4000" xml:space="preserve">eſſe vt, MO, ad, OX, vel vt quadratum, M, O, ad </s>
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