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

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        <div xml:id="echoid-div1239" type="section" level="1" n="748">
          <p>
            <s xml:id="echoid-s13996" xml:space="preserve">
              <pb o="537" file="0557" n="557" rhead="LIBER VII."/>
            iuxta datam regulam, ſiue ſecundam illam definitionem abſolutè,
              <lb/>
            ſiue per eandem ſic modificatam, vt hæc ſimilaria ſolida ab infini-
              <lb/>
            tatis conceptu, ſeu ab indiuiſibilium methodo, eximerentur; </s>
            <s xml:id="echoid-s13997" xml:space="preserve">Non
              <lb/>
            eſt autem difficile inſuper intelligere quadrata ſolida quarumcũq;
              <lb/>
            </s>
            <s xml:id="echoid-s13998" xml:space="preserve">planarum figurarum, in ambitu eorundem exiſtentium, eſſe etiam
              <lb/>
            ſolida ſimilaria, genita ex eiſdem figuris, quarum dicuntur qua-
              <lb/>
            drata ſolida, iuxta eaſdem regulas, iuxta quas quadrata ſolida di-
              <lb/>
            cebantur: </s>
            <s xml:id="echoid-s13999" xml:space="preserve">& </s>
            <s xml:id="echoid-s14000" xml:space="preserve">è conuerſo ſolida ſimilaria, genita ex quibuſcumq; </s>
            <s xml:id="echoid-s14001" xml:space="preserve">
              <lb/>
            figuris iuxta quaſuis regulas, quarum figuræ, à genitricium lineis
              <lb/>
            homologis deſcriptæ tamquam à lateribus, ſint quadrata, eſſe pa-
              <lb/>
            riter quadrata ſolida earundem figurarum iuxta eaſdem regulas. </s>
            <s xml:id="echoid-s14002" xml:space="preserve">
              <lb/>
            Igitur ad rem noſtram manifeſtum eſt, quod quæcumq; </s>
            <s xml:id="echoid-s14003" xml:space="preserve">ſolida ad
              <lb/>
            inuicem ſimilaria, genita ex figuris lib. </s>
            <s xml:id="echoid-s14004" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14005" xml:space="preserve">hic denuò conſideratis,
              <lb/>
            iuxta aſſumptas regulas (quarum patefacta eſt ratio quadratorum
              <lb/>
            ſolidorum) habebunt rationem notam, per quod ſuppletur Propo-
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s14006" xml:space="preserve">34. </s>
            <s xml:id="echoid-s14007" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14008" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14009" xml:space="preserve">colligentur autem vt ibi factum eſt ſequentia Corol-
              <lb/>
            laria vſq; </s>
            <s xml:id="echoid-s14010" xml:space="preserve">ad finem eiuſdem lib. </s>
            <s xml:id="echoid-s14011" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14012" xml:space="preserve">mutatis tantum ſæpè dictis no-
              <lb/>
            minibus, vbi neceſſe fuerit, quod enim ibi per omnia quadrata hic
              <lb/>
            per quadrata ſolida conſideratarum figurarum colligetur. </s>
            <s xml:id="echoid-s14013" xml:space="preserve">Do-
              <lb/>
            ctrina autem ſcholij ſubſequentis etiam pro hac noua methodo
              <lb/>
            ſubſiſtit, ſi tamen vice omnium figurarum, ſeu omnium planorum,
              <lb/>
            ſubſtitutas intelligamus quotcumque figuras, ſeu quotcumque
              <lb/>
            plana, cætera cnim à methodo indiuiſibilium exempta ſunt, & </s>
            <s xml:id="echoid-s14014" xml:space="preserve">hæc
              <lb/>
            ſufficiant circa examen lib. </s>
            <s xml:id="echoid-s14015" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14016" xml:space="preserve">nunc autem Prop. </s>
            <s xml:id="echoid-s14017" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14018" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14019" xml:space="preserve">ſimiliter
              <lb/>
            perluſtrabimus.</s>
            <s xml:id="echoid-s14020" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1240" type="section" level="1" n="749">
          <head xml:id="echoid-head782" xml:space="preserve">THEOREMA XXIII. PROPOS. XXIII.</head>
          <p>
            <s xml:id="echoid-s14021" xml:space="preserve">ASſumpta ex ſchemate Prop. </s>
            <s xml:id="echoid-s14022" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14023" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s14024" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14025" xml:space="preserve">ſemiparabola,
              <lb/>
            CHG, cum parallelogrammo, EG, viſa tamen etiam
              <lb/>
            illa figura, oſtendemus parallelogrammum, EF, ſexquial-
              <lb/>
            terum eſſe parabolæ, HCF.</s>
            <s xml:id="echoid-s14026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14027" xml:space="preserve">Producta enim diametro, CG, vtcumq; </s>
            <s xml:id="echoid-s14028" xml:space="preserve">in, V, deſcribatur qua-
              <lb/>
            drans circuli, vel ellipſis, HGV, iuxta duas ſemidiametros coniu-
              <lb/>
            gatas, HG, GV, & </s>
            <s xml:id="echoid-s14029" xml:space="preserve">per, H, ducta, EP, parallela, CV, & </s>
            <s xml:id="echoid-s14030" xml:space="preserve">indefinitè
              <lb/>
            extenſa, agantur ſimiliter à punctis, CV, parallele, HG, ipſæ, EC,
              <lb/>
            PV, erunt ergo parallelogramma, EG, GP, EG, quidem circum-
              <lb/>
            ſcriptum ſemiparabolæ, HCG, &</s>
            <s xml:id="echoid-s14031" xml:space="preserve">, PG, quadrati, HGV, ſit inſu-
              <lb/>
            per quæcumq; </s>
            <s xml:id="echoid-s14032" xml:space="preserve">MO, ordinatim ad, HG, applicata, regula, CG, </s>
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