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

Table of Notes

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            <s xml:id="echoid-s6454" xml:space="preserve">
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            logrammo, FP, quod dicimus ſimilare, ſemper eſſe cylindricum, geni-
              <lb/>
            tum verò ex triangulo, DEP, ſemper eſſe conicum, vt etiam accidit in
              <lb/>
            omni parallelogrammo, & </s>
            <s xml:id="echoid-s6455" xml:space="preserve">triangulo, dummodò regula ſit vnum laterum
              <lb/>
            eorundem, ſolida igitur ſimilariagenita ex parallelogrammis ſunt cy-
              <lb/>
            lindrici, genita verò ex triangulis ſunt conici, genita inquam, regula,
              <lb/>
            vno laterum eorundem exiſtente; </s>
            <s xml:id="echoid-s6456" xml:space="preserve">quod ſi figuræ quæ dicuntur omnes fi-
              <lb/>
            guræ ſimiles par allelogrammidati, regula vno laterum, ſint eirculi, ille
              <lb/>
            cylindricus erit cylindrus; </s>
            <s xml:id="echoid-s6457" xml:space="preserve">& </s>
            <s xml:id="echoid-s6458" xml:space="preserve">ſi, quæ dicuntur omnes figuræ ſimiles dati
              <lb/>
            trianguli ſint pariter cirouli, regula vno laterum, conicus erit conus;
              <lb/>
            </s>
            <s xml:id="echoid-s6459" xml:space="preserve">nomine ergo communi bic cylindrus, & </s>
            <s xml:id="echoid-s6460" xml:space="preserve">conus dicti ſunt ſolida ſimila-
              <lb/>
            ria nomine particulari dicti ſunt cylindricus, & </s>
            <s xml:id="echoid-s6461" xml:space="preserve">conicus, ſed nomine,
              <lb/>
            magis particulari, & </s>
            <s xml:id="echoid-s6462" xml:space="preserve">proprio dicuntur cylindrus, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">conus, quotieſcun-
              <lb/>
              <note position="left" xlink:label="note-0278-01" xlink:href="note-0278-01a" xml:space="preserve">_34. Lib. 2._</note>
            que dictæ figuræ ſint circuli, iuxta alibi à me oſtenſa.</s>
            <s xml:id="echoid-s6464" xml:space="preserve"/>
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            <s xml:id="echoid-s6465" xml:space="preserve">Pariter ſi figuræ genitrices ſolidorum ſint circuli, vel ellipſes, illæ
              <lb/>
            autem, quæ dicuntur @omnes figuræ ſimiles earundem ſumptæ cum datis
              <lb/>
            regulis) ſint pariter circuli, quorum deſcribentes rectæ lineæ in figuris
              <lb/>
            genitricibus ſint eorundem diametri, ſolida ſimilaria genita ex eiſdem,
              <lb/>
            iuxta eaſdem regulas, erunt, alterum ſpbæra, quod ſcilicet gignitur ex
              <lb/>
              <note position="left" xlink:label="note-0278-02" xlink:href="note-0278-02a" xml:space="preserve">_@6. Lib. 1._</note>
            circulo, alterum ſphæroides quod ſcilicet gignitur ex ellipſi, ſi figuræ
              <lb/>
            ſimiles rectè ſecent axem ellipſis, & </s>
            <s xml:id="echoid-s6466" xml:space="preserve">ſint erectæ tum circulo, tum ellipſi;
              <lb/>
            </s>
            <s xml:id="echoid-s6467" xml:space="preserve">
              <note position="left" xlink:label="note-0278-03" xlink:href="note-0278-03a" xml:space="preserve">_47. Eiuſd._
                <lb/>
              _lib. 1._</note>
            poterit etiam eſſe ſpbæroides, etiamſi figuræ ſimiles non ſint circuli, ſed
              <lb/>
            ellipſes iuxta alibi oſtenſa; </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quæ igitur in boc caſu nomine communi di-
              <lb/>
            cuntur, ſolida ſimilaria genita ex circulo, vel ellipſi, iuxta datas regu-
              <lb/>
            las, nomine particulari, & </s>
            <s xml:id="echoid-s6469" xml:space="preserve">proprio, dicuntur ſphæra, vel ſphæroides:
              <lb/>
            </s>
            <s xml:id="echoid-s6470" xml:space="preserve">Et quæ pariter dicerentur nomine communi ſolida ſimilaria genita ex
              <lb/>
            portione tali, vel tali, iuxta talem regulam, portione inquam circuli,
              <lb/>
            vel ellipſis, quotieſcunque figuræ, quæ dicuntur, omnes figuræ ſimiles
              <lb/>
            talis portionis iuxta eandem regulam, ſint circuli erecti genitricibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s6471" xml:space="preserve">figura genitrix pontio circuli, erit, & </s>
            <s xml:id="echoid-s6472" xml:space="preserve">dicetur nomine particulari, & </s>
            <s xml:id="echoid-s6473" xml:space="preserve">
              <lb/>
            proprio, portio ſphæræ; </s>
            <s xml:id="echoid-s6474" xml:space="preserve">ſi verò ſigura genitrix ſit ellipſis portio, & </s>
            <s xml:id="echoid-s6475" xml:space="preserve">ſi-
              <lb/>
              <note position="left" xlink:label="note-0278-04" xlink:href="note-0278-04a" xml:space="preserve">_46. Lib. 1._</note>
            guræ ſimiles ſint circuli erecti genitricibus, rectè axem portionis ſecan-
              <lb/>
              <note position="left" xlink:label="note-0278-05" xlink:href="note-0278-05a" xml:space="preserve">_47. Lib. 1._</note>
            tes, ſiet portio ſphæroidis, quod ſi ſint ellipſes erectæ genitricibus, dia-
              <lb/>
            metros habentes, vt poſtulat Propoſ. </s>
            <s xml:id="echoid-s6476" xml:space="preserve">47. </s>
            <s xml:id="echoid-s6477" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s6478" xml:space="preserve">1. </s>
            <s xml:id="echoid-s6479" xml:space="preserve">fiet etiam portio ſphæ-
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            roidis: </s>
            <s xml:id="echoid-s6480" xml:space="preserve">Sic igitur nommibus particularibus hæc ſolida vocari conſuene-
              <lb/>
            runt. </s>
            <s xml:id="echoid-s6481" xml:space="preserve">Cum verò figuræ ſimiles non ſunt neq; </s>
            <s xml:id="echoid-s6482" xml:space="preserve">circuli, neq; </s>
            <s xml:id="echoid-s6483" xml:space="preserve">ellipſes ſum-
              <lb/>
            ptæ, vt dictum eſt, ſufficiet eadem vocare nomine communi ſolidi ſimi-
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            Laris, &</s>
            <s xml:id="echoid-s6484" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6485" xml:space="preserve">licet ad variationem, & </s>
            <s xml:id="echoid-s6486" xml:space="preserve">nominationem ſimilium figurarum,
              <lb/>
            conſequenter & </s>
            <s xml:id="echoid-s6487" xml:space="preserve">eadem varia ſolida, variè nominari poſſent; </s>
            <s xml:id="echoid-s6488" xml:space="preserve">fortè autem
              <lb/>
            in ſequentibus ex genitricium figurarum variatione varia nomina com-
              <lb/>
            ponemus, interim hæc teneantur, hoc animaduerſo, quod in ſuperiori-
              <lb/>
            bus, dum ſit ſphæra, vel ſphæroides, vel eorundem portio, ſuppono li-
              <lb/>
            neas, quæ ſunt in genitricibus ſiguris, & </s>
            <s xml:id="echoid-s6489" xml:space="preserve">circulos, vel ellipſes </s>
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