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

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            <s xml:id="echoid-s95" xml:space="preserve">
              <pb file="0015" n="15"/>
            menſuram mihi co mpar arem, res, puto, iuxta vota ſucceſſit, vt
              <lb/>
            perlegenti patebit. </s>
            <s xml:id="echoid-s96" xml:space="preserve">Artificio autem tali v ſus ſum, quale ad pro-
              <lb/>
            poſitas quæſtiones ab ſoluendas Algebratici adhibere ſolent; </s>
            <s xml:id="echoid-s97" xml:space="preserve">qui
              <lb/>
            quidem numerorum radices, quamuis ineffabiles, ſurdas, ac igno-
              <lb/>
            tas, nihilominus ſimul aggregantes, ſubtrahentes, multiplican-
              <lb/>
            tes, ac diuidentes, dummodo propoſitę rei exoptatam ſibi notitiã
              <lb/>
            enucleare valeant, ſua ſatis obyſſe munera ſibi perſuadent, Non
              <lb/>
            aliter ipſe ergo indiuiſibilium ſine linearum, liue planorum con-
              <lb/>
            gerie (ijſdem vt in lib. </s>
            <s xml:id="echoid-s98" xml:space="preserve">2. </s>
            <s xml:id="echoid-s99" xml:space="preserve">explicatur aſſumptis) licet quoad eo-
              <lb/>
            rundem numerum innominabili, ſurda, ac ignota, quoad ma-
              <lb/>
            gnitudinem tamen conſpicuis limitibus clauſa, ad continuorum
              <lb/>
            inueſtigandam menſuram vſus ſum, vt legenti in proceſſu ope-
              <lb/>
            ris apparebit. </s>
            <s xml:id="echoid-s100" xml:space="preserve">Propoſitum mihi eſt autem ò Geometra in his ſe-
              <lb/>
            ptem libris quamplurium tam planarum, quam ſolidarum figu-
              <lb/>
            rarum dimenſionem adinuenire, quarum aliquæ etiam ab alijs,
              <lb/>
            ac præcipuè ab Euclide, & </s>
            <s xml:id="echoid-s101" xml:space="preserve">Archimede pertractatę fuerunt, reli-
              <lb/>
            qua verò nemini, quod ſciam bucuſq; </s>
            <s xml:id="echoid-s102" xml:space="preserve">attentatæ; </s>
            <s xml:id="echoid-s103" xml:space="preserve">vno tamem ex-
              <lb/>
            cepto Keplero, quioccaſionę Dolij Auſtriaci per virgam menſo-
              <lb/>
            riam dimetiendi, poſtquam in ſua Stereometria Archimedea
              <lb/>
              <note symbol="p" position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve">_Kepleri_
                <lb/>
              _Storcome_
                <lb/>
              _tria Dolio_
                <lb/>
              _rum._</note>
            ſummariè ipſius Archimedis adinuenta ſibi opportuna recenſuit,
              <lb/>
            nouis aliquando, qualeſcumq; </s>
            <s xml:id="echoid-s104" xml:space="preserve">ſint, adiectis rationibus, tandem
              <lb/>
            cam partem ſuperaddidit, quam Stereometria Archimedeæ ſup-
              <lb/>
            plementum nuncupauit, in qua multiplicem Sectionum conica-
              <lb/>
            rum, Circuli nempè, Parabolæ, Hyperbolæ, & </s>
            <s xml:id="echoid-s105" xml:space="preserve">Ellipſis, necnon ea-
              <lb/>
            rundem portionum circa diu erſos axes reuolutionem contempla-
              <lb/>
            tus, ſolida numero octuaginta ſeptem, præter quinque Archime-
              <lb/>
            dea, Sphæram ſcilicet, Conoides parabolicum, Conoides hyperbo-
              <lb/>
            licum, Sphæroides oblongum, & </s>
            <s xml:id="echoid-s106" xml:space="preserve">prolatum Geometris perquam
              <lb/>
            eleganti præconio promulgauit. </s>
            <s xml:id="echoid-s107" xml:space="preserve">Cum ergo iam expoſitam me-
              <lb/>
            tiendarum figurarum nouam, ac, ſi dicere fas ſit, valde compen-
              <lb/>
            dioſam methodum adinueniſſem, fæliciter mecum actum eſſe exi-
              <lb/>
            ſtimaui, vt hæc ſolida, præter illa Archimedea, mihi ſuppedita-
              <lb/>
            rentur, circa quæ illius vim ac energiam, experiri liceret. </s>
            <s xml:id="echoid-s108" xml:space="preserve">Ne
              <lb/>
            quis tamen putet me omnium dictorum ſolidorum dimenſionem
              <lb/>
            fuiſſe conſequutum, ſicuti neq; </s>
            <s xml:id="echoid-s109" xml:space="preserve">Keplero contingere potuit, niſi
              <lb/>
            paucorum, nec ſatis fęliciter, vt prædictam Stereometriam, </s>
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