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

Table of handwritten notes

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            <s xml:id="echoid-s73" xml:space="preserve">
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            eorum g quadrata inuicem habebunt. </s>
            <s xml:id="echoid-s74" xml:space="preserve">His verò perſpectis cum
              <lb/>
              <note symbol="g" position="left" xlink:label="note-0014-01" xlink:href="note-0014-01a" xml:space="preserve">_Cor. 1._
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              _11.l.3._</note>
            ad planarum, ac ſolidarum figurarum quoq; </s>
            <s xml:id="echoid-s75" xml:space="preserve">grauitatum centra
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            reſpicerem, ſimilemque varietatem nactus eſſem, adhuc auge-
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            batur admiratio; </s>
            <s xml:id="echoid-s76" xml:space="preserve">in cono enim centrum grauitatis eſt in axe per
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              <note symbol="h" position="left" xlink:label="note-0014-02" xlink:href="note-0014-02a" xml:space="preserve">_Luc. Val_
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              _39 l.1_</note>
            quartam partem diſtant à baſi, in triangulo verò ipſum gignen-
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              <note symbol="i" position="left" xlink:label="note-0014-03" xlink:href="note-0014-03a" xml:space="preserve">_Idem 19._
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              _l.1._</note>
            te eſt in eodem axæ, dictans ab eadem per tertiam partem eiuſ-
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            dem axis. </s>
            <s xml:id="echoid-s77" xml:space="preserve">Similiter in conoide parabolico illiud ect in axe per
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              <note symbol="k" position="left" xlink:label="note-0014-04" xlink:href="note-0014-04a" xml:space="preserve">_Idë 41._
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              _l.2._</note>
            tertiam partem diſtans à baſi, in parabola verò ipſum generante
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              <note symbol="l" position="left" xlink:label="note-0014-05" xlink:href="note-0014-05a" xml:space="preserve">_Arch. 8._
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              _Se. ęquep_</note>
            per duas tertias eiuſdem axis remouetur ab ipſabaſi. </s>
            <s xml:id="echoid-s78" xml:space="preserve">cum er-
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            go talem varietatem in plurimis alijs ſiguris ſæpius, ac ſæpè fuiſsẽ
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            meditatus, vbi prius ex. </s>
            <s xml:id="echoid-s79" xml:space="preserve">g. </s>
            <s xml:id="echoid-s80" xml:space="preserve">cylindrum ex indefinitis numero pa-
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            rallelogrammis, conum verò in eadem baſi, & </s>
            <s xml:id="echoid-s81" xml:space="preserve">circa eundẽ axim
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            cum cylindro conſtitutum, ex indefinitis numero triangulis per
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            axem tranſeuntibus veluti compactum effingens, habita dictorũ
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            planorum mutua ratione, illicò & </s>
            <s xml:id="echoid-s82" xml:space="preserve">ipſorum ſolidor um ab ipſis ge-
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            nitorum emergere rationem exiſtimabam, cum iam planè conſta-
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            ret planorum rationi genitorum ab ijſdem ſolidorum rationem
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            minimè concordare, figurarum menſuram tali ratione inquiren-
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            temoleum, & </s>
            <s xml:id="echoid-s83" xml:space="preserve">operam perdere, ac ex inanibus paleis trituram fa-
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            cturum eſſe, mihi iure cenſendum videbatur. </s>
            <s xml:id="echoid-s84" xml:space="preserve">Verum paulò pro-
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            fundius rem contemplatus in hanc tandem deueni ſententiam,
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            nempè ad rem noſtram lineas, & </s>
            <s xml:id="echoid-s85" xml:space="preserve">plana, non ad inuicem coinci-
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            dentia, ſed æquidiſtantia aſſumenda eſſe; </s>
            <s xml:id="echoid-s86" xml:space="preserve">ſic enim in plurimis ra-
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            tione inueſtigata reperij tum corporum proportioni ipſorum plano-
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            rum, tum planorum proportiom ipſarum linearum proportionem
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            (ſi eo modo ſumantur, quo lib. </s>
            <s xml:id="echoid-s87" xml:space="preserve">2. </s>
            <s xml:id="echoid-s88" xml:space="preserve">explicatur) ad amuſſim in
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              <note symbol="m" position="left" xlink:label="note-0014-06" xlink:href="note-0014-06a" xml:space="preserve">_Def. I._
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              _& 2.l.2._</note>
            omnibus reſpondere. </s>
            <s xml:id="echoid-s89" xml:space="preserve">Cylindrumigitur, & </s>
            <s xml:id="echoid-s90" xml:space="preserve">conum, iam dictos
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            non amplius per axem ſed æquidiſt anter baſiceu ſectos cõtempla-
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            tus, eandem ſanè rationem habere illa comperij, quæ lib. </s>
            <s xml:id="echoid-s91" xml:space="preserve">2. </s>
            <s xml:id="echoid-s92" xml:space="preserve">voco
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            omnia plana cylindri ad omnia plana coni, regula communi
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              <note symbol="n" position="left" xlink:label="note-0014-07" xlink:href="note-0014-07a" xml:space="preserve">_Def. 1. &_
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              _2.l.2._</note>
            baſi (nempè circulorum congeriem, quæ intra cylindrũ, & </s>
            <s xml:id="echoid-s93" xml:space="preserve">conum,
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            veluti vefligia plani à b aſi ad oppoſitam baſim continuò illi æqui-
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              <note symbol="o" position="left" xlink:label="note-0014-08" xlink:href="note-0014-08a" xml:space="preserve">_Def. 1. &_
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              _2.l.2._</note>
            diſtanter fluentis quodammodo relinqui intelliguntur) ei, quam
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            babet cylindrus ad conum. </s>
            <s xml:id="echoid-s94" xml:space="preserve">Optimam ergo methodum figurarum
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            ſcrutanda menſuræ indicaui prius line arum pro planis, & </s>
            <s xml:id="echoid-s95" xml:space="preserve">plano-
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            rum pro ſolidis rationes indagare, vt illicò ipſarum </s>
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