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

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            <s xml:id="echoid-s12360" xml:space="preserve">
              <pb o="483" file="0503" n="503" rhead="LIBER VII"/>
            lea quidem armareſiſtere poſſe exiſtimantur. </s>
            <s xml:id="echoid-s12361" xml:space="preserve">His tamen ego per ea,
              <lb/>
            quæ Lib. </s>
            <s xml:id="echoid-s12362" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12363" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s12364" xml:space="preserve">1. </s>
            <s xml:id="echoid-s12365" xml:space="preserve">ac illius Scholio præcipuè declarata, ac demon-
              <lb/>
            ſtrataſunt, ſatisfieri poſſe dijudicaui: </s>
            <s xml:id="echoid-s12366" xml:space="preserve">quoad conceptum enim omniã
              <lb/>
            linearum, ſeu omnium planorum efformandum, facilè hoc per nega-
              <lb/>
            tionem nos conſequi poſſe exiſtimaui, ita nempè vt nulla linearum,
              <lb/>
            ſeu planorum, excludi intelligatur. </s>
            <s xml:id="echoid-s12367" xml:space="preserve">Quoad continui autem compo.
              <lb/>
            </s>
            <s xml:id="echoid-s12368" xml:space="preserve">ſitionem manifeſtum eſt ex præoſtenſis ad ipſum ex indiuiſibilibus cõ-
              <lb/>
            ponendum nos minimè cogi, ſolum enim continua ſequi indiuiſibilium
              <lb/>
            proportionem, & </s>
            <s xml:id="echoid-s12369" xml:space="preserve">è conuersò, probare intentum ſuit, quod quidem cũ
              <lb/>
            vtraq; </s>
            <s xml:id="echoid-s12370" xml:space="preserve">poſitione ſtare poteſt. </s>
            <s xml:id="echoid-s12371" xml:space="preserve">Tandem verò dicta indiuiſibilium aggre-
              <lb/>
            gata non ita pertractauimus vt infinitatis rationem, propter infinitas
              <lb/>
            lineas, ſeu plana, ſubire videntur, ſed quatenus finitatis quandam
              <lb/>
            conditionem, & </s>
            <s xml:id="echoid-s12372" xml:space="preserve">naturam ſortiuntur, vt propterea, & </s>
            <s xml:id="echoid-s12373" xml:space="preserve">augeri, & </s>
            <s xml:id="echoid-s12374" xml:space="preserve">
              <lb/>
            diminui poſſint, vt ibidem oſtenſum fuit, ſi ipſa prout diffinita ſunt
              <lb/>
            accipiantur. </s>
            <s xml:id="echoid-s12375" xml:space="preserve">Sed his nihilominus fortè obſtrepent Philoſophi, vecla-
              <lb/>
            mabuntq; </s>
            <s xml:id="echoid-s12376" xml:space="preserve">Geometræ, qui puriſſimos veritatis latices ex clariſſimis
              <lb/>
            baurire fontibus conſueſcunt ſic obijcientes. </s>
            <s xml:id="echoid-s12377" xml:space="preserve">Hic dicendi modus ad. </s>
            <s xml:id="echoid-s12378" xml:space="preserve">
              <lb/>
            buc videtur ſubobſcurus, durior quam par eſt euadit hic omnium li-
              <lb/>
            nearum, ſeu omnium planorum conceptus, quapropter bun@ tuæ
              <lb/>
            Geometriæ ceu Gordium nodum aut auſeras, aut ſaltem frangas, niſi
              <lb/>
            diſſoluas. </s>
            <s xml:id="echoid-s12379" xml:space="preserve">Fregiſſem qu idem fateor, ò Geometræ, vel emninò à prio-
              <lb/>
            ribus Libris ſuſtuli ſſem, niſi indignum facinus mihi viſum fuiſſet no-
              <lb/>
            ua hæc Geometriæ veluti myſteria ſapientiſſimis abſcondere viris; </s>
            <s xml:id="echoid-s12380" xml:space="preserve">vt,
              <lb/>
            his fundamentis, quibus tot concluſionum ab alijs quoq; </s>
            <s xml:id="echoid-s12381" xml:space="preserve">oſtenſarum
              <lb/>
            veritates adeò mirè concordant, alicuius induſtria melius fortè con-
              <lb/>
            cinnatis, huiuſce nodi exoptatam illis diſſolutionem aliquando præ-
              <lb/>
            ſtare poſſint. </s>
            <s xml:id="echoid-s12382" xml:space="preserve">Interim qualiſcumq; </s>
            <s xml:id="echoid-s12383" xml:space="preserve">mea ſuerit illius tentata diſſolu-
              <lb/>
            tio, ipſum tamen in præſenti Libro, nouis alijs denuò ſtratis funda-
              <lb/>
            mentis, quibus ea omnia, quæ indiuiſibilium methodo in antecedenti-
              <lb/>
            bus Libris iam oſtenſa ſunt, alia ratione ab infinitatis exempta conce-
              <lb/>
            ptu comprobantur, omninò è medio tollendum eſſe cenſui. </s>
            <s xml:id="echoid-s12384" xml:space="preserve">Hoc verò
              <lb/>
            præcipuè à nobis factum eſt, tum vt apud eos, quibus noſtra hæc indi-
              <lb/>
            uiſibilium methodus minus probabitur, non indignè noſtram banc de
              <lb/>
            Continuis doctrinam Geometriæ titulo inſigniri clarius eluceſcat; </s>
            <s xml:id="echoid-s12385" xml:space="preserve">tum
              <lb/>
            etiam vt appareat, quod non leui ratione ducti, cum poſſemus cuncta
              <lb/>
            per indiuiſibilium methodum præoſtenſa, tantum per huius Libri fun-
              <lb/>
            damenta demonſtrare, illam quoque methodum tanquam nouam, ac
              <lb/>
            conſideratione dignam, fuimus preſequuti. </s>
            <s xml:id="echoid-s12386" xml:space="preserve">Nodum verò ipſum, cui
              <lb/>
            negotium faceſſeret, non inaniter in præcedentibus Libris relictum eſ-
              <lb/>
            ſe, quinimmo nos ipſum alicui Alexandro aut frangendum, aut iuxta
              <lb/>
            ſcrupoliſiſsimi cuiuſq; </s>
            <s xml:id="echoid-s12387" xml:space="preserve">Geometræ vota diſſoluendum, meritò reſer-
              <lb/>
            uaſſe, nõ ineptè quiſpiam iudicabit.</s>
            <s xml:id="echoid-s12388" xml:space="preserve"/>
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