Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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            <s xml:id="echoid-s2180" xml:space="preserve">
              <pb o="62" file="0086" n="86" rhead=""/>
            noſtræ æquidiſtantium portiones non ſint MINIMAE, quæ à punctis alterutrius
              <lb/>
            ſectionis ſuper aliam educi queant: </s>
            <s xml:id="echoid-s2181" xml:space="preserve">unde ob hoc Hieronymum Cardanum aſſectari
              <lb/>
            nos debuiſſe, qui iuxta perpendiculares à punctis hyperbolicæ ſectionis ſuper aſym-
              <lb/>
            pton ductas, ipſarum linearum interualla meditatus eſt; </s>
            <s xml:id="echoid-s2182" xml:space="preserve">quod nullos alios, admi-
              <lb/>
            randum Apollonij hoc Theorema diſcutientes, animaduerſos fuiſſe, idem Barocius
              <lb/>
            in ſuo quodam commentario Geometrico ſæpiùs admonuit, inter alia hæc proferens;
              <lb/>
            </s>
            <s xml:id="echoid-s2183" xml:space="preserve">_quem errorem, omnes quos vidihuius rei Auctores commiſerunt, præter Car-_
              <lb/>
            _danum_. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">Sed bùc tã bonum Virum edoctum velimus, hoc idem iamdiu nobis innotuiſſe,
              <lb/>
            verùm deditaopera, æ libenter in hoc deſicere nobis placuiſſe cum ſummis Viris, qua-
              <lb/>
            les, eos inter quos maximè colimus, ſunt Torricellius, & </s>
            <s xml:id="echoid-s2185" xml:space="preserve">Gregorius à S. </s>
            <s xml:id="echoid-s2186" xml:space="preserve">Vincentio,
              <lb/>
            immo ipſemet Apollonius tam reconditi ſymptomatis fortaſſe primus, & </s>
            <s xml:id="echoid-s2187" xml:space="preserve">acutiſsimus
              <lb/>
            indagator. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Præterea, nos quoque ſatis agnouiſſe, vnius puncti diſtantiam à quacun-
              <lb/>
            que ſeu recta, ſeu curua linea, ſtrictim aſſumendam eſſe iuxta MINIMAM ex
              <lb/>
            eodem puncto, ſuper datam lineam eductam. </s>
            <s xml:id="echoid-s2189" xml:space="preserve">Inſuper ipſam MINIMAM d@m@ſſas
              <lb/>
            quel, datæ rectæ, vel contingenti ad datam curuam in puncto occurſus perpendicu-
              <lb/>
            lariter inſiſtetc quæ omnia hùc in proximo noſtro libello perſpicuè apparebunt: </s>
            <s xml:id="echoid-s2190" xml:space="preserve">at-
              <lb/>
            tamen hiſce, alijſque notionibus de his inſtructi, alteram methodum conſultò eli-
              <lb/>
            gere maluimus. </s>
            <s xml:id="echoid-s2191" xml:space="preserve">Itaquè ab humaniſsimo Barocio de hoc, cui ſanè criminis nomen
              <lb/>
            falsò tribuitur, veniam expectamus; </s>
            <s xml:id="echoid-s2192" xml:space="preserve">dum nos etiam, & </s>
            <s xml:id="echoid-s2193" xml:space="preserve">ſua, quæquæ ſint ab ipſo
              <lb/>
            ſparſim prolata reticere parati ſumus. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">Interea concedat quæſo, vt ad inuentionem
              <lb/>
            MAXIMARVM MINIMARV Mque coni- ſectionum per diuerſos vertices inſcri-
              <lb/>
            ptibilium, aut circumſcriptibilium, vel ſaltim vt genio quodam noſtro indulgendo,
              <lb/>
            harum ſectionum diſtantias per æquidiſtantium interpoſita ſegmenta nobis perſcru-
              <lb/>
            tari liceat. </s>
            <s xml:id="echoid-s2195" xml:space="preserve">Perlegat inſuper, ſimulque has meditationes percipiat; </s>
            <s xml:id="echoid-s2196" xml:space="preserve">quod ſi ex hac
              <lb/>
            hypotheſi ipſas euidenter comprobatas inuenerit, fateatur, ſi lubet, nos abundè in
              <lb/>
            his Geometræ partem expleuiſſe; </s>
            <s xml:id="echoid-s2197" xml:space="preserve">ſin aliter, incuſatione dignos exiſtimet.</s>
            <s xml:id="echoid-s2198" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2199" xml:space="preserve">Scias itaque, ac iterum ſcias candide Lector nos, tum in decima huius, tum
              <lb/>
            in ſuperioribus, ac deinceps, vbi de non coincidentibus lineis diſſerimus, harum inter-
              <lb/>
            ualla ſemper aſſumpſiſſe iuxta interiecta parallelarum ſegmenta, licet hoc ſæpenu-
              <lb/>
            mero prætermittatur, cum ex ipſo demonſtrationum proceſſu id ſatis ſuperque ſe in
              <lb/>
            conſpectum præbeat. </s>
            <s xml:id="echoid-s2200" xml:space="preserve">Zuod ſi ſubijciat Barocius, non quidem intercapedines à pun-
              <lb/>
            ctis vnius ad alteram coni- ſectionem, verùm longitudines tantùm illarum æqui-
              <lb/>
            diſtantium portionum ſic meditari; </s>
            <s xml:id="echoid-s2201" xml:space="preserve">illum æquiter ratiocinaſſe nos ipſi profectò fa-
              <lb/>
            tebimur, quamuis & </s>
            <s xml:id="echoid-s2202" xml:space="preserve">eædem parallelarum portiones verè dici poſsint diſtantiæ à
              <lb/>
            punctis vnius ſectionis ad aliam; </s>
            <s xml:id="echoid-s2203" xml:space="preserve">prout lineæ omnes, ab vno eodemque puncto duci-
              <lb/>
            biles, dicuntur interualla ab ipſo puncto ad eandem lineam, etiamſi eductæ inter
              <lb/>
            ſe plurimùm differant longitudine.</s>
            <s xml:id="echoid-s2204" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2205" xml:space="preserve">Zuò verò ad methodum iuxta MINIMAS, plura ſunt, quæ à nobis huc eſſent
              <lb/>
            in medium afferenda, ſed non eſt cur in præſens futilem diſceptationem aggredia-
              <lb/>
            mur. </s>
            <s xml:id="echoid-s2206" xml:space="preserve">At ſi quis nos ad huius Pelagi traiectionem deuinctos cenſeret (quamuis præ-
              <lb/>
            ſtantiori fortaſſe luce orbati, nempe conica Apollonij ineditorum librorum doctri-
              <lb/>
            na) diuino tamen præſidio, noſtris quibuſdam inuentis mox huc edendis innixi, na-
              <lb/>
            ue integra ad portum appellere non dubitaremus; </s>
            <s xml:id="echoid-s2207" xml:space="preserve">ſed interim eum, non proprij of-
              <lb/>
            ficij cauſa, ſed pro ſua tantùm humanitate, nonnulla valde iucunda Problemata
              <lb/>
            enodanda recipere exoptaremus, quæ nobis circa nouam quandam meditationem
              <lb/>
            nuper aſſequi datum eſt. </s>
            <s xml:id="echoid-s2208" xml:space="preserve">Sed miſsis parergis rem iam ſuſceptam progrediamur.</s>
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