Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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          <head xml:id="echoid-head277" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s6429" xml:space="preserve">EX hac facilè elicietur methodus, qua precipuas quorumlibet Acumi-
              <lb/>
            natorum paſſiones oſtendi poſſint, nempe: </s>
            <s xml:id="echoid-s6430" xml:space="preserve">ipſa Acuminata à diame-
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            tris bifariam ſecari: </s>
            <s xml:id="echoid-s6431" xml:space="preserve">& </s>
            <s xml:id="echoid-s6432" xml:space="preserve">Proportionalia Acuminata ęqualium altitudinum
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            inter ſe eſſe vt baſes: </s>
            <s xml:id="echoid-s6433" xml:space="preserve">& </s>
            <s xml:id="echoid-s6434" xml:space="preserve">(tanquam Corollarium) Acuminata proportio-
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            nalia æqualium baſium eſſe inter ſe vt altitudines: </s>
            <s xml:id="echoid-s6435" xml:space="preserve">item duo quæcunque
              <lb/>
            Acuminata proportionalia habere inter ſe rationem compoſitam ex ratio-
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            ne baſium, & </s>
            <s xml:id="echoid-s6436" xml:space="preserve">ex ratione altitudinum: </s>
            <s xml:id="echoid-s6437" xml:space="preserve">& </s>
            <s xml:id="echoid-s6438" xml:space="preserve">ad inſcripta triangula, vel cir-
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            cumſcripta parallelogramma eandem retinere rationem, aliaque his ſimi-
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            lia: </s>
            <s xml:id="echoid-s6439" xml:space="preserve">& </s>
            <s xml:id="echoid-s6440" xml:space="preserve">quod de proportionalibus Acuminatis, idem penitus euenire de ſi-
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            milibus menſalibus proportionalium Acuminatorum, præmiſſa priùs ha-
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            rum menſalium definitione, &</s>
            <s xml:id="echoid-s6441" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6442" xml:space="preserve">quæ omnia infinitas figurarum ſpecies
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              <gap/>
            , ne dum hactenus tractatis Parabolis, Hyperbolis, &</s>
            <s xml:id="echoid-s6443" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6444" xml:space="preserve">maximè con-
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            ducunt. </s>
            <s xml:id="echoid-s6445" xml:space="preserve">Sed hæc aliàs, quę tamen cum ſint haud obſcurę indagationis,
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            & </s>
            <s xml:id="echoid-s6446" xml:space="preserve">huic noſtro inſtituto prorſus aliena, erudito Lectori ſic præmonſtraſſe
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            ſuſſiciat.</s>
            <s xml:id="echoid-s6447" xml:space="preserve"/>
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        <div xml:id="echoid-div674" type="section" level="1" n="269">
          <head xml:id="echoid-head278" xml:space="preserve">LEMMA XI. PROP. XXXVIII.</head>
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            <s xml:id="echoid-s6448" xml:space="preserve">Si duæ rectæ lineæ inter ſe æquales fuerint, & </s>
            <s xml:id="echoid-s6449" xml:space="preserve">parallelæ, & </s>
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            ab earum extremis terminis ducantur lineæ quemlibet angulum
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            efficientes, ab alteris autem terminis aliæ ipſis æquidiſtantes;
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            </s>
            <s xml:id="echoid-s6451" xml:space="preserve">hæ quoque angulum inter datas conſtituent, & </s>
            <s xml:id="echoid-s6452" xml:space="preserve">recta angulo-
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            rum vertices coniungens erit vtrique datarum æqualis, & </s>
            <s xml:id="echoid-s6453" xml:space="preserve">pa-
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            rallela.</s>
            <s xml:id="echoid-s6454" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6455" xml:space="preserve">Si verò datæ rectæ lineæ terminatæ ad quemcunque angulum
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            applicatæ fuerint, & </s>
            <s xml:id="echoid-s6456" xml:space="preserve">vbicunque proportionaliter ſectę, aut pro-
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            ductæ, atque ab homologis earum punctis, hoc eſt, vel ab ex-
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            tremis terminis, vel ab inter-ſectionum, aut productionum pun-
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            ctis, ductæ fuerint intra datum angulum aliæ rectæ lineæ, quæ
              <lb/>
            item angulum quemlibet conſtituant, à reliquis verò punctis aliæ
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            ipſis æquidiſtanter ducantur, hæ pariter tertium angulum effi-
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            cient intra datum, & </s>
            <s xml:id="echoid-s6457" xml:space="preserve">horum trium angulorum vertices in vna
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            eademque recta linea reperientur.</s>
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          </p>
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            <s xml:id="echoid-s6459" xml:space="preserve">SIt, in prima figura, recta A B æqualis, & </s>
            <s xml:id="echoid-s6460" xml:space="preserve">parallela ad C D, & </s>
            <s xml:id="echoid-s6461" xml:space="preserve">exter-
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            minis A, C inter eas conſtituatur angulus quicunque A E C ducta-
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            que B F parallela ad A E, D F verò ad C E. </s>
            <s xml:id="echoid-s6462" xml:space="preserve">Dico B F, D F inter datas
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            æquidiſtantes conuenire, & </s>
            <s xml:id="echoid-s6463" xml:space="preserve">E F iungentem angulorum vertices, alteri A
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            B, vel C D eſſe æqualem, & </s>
            <s xml:id="echoid-s6464" xml:space="preserve">parallelam.</s>
            <s xml:id="echoid-s6465" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6466" xml:space="preserve">Iungantur A C, B D: </s>
            <s xml:id="echoid-s6467" xml:space="preserve">& </s>
            <s xml:id="echoid-s6468" xml:space="preserve">quoniam B F eſt parallela ad A E, erit angu-
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            lus G B F æqualis angulo B A E; </s>
            <s xml:id="echoid-s6469" xml:space="preserve">cumque A B ſit æqualis, & </s>
            <s xml:id="echoid-s6470" xml:space="preserve">parallela </s>
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