Angeli, Stefano degli, Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

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            <s xml:id="echoid-s3273" xml:space="preserve">
              <pb o="178" file="0190" n="190"/>
            diolanenſis eruditiſſimus geometra in ſua geometria
              <lb/>
            applicationum, ampliauit ad altiores poteſtates, o-
              <lb/>
            ſtendendo applicationem aliarum poteſtatum ſerua-
              <lb/>
            re ſimilem ordinem partium ad quas fit applicatio;
              <lb/>
            </s>
            <s xml:id="echoid-s3274" xml:space="preserve">adeo vt magnitudo ad quam fieri debet applicatio
              <lb/>
            ſit ſecanda in tot partes quota eſt magnitudo, quæ
              <lb/>
            debet applicari, in ordine graduum; </s>
            <s xml:id="echoid-s3275" xml:space="preserve">& </s>
            <s xml:id="echoid-s3276" xml:space="preserve">applicatio
              <lb/>
            ſit facienda ad illarum vnicam. </s>
            <s xml:id="echoid-s3277" xml:space="preserve">V.</s>
            <s xml:id="echoid-s3278" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3279" xml:space="preserve">ſi ad partem
              <lb/>
            datæ A B, ſit applicandum parallelogrammum di-
              <lb/>
            ficiens, & </s>
            <s xml:id="echoid-s3280" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3281" xml:space="preserve">hoc eſt
              <lb/>
              <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a" number="78">
                <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/PVNDER1Y/figures/0190-01"/>
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            ſi A B, ſit ſic ſe-
              <lb/>
            canda in C, vtre-
              <lb/>
            ctangulum A C B,
              <lb/>
            ſit omnium maxi-
              <lb/>
            mum illorum, quæ
              <lb/>
            poſſunt fieri ex
              <lb/>
            partibus A B; </s>
            <s xml:id="echoid-s3282" xml:space="preserve">pun-
              <lb/>
            ctum C, ſit illud
              <lb/>
            quod biſſecat A C.
              <lb/>
            </s>
            <s xml:id="echoid-s3283" xml:space="preserve">Si veto ſit applicandum parallelepipedum, hoc eſt ſi
              <lb/>
            A B, taliter ſit ſecanda in C, vt ſolidum factum ſub
              <lb/>
            A C, in quadratum C B, ſit omnium maximum; </s>
            <s xml:id="echoid-s3284" xml:space="preserve">
              <lb/>
            A C, debet eſſe tertia pars A B. </s>
            <s xml:id="echoid-s3285" xml:space="preserve">Si vero ſit appli-
              <lb/>
            candum planoplanum, adeo vt factum ſub A C, in
              <lb/>
            cubum C B, ſit omnium maximum. </s>
            <s xml:id="echoid-s3286" xml:space="preserve">A C; </s>
            <s xml:id="echoid-s3287" xml:space="preserve">debet
              <lb/>
            eſſe quarta pars A B. </s>
            <s xml:id="echoid-s3288" xml:space="preserve">Et ſic in infinitum in altiori-
              <lb/>
            bus poteſtatibus. </s>
            <s xml:id="echoid-s3289" xml:space="preserve">Hæc ergo doctrina nobis eſt ne-
              <lb/>
            ceſſaria pro impoſterum dicendis. </s>
            <s xml:id="echoid-s3290" xml:space="preserve">Quam etiam </s>
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