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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          <p>
            <s xml:id="echoid-s904" xml:space="preserve">
              <pb o="48" file="0060" n="60"/>
            dricum LEM; </s>
            <s xml:id="echoid-s905" xml:space="preserve">huius ad cylindrum T F; </s>
            <s xml:id="echoid-s906" xml:space="preserve">& </s>
            <s xml:id="echoid-s907" xml:space="preserve">hu-
              <lb/>
            ius ad ſegmentum E N O F. </s>
            <s xml:id="echoid-s908" xml:space="preserve">Cum autem differen-
              <lb/>
            tia fruſtorum conoideorum ſit, ex ſupradictis, æqua-
              <lb/>
            lis differentiæ fruſtorum conorum inſcriptorum in
              <lb/>
            ipſis; </s>
            <s xml:id="echoid-s909" xml:space="preserve">& </s>
            <s xml:id="echoid-s910" xml:space="preserve">cum differentia fruſtorum conorum ſit ad
              <lb/>
            tubum L E M, vt facile poteſt deduci ex dictis in
              <lb/>
            ſchol. </s>
            <s xml:id="echoid-s911" xml:space="preserve">4. </s>
            <s xml:id="echoid-s912" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s913" xml:space="preserve">14. </s>
            <s xml:id="echoid-s914" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s915" xml:space="preserve">2. </s>
            <s xml:id="echoid-s916" xml:space="preserve">vt D B, cum B K, & </s>
            <s xml:id="echoid-s917" xml:space="preserve">
              <lb/>
            cum harum tertia minori proportionali ad tres D B.
              <lb/>
            </s>
            <s xml:id="echoid-s918" xml:space="preserve">Sequitur etiam differentiam ſegmentorum conoi-
              <lb/>
            deorum, eſſe ad tubum cylindricum L E M, vt D B,
              <lb/>
            B K, & </s>
            <s xml:id="echoid-s919" xml:space="preserve">illa tertia proportionalis ad tres D B. </s>
            <s xml:id="echoid-s920" xml:space="preserve">Cum
              <lb/>
            verò L E M, tubus ſit ad cylindrum T F, vt re-
              <lb/>
            ctangulum A E C, ad quadratum E D, nempe
              <lb/>
            diuidendo, ex hypotheſi frequenter vſa, vt D B,
              <lb/>
            ad B G, ſeù vt tripla D B, ad triplam G B. </s>
            <s xml:id="echoid-s921" xml:space="preserve">Ergo
              <lb/>
            ex æquali, erit differentia ſegmentorum conoideo-
              <lb/>
            rum ad cylindrum T F, vt D B, B k, cum illa ter-
              <lb/>
            tia proportionali ad triplam G B. </s>
            <s xml:id="echoid-s922" xml:space="preserve">Cylindrus T F,
              <lb/>
            eſt ad ſegmentum E N O F, vt dicetur inferius, vt
              <lb/>
            dupla D B, ad D B, cum B K. </s>
            <s xml:id="echoid-s923" xml:space="preserve">Ergo à primo ad
              <lb/>
            vltimum, differentia ſegmentorum conoideorum. </s>
            <s xml:id="echoid-s924" xml:space="preserve">
              <lb/>
            ad ſegmentum E N O F, habebit rationem com-
              <lb/>
            poſitam ex ratione D B, B k, & </s>
            <s xml:id="echoid-s925" xml:space="preserve">harum tertiæ pro-
              <lb/>
            portionalis ad triplam B G, & </s>
            <s xml:id="echoid-s926" xml:space="preserve">ex ratione duplæ D B,
              <lb/>
            ad D B, B k. </s>
            <s xml:id="echoid-s927" xml:space="preserve">Sed ex dictis rationibus componitur
              <lb/>
            quoque ratio duorum quadratorum B D, duorum
              <lb/>
            rectangulorum D B K, & </s>
            <s xml:id="echoid-s928" xml:space="preserve">duorum rectangulorum. </s>
            <s xml:id="echoid-s929" xml:space="preserve">
              <lb/>
            ſub D B, & </s>
            <s xml:id="echoid-s930" xml:space="preserve">ſub illa tertia proportionali (quæ duo
              <lb/>
            vltima rectangula ſunt æqualia duobus </s>
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