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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        <div xml:id="echoid-div168" type="section" level="1" n="107">
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            <s xml:id="echoid-s3402" xml:space="preserve">HÆc propoſit. </s>
            <s xml:id="echoid-s3403" xml:space="preserve">oſtenditur etiam ab Albio in
              <lb/>
            hemiſphæ. </s>
            <s xml:id="echoid-s3404" xml:space="preserve">diſſec. </s>
            <s xml:id="echoid-s3405" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s3406" xml:space="preserve">44. </s>
            <s xml:id="echoid-s3407" xml:space="preserve">Sed ſuppona-
              <lb/>
            mus A B C, E D O, eſſe conos, & </s>
            <s xml:id="echoid-s3408" xml:space="preserve">D F, eſſe tertiam
              <lb/>
            partem D B. </s>
            <s xml:id="echoid-s3409" xml:space="preserve">Dico conum E D O, eſſe maximum
              <lb/>
            omnium, &</s>
            <s xml:id="echoid-s3410" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3411" xml:space="preserve">Nam, cum conus A B C, ad conum
              <lb/>
            E D O, habeat rationem compoſitam ex ratione
              <lb/>
            quadrati A D, ad quadratum E F (nempe quadra-
              <lb/>
            ti D B, ad quadratum B F) & </s>
            <s xml:id="echoid-s3412" xml:space="preserve">ex ratione D B, ad
              <lb/>
            D F; </s>
            <s xml:id="echoid-s3413" xml:space="preserve">& </s>
            <s xml:id="echoid-s3414" xml:space="preserve">cum hæ duæ rationes componant rationem
              <lb/>
            cubi B D, ad factum ſub quadrato B F, & </s>
            <s xml:id="echoid-s3415" xml:space="preserve">ſub F D;
              <lb/>
            </s>
            <s xml:id="echoid-s3416" xml:space="preserve">ergo A B C, erit ad E D O, vt cubus B D, ad fa-
              <lb/>
            ctum ſub quadrato F B, & </s>
            <s xml:id="echoid-s3417" xml:space="preserve">ſub F D. </s>
            <s xml:id="echoid-s3418" xml:space="preserve">Cum ergo hoc
              <lb/>
            factum ſit maximum omnium homogeneorum ipſi
              <lb/>
            factorum ex partibus B D, in puncto diuiſæ. </s>
            <s xml:id="echoid-s3419" xml:space="preserve">Ergo
              <lb/>
            etiam conus E D O, erit maximus omnium inſcri-
              <lb/>
            ptibilium &</s>
            <s xml:id="echoid-s3420" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3421" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s3422" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3423" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div169" type="section" level="1" n="108">
          <head xml:id="echoid-head120" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s3424" xml:space="preserve">Sed hìc etiam obiter notetur centrum grauitatis
              <lb/>
            amborum conorum eſſe idem punctum. </s>
            <s xml:id="echoid-s3425" xml:space="preserve">Sit enim
              <lb/>
            rurſum H, centrum grauitatis coni A B C. </s>
            <s xml:id="echoid-s3426" xml:space="preserve">Ergo
              <lb/>
            qualium B D, eſt 12, D F, 4, & </s>
            <s xml:id="echoid-s3427" xml:space="preserve">D H, 3, talium
              <lb/>
            H F, eſt 1. </s>
            <s xml:id="echoid-s3428" xml:space="preserve">Ergo H, erit centrum grauitatis etiam
              <lb/>
            coni E D O.</s>
            <s xml:id="echoid-s3429" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3430" xml:space="preserve">Pariter notetur, conum A B C, eſſe ad conum
              <lb/>
            E D O, vt 27, ad 4. </s>
            <s xml:id="echoid-s3431" xml:space="preserve">Nam ſic eſt cubus B D, ad
              <lb/>
            factum ſub quadrato B F, & </s>
            <s xml:id="echoid-s3432" xml:space="preserve">ſub F D.</s>
            <s xml:id="echoid-s3433" xml:space="preserve"/>
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