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-div181" type="section" level="1" n="117">
          <pb o="194" file="0206" n="206"/>
          <p>
            <s xml:id="echoid-s3570" xml:space="preserve">Sicuti facile agnoſcet D B, taliter ſecari in F, vt
              <lb/>
            B F, ſit ad F D, vt vnitas ad dimidium numeri co-
              <lb/>
            noidis. </s>
            <s xml:id="echoid-s3571" xml:space="preserve">Nempe in cono vt 1, ad dimidium, ſeù vt
              <lb/>
            2. </s>
            <s xml:id="echoid-s3572" xml:space="preserve">ad 1. </s>
            <s xml:id="echoid-s3573" xml:space="preserve">In conoide quadratico, vt 1, ad 1. </s>
            <s xml:id="echoid-s3574" xml:space="preserve">In cu-
              <lb/>
            bico vt 1, ad 1, cum dimidio, & </s>
            <s xml:id="echoid-s3575" xml:space="preserve">ſic in infinitum.
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            </s>
            <s xml:id="echoid-s3576" xml:space="preserve">In cono res ſupra patuit in propoſit. </s>
            <s xml:id="echoid-s3577" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3578" xml:space="preserve">In alijs co-
              <lb/>
            noidibus ſic patebit. </s>
            <s xml:id="echoid-s3579" xml:space="preserve">Nam cum E B, ſit ad B F,
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            vt numerus conoidis vnitate minutus ad vnitatem,
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            erit componendo, E F, ad F B, vt numerus conoidis
              <lb/>
            ad vnitatem. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">Cumautem D F, ſit dimidium F E, pa-
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            tet conuertendo, propoſitum.</s>
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        <div xml:id="echoid-div182" type="section" level="1" n="118">
          <head xml:id="echoid-head130" xml:space="preserve">PROPOSITIO LIX.</head>
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            <s xml:id="echoid-s3582" xml:space="preserve">Si A B, taliter ſecetur in C, & </s>
            <s xml:id="echoid-s3583" xml:space="preserve">D, vt A C, ſit duo
              <lb/>
            tertia A B. </s>
            <s xml:id="echoid-s3584" xml:space="preserve">C D, erit tertia pars A D, minus
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            duobus tertijs D B.</s>
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            <s xml:id="echoid-s3586" xml:space="preserve">CVm enim A C, ſit duo tertia A B, ergo C D,
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            erit tertia pars A B; </s>
            <s xml:id="echoid-s3587" xml:space="preserve">nempe tertia pars A D,
              <lb/>
            plus tertia parte D B. </s>
            <s xml:id="echoid-s3588" xml:space="preserve">Quare C D, ſola erit tertia
              <lb/>
            pars A D, minus duobustertijs D B. </s>
            <s xml:id="echoid-s3589" xml:space="preserve">Quod &</s>
            <s xml:id="echoid-s3590" xml:space="preserve">c.</s>
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        <div xml:id="echoid-div183" type="section" level="1" n="119">
          <head xml:id="echoid-head131" xml:space="preserve">PROPOSITIO LX.</head>
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            <s xml:id="echoid-s3592" xml:space="preserve">Datam A D, taliter producere in B, vt B D, ſit ad
              <lb/>
            exceßum D A, ſupra duo tertia A B, in
              <lb/>
            data proportione.</s>
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