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

List of thumbnails

< >
221
221 (209) 		222
222 (210)
223
223 (211) 		224
224 (212)
225
225 (213) 		226
226 (214)
227
227 (215) 		228
228
229
229 		230
230
< >
page |< < (213) of 232 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div196" type="section" level="1" n="130">
          <p>
            <s xml:id="echoid-s3873" xml:space="preserve">
              <pb o="213" file="0225" n="225"/>
            poteſtas ad tales poteſtates ſic, D A, ad tot numero
              <lb/>
            A Q. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">Ergo ratio coni ad conum componetur ex ra-
              <lb/>
            tionibus A D, ad tot A k, & </s>
            <s xml:id="echoid-s3875" xml:space="preserve">eiuſdem A D, ad
              <lb/>
            tot Q A, quotus eſt duplus numerus fuſi: </s>
            <s xml:id="echoid-s3876" xml:space="preserve">nimirum
              <lb/>
            crit conus ad conum vt quadratum A D, ad rectan-
              <lb/>
            gulum ſub illis tot k A, & </s>
            <s xml:id="echoid-s3877" xml:space="preserve">A Q, quotus eſt duplus
              <lb/>
            numerus fuſi. </s>
            <s xml:id="echoid-s3878" xml:space="preserve">Aſt quoniam ex propoſit. </s>
            <s xml:id="echoid-s3879" xml:space="preserve">16, lib 2. </s>
            <s xml:id="echoid-s3880" xml:space="preserve">eſt
              <lb/>
            conuertendo, ſemifuſus ex ſemiparabola B A D, ad
              <lb/>
            cylindrum ſibi circumſcriptum, vt quadratũ num eri
              <lb/>
            parabolę ad rectangulũ ſub dimidio numeri parabolę
              <lb/>
            vnitate aucti, & </s>
            <s xml:id="echoid-s3881" xml:space="preserve">ſub duplo numero parabolæ vnitate
              <lb/>
            aucto; </s>
            <s xml:id="echoid-s3882" xml:space="preserve">vel vt duplum ad duplum; </s>
            <s xml:id="echoid-s3883" xml:space="preserve">nempe vt duplum
              <lb/>
            quadratum numeri parabolæ ad rectangulum ſub nu-
              <lb/>
            mero vnitate aucto, & </s>
            <s xml:id="echoid-s3884" xml:space="preserve">ſub duplo numero vnitate au-
              <lb/>
            cto, vnde eſt ſemifuſus ad tertiam partem cylindri,
              <lb/>
            nempe ad conum ex triangulo B A D, vt antece-
              <lb/>
            dens, ad tertiam partem conſequentis; </s>
            <s xml:id="echoid-s3885" xml:space="preserve">& </s>
            <s xml:id="echoid-s3886" xml:space="preserve">vt antece-
              <lb/>
            dens ad tertiam partem conſequentis, ſic tot partes
              <lb/>
            quot vnitates continet duplum quadratum numeri
              <lb/>
            fuſi (hoc eft rectangulum ſub numero, & </s>
            <s xml:id="echoid-s3887" xml:space="preserve">ſub duplo
              <lb/>
            numero) quadrati A D, diuiſi in tot paites quot vni-
              <lb/>
            tates continet tertia pars rectanguli ſub numero fuſi
              <lb/>
            vnitate aucto, & </s>
            <s xml:id="echoid-s3888" xml:space="preserve">ſub duplo numero vnitate aucto, ad
              <lb/>
            quadratum A D. </s>
            <s xml:id="echoid-s3889" xml:space="preserve">Ergo ex æquali, erit ſemifuſus ad
              <lb/>
            conum ex G Q D, vt tot partes quadrati A D, diuiſi
              <lb/>
            vt dictum eſt, quot vnitates continet rectangulum
              <lb/>
            ſub numero fuſi, & </s>
            <s xml:id="echoid-s3890" xml:space="preserve">ſub duplo numero, ad tot rectan-
              <lb/>
            gula ſub tot K A, & </s>
            <s xml:id="echoid-s3891" xml:space="preserve">ſub tot A Q, quotus eſt du-
              <lb/>
            plus numerus fuſi. </s>
            <s xml:id="echoid-s3892" xml:space="preserve">Cum vero numerus </s>
          </p>
        </div>
      </text>
    </echo>
Impressum