Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Table of figures

< >
[Figure 241]
Page: 296
[Figure 242]
Page: 298
[Figure 243]
Page: 300
[Figure 244]
Page: 301
[Figure 245]
Page: 303
[Figure 246]
Page: 304
[Figure 247]
Page: 305
[Figure 248]
Page: 307
[Figure 249]
Page: 308
[Figure 250]
Page: 313
[Figure 251]
Page: 314
[Figure 252]
Page: 316
[Figure 253]
Page: 317
[Figure 254]
Page: 318
[Figure 255]
Page: 319
[Figure 256]
Page: 321
[Figure 257]
Page: 323
[Figure 258]
Page: 325
[Figure 259]
Page: 326
[Figure 260]
Page: 329
[Figure 261]
Page: 329
[Figure 262]
Page: 331
[Figure 263]
Page: 332
[Figure 264]
Page: 333
[Figure 265]
Page: 334
[Figure 266]
Page: 335
[Figure 267]
Page: 336
[Figure 268]
Page: 337
[Figure 269]
Page: 338
[Figure 270]
Page: 339
< >
page |< < (139) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div939" type="section" level="1" n="376">
          <p>
            <s xml:id="echoid-s9044" xml:space="preserve">
              <pb o="139" file="0325" n="325" rhead=""/>
            & </s>
            <s xml:id="echoid-s9045" xml:space="preserve">cum baſi A C erit recta N S O, (quæ ad rectam G D H erit perpendi-
              <lb/>
            cularis, & </s>
            <s xml:id="echoid-s9046" xml:space="preserve">ipſius Parabolæ baſis) quæ baſes inter ſe æquales erunt, cum ſint
              <lb/>
            rectæ in circulo A C à centro D æqualiter diſtantes, atque huiuſmodi Pa-
              <lb/>
            rabolarum diametri P I, Q S proportionaliter diſtent à lateribus, ſeu ab ip-
              <lb/>
            ſarum regulis B A, B G, ita vt ſit B P ad P C, vel A I ad I C, vt B Q ad
              <lb/>
            Q H, vel G S ad S H. </s>
            <s xml:id="echoid-s9047" xml:space="preserve">Dico altitudinem Parabolæ per P I ad altitudinem
              <lb/>
            Parabolæ per Q S (quæ ſunt Parabolæ æqualium baſium) habere eandem
              <lb/>
            rationem, ac perpendicularis ex vertice B ſuper contingentem ex A, ter-
              <lb/>
            mino lateris B A, ad perpendicularem ex B ſuper contingentem ex G,
              <lb/>
            termino lateris B G. </s>
            <s xml:id="echoid-s9048" xml:space="preserve">Et è conuerſo, &</s>
            <s xml:id="echoid-s9049" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9051" xml:space="preserve">Nam ſit A F baſim contingens
              <lb/>
              <figure xlink:label="fig-0325-01" xlink:href="fig-0325-01a" number="258">
                <image file="0325-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0325-01"/>
              </figure>
            ad A, ſiue perpendicularis ad
              <lb/>
            diametrum A C, quę erit quoq;</s>
            <s xml:id="echoid-s9052" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0325-01" xlink:href="note-0325-01a" xml:space="preserve">1. Co-
                <lb/>
              roll. 98. h.</note>
            cum A B perpendicularis: </s>
            <s xml:id="echoid-s9053" xml:space="preserve">ſitque
              <lb/>
            G R contingens ad G, quæ item
              <lb/>
            cum diametro G D H rectos an-
              <lb/>
            gulos efficiet; </s>
            <s xml:id="echoid-s9054" xml:space="preserve">atque ex E Coni
              <lb/>
            verticis veſtigio, ducatur E R pa-
              <lb/>
            rallela ad H D G, iungaturque B
              <lb/>
            R, quæ ſuper contingentem G R
              <lb/>
            erit perpendicularis,
              <note symbol="b" position="right" xlink:label="note-0325-02" xlink:href="note-0325-02a" xml:space="preserve">2. Co-
                <lb/>
              roll. ibid.</note>
            H R, quæ rectam G S N ſecet in
              <lb/>
            T, agatur recta Q T.</s>
            <s xml:id="echoid-s9055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9056" xml:space="preserve">Iam cum ſit I M parallela ad A
              <lb/>
            F, (vtraque enim perpendicularis
              <lb/>
            eſt ad A C) & </s>
            <s xml:id="echoid-s9057" xml:space="preserve">I P ad A B, erit
              <lb/>
            angulus P I M æqualis angulo
              <note symbol="c" position="right" xlink:label="note-0325-03" xlink:href="note-0325-03a" xml:space="preserve">10. vnd.
                <lb/>
              Elem.</note>
            A F, nempe rectus, quare ipſa P I erit altitudo Parabolicæ portionis, quæ
              <lb/>
            ducitur per P I iuxta latus B A, cum ſit M I L eius baſis. </s>
            <s xml:id="echoid-s9058" xml:space="preserve">Præterea cum ſit
              <lb/>
            R H ad H T, vt G H ad H S, (ob parallelas R G, T S in triangulo G H R)
              <lb/>
            vel vt B H ad H Q (ob æquidiſtantes G B, S Q in triangulo G H B) erit
              <lb/>
            in triangulo R H B recta B R parallela ad Q T, eſtque R G parallela ad T
              <lb/>
            S, ergo angulus Q T S æquabitur angulo B R G, ſiue rectus erit, ex
              <note symbol="d" position="right" xlink:label="note-0325-04" xlink:href="note-0325-04a" xml:space="preserve">ibidem.</note>
            ipſa Q T erit altitudo Parabolicæ portionis ductæ per Q S iuxta latus
              <lb/>
            B G, cum N S O ſit baſis ipſius Parabolæ. </s>
            <s xml:id="echoid-s9059" xml:space="preserve">Et quoniam demonſtrata eſt B
              <lb/>
            R parallela ad Q T, erit B R ad Q T, vt B H ad H Q in triangulo B H R,
              <lb/>
            vel vt B C ad C P, ex hypotheſi, vel vt B A ad P I, ob parallelas in trian-
              <lb/>
            gulo A B C, & </s>
            <s xml:id="echoid-s9060" xml:space="preserve">permutando B R, quæ eſt perpendicularis ex vertice B ſu-
              <lb/>
            per contingentem G R, ad B A, quæ eſt perpendicularis ex B ſuper con-
              <lb/>
            tingentem A F, ita Q T, quæ eſt altitudo Parabolæ per Q S, ad P I, quæ
              <lb/>
            eſt altitudo Parabolæ per P I, & </s>
            <s xml:id="echoid-s9061" xml:space="preserve">hoc ſemper; </s>
            <s xml:id="echoid-s9062" xml:space="preserve">quare patet propoſitum.</s>
            <s xml:id="echoid-s9063" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div943" type="section" level="1" n="377">
          <head xml:id="echoid-head386" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s9064" xml:space="preserve">HInc eſt, quod Parabolarum in Cono genitarum, iuxta quodlibet latus
              <lb/>
            trianguli per axem ad baſem recti, eędẽ ſunt diametri, ac altitudines.
              <lb/>
            </s>
            <s xml:id="echoid-s9065" xml:space="preserve">Superiùs enim oſtendimus diametrum Parabolæ per P I in triangulo per
              <lb/>
            axem A B C iuxta latus B A, eſſe quoque altitudinem eiuſdem Parabolæ.</s>
            <s xml:id="echoid-s9066" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum