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

Table of contents

< >
[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
[281.] THEOR. XXVI. PROP. XLV.
Page: 242 (58)
[282.] COROLL.
Page: 243 (59)
[283.] THEOR. XXVII. PROP. XLVI.
Page: 243 (59)
[284.] COROLL. I.
Page: 245 (61)
[285.] COROLL. II.
Page: 245 (61)
[286.] THEOR. XXVIII. PROP. XLVII.
Page: 245 (61)
[287.] THEOR. XXIX. PROP. XLVIII.
Page: 247 (63)
[288.] THEOR. XXX. PROP. XLIX.
Page: 248 (64)
[289.] THEOR. XXXI. PROP. L.
Page: 249 (65)
[290.] COROLL.
Page: 250 (66)
[291.] THEOR. XXXII. PROP. LI.
Page: 251 (67)
[292.] SCHOLIVM.
Page: 252 (68)
[293.] THEOR. XXXIII. PROP. LII.
Page: 253 (69)
[294.] THEOR. XXXIV. PROP. LIII.
Page: 253 (69)
[295.] ALITER.
Page: 254 (70)
[296.] THEOR. XXXV. PROP. LIV.
Page: 255 (71)
[297.] THEOR. XXXIV. PROP. LV.
Page: 256 (72)
[298.] THEOR. XXXVII. PROP. LVI.
Page: 257 (73)
[299.] PROBL. VIII. PROP. LVII.
Page: 259 (75)
[300.] PROBL. IX. PROP. LVIII.
Page: 260 (76)
< >
page |< < (92) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div799" type="section" level="1" n="314">
          <pb o="92" file="0278" n="278" rhead=""/>
        </div>
        <div xml:id="echoid-div800" type="section" level="1" n="315">
          <head xml:id="echoid-head324" xml:space="preserve">DEFINITIONES.
            <lb/>
          I.</head>
          <p>
            <s xml:id="echoid-s7764" xml:space="preserve">PLANA ACVMINATA SIMILIA vocentur illa, quæ inter ſe ſint
              <lb/>
            proportionalia, & </s>
            <s xml:id="echoid-s7765" xml:space="preserve">quorum diametri ſuper baſes ſint æqualiter inclinatæ, ac
              <lb/>
            ijſdem baſibus proportionales.</s>
            <s xml:id="echoid-s7766" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7767" xml:space="preserve">Hoc eſt ſi ſint duo quælibet plana Acuminata proportionalia A B C, D
              <lb/>
            E F, quorum diametri B G, E H cum baſibus A C, D F æquales angulos
              <lb/>
            alterum alteri conſtituant, nempe A G B
              <lb/>
            ipſi D H E, & </s>
            <s xml:id="echoid-s7768" xml:space="preserve">qui ei eſt deinceps C G B
              <lb/>
              <figure xlink:label="fig-0278-01" xlink:href="fig-0278-01a" number="227">
                <image file="0278-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0278-01"/>
              </figure>
            reliquo F H E ſit æqualis, ſitque diame-
              <lb/>
            ter B G ad baſim A C, vt diameter E H
              <lb/>
            ad baſim D F; </s>
            <s xml:id="echoid-s7769" xml:space="preserve">huiuſmodi plana inter ſe
              <lb/>
            vocentur SIMILIA ACVMINATA.
              <lb/>
            </s>
            <s xml:id="echoid-s7770" xml:space="preserve">Vnde, & </s>
            <s xml:id="echoid-s7771" xml:space="preserve">duæ ſimiles Ellipſes vocari pote-
              <lb/>
            runt ſimilia Acuminata, cum vtraque ex
              <lb/>
            duobus proportionalibus Acuminatis con-
              <lb/>
            ſtet, ſiue ex dua
              <unsure/>
            bus ſemi-Ellipſibus, per diametros æqualiter inclinatas diſ-
              <lb/>
            ſectis, quarum diametri ſunt baſibus proportionales, &</s>
            <s xml:id="echoid-s7772" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7773" xml:space="preserve">Idemque de duo-
              <lb/>
            bus circulis, &</s>
            <s xml:id="echoid-s7774" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7775" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div802" type="section" level="1" n="316">
          <head xml:id="echoid-head325" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s7776" xml:space="preserve">SOLIDVM ACVMINATVM REGVLARE, vel tantùm SOLIDVM
              <lb/>
            ACVMINATVM, voco omnem figuram ſolidam ad alteram partem defi-
              <lb/>
            cientem, circa planum Acuminatum deſcriptam, cuius omnia plana baſi ſo-
              <lb/>
            lidi æquidiſtantia per Acuminati applicatas ducta, ſint quoque plana Acu-
              <lb/>
            minata, eidem baſi, ac inter ſe ſimilia, & </s>
            <s xml:id="echoid-s7777" xml:space="preserve">ſimiliter poſita, & </s>
            <s xml:id="echoid-s7778" xml:space="preserve">quorum homo-
              <lb/>
            logæ diametri ſint ipſæ applicatæ prædicti Acuminati, &</s>
            <s xml:id="echoid-s7779" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7780" xml:space="preserve"/>
          </p>
          <figure number="228">
            <image file="0278-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0278-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s7781" xml:space="preserve">Eſto planum quodcunque Acuminatum A B C, cuius baſis A C, dia-
              <lb/>
            meter B D, vertex B, & </s>
            <s xml:id="echoid-s7782" xml:space="preserve">ipſa A C, ſit vel diameter circuli, aut Ellipſis,
              <lb/>
            vel cuiuſcun que ipſarum figurarum portionis, aut diameter Parabolæ,
              <lb/>
            vel Hyperbolæ, vel cuiuslibet alij plani Acuminati A E C F, quod tan-
              <lb/>
            quam baſis, ad quemlibet inclinationis angulum cum plano A B C </s>
          </p>
        </div>
      </text>
    </echo>
Impressum