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

Table of contents

< >
[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)
[301.] PROBL. X. PROP. LIX.
Page: 261 (77)
[302.] PROBL. XI. PROP. LX.
Page: 262 (78)
[303.] PROBL. XII. PROP. LXI.
Page: 262 (78)
[304.] PROBL. XIII. PROP. LXII.
Page: 265 (79)
[305.] MONITVM.
Page: 268 (82)
[306.] THEOR. XXXVIII. PROP. LXIII.
Page: 268 (82)
[307.] THEOR. XXXIX. PROP. LXIV.
Page: 270 (84)
[308.] THEOR. XL. PROP. LXV.
Page: 271 (85)
[309.] THEOR. XLI. PROP. LXVI.
Page: 273 (87)
[310.] LEMMA XIII. PROP. LXVII.
Page: 274 (88)
< >
page |< < (98) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div822" type="section" level="1" n="325">
          <pb o="98" file="0284" n="284" rhead=""/>
        </div>
        <div xml:id="echoid-div823" type="section" level="1" n="326">
          <head xml:id="echoid-head335" xml:space="preserve">THEOR. XLIII. PROP. LXX.</head>
          <p>
            <s xml:id="echoid-s7933" xml:space="preserve">Portiones eiuſdem, vel diuerſorum Conorum, aut Conoidum
              <lb/>
            Parabolicorum, ſunt ſolida Acuminata proportionalia. </s>
            <s xml:id="echoid-s7934" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s7935" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7936" xml:space="preserve">Portiones eiuſdem, vel diuerſorum Conoidum Hyperbolico-
              <lb/>
            rum, vel Sphærarum, aut Sphæroidum, quarum ſegmenta diame-
              <lb/>
            trorum in portionibus genitricium earum ſectionum ad baſes ere-
              <lb/>
            ctis intercepta, ad ſuas ſemi-diametros eandem homologam ha-
              <lb/>
            beant rationem, ſunt pariter ſolida Acuminata proportionalia.</s>
            <s xml:id="echoid-s7937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7938" xml:space="preserve">SInt primò duæ quæcunque portiones A B C, D E F eiuſdem, vel diuer-
              <lb/>
            ſorum Conorum, vt in prima figura, vel eiuſdem, aut diu erſorum Co-
              <lb/>
            noidum Parabolicorum, vt in ſecunda, quarum axes ſint B G, E H, baſes
              <lb/>
            verò circuli, aut Ellipſes A C, D F, ipſæque portiones ſolidæ, (quæ iam
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0284-01" xlink:href="note-0284-01a" xml:space="preserve">69. h.</note>
            per primum Scholium precedentis ſunt ſolida Acuminata) planis per eorum
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0284-02" xlink:href="note-0284-02a" xml:space="preserve">ibid. 1.
                <lb/>
              Schol.</note>
            ſolidorum axes ductis ad baſes rectis ſecentur, & </s>
            <s xml:id="echoid-s7939" xml:space="preserve">ſient in ſolidis recti
              <note symbol="c" position="left" xlink:label="note-0284-03" xlink:href="note-0284-03a" xml:space="preserve">ex 12.
                <lb/>
              Archim.
                <lb/>
              de Co-
                <lb/>
              noid. &
                <lb/>
              Comand.
                <lb/>
              ſuppleta.</note>
            nones A B C, D E F, qui erunt portiones ſectionum ſolida & </s>
            <s xml:id="echoid-s7940" xml:space="preserve">communes ſectiones ipſorum cum baſibus erunt rectæ A C, D F, quæ circulorum, aut Ellipſium erunt axes. </s>
            <s xml:id="echoid-s7941" xml:space="preserve">Dico in vtraque ſigura ſolidas por- tiones A B C, D E F eſſe Acuminata ſolida proportionalia.</s>
            <s xml:id="echoid-s7942" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7943" xml:space="preserve">Etenim horum Acuminato-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-0284-04" xlink:href="note-0284-04a" xml:space="preserve">3. vnd.
                <lb/>
              Elem.</note>
              <figure xlink:label="fig-0284-01" xlink:href="fig-0284-01a" number="233">
                <image file="0284-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0284-01"/>
              </figure>
            rum ſolidorum axibus B G, E
              <lb/>
            H proportionaliter vtcunque
              <lb/>
              <note symbol="e" position="left" xlink:label="note-0284-05" xlink:href="note-0284-05a" xml:space="preserve">ex 13.
                <lb/>
              Archim.
                <lb/>
              ibidem.</note>
            ſectis in I, L, ducantur per I,
              <lb/>
            L plana M N, O P baſibus A
              <lb/>
            C, D F æquidiſtantia, quæ in
              <lb/>
            ſolidis efficient ſectiones ipſa-
              <lb/>
            rum baſibus ſimiles earumq;</s>
            <s xml:id="echoid-s7944" xml:space="preserve">
              <note symbol="f" position="left" xlink:label="note-0284-06" xlink:href="note-0284-06a" xml:space="preserve">ex Co-
                <lb/>
              roll. 15. ib.</note>
            communes ſectiones cum pla-
              <lb/>
              <note symbol="g" position="left" xlink:label="note-0284-07" xlink:href="note-0284-07a" xml:space="preserve">3. vnd.
                <lb/>
              Elem.</note>
            nis A B C, D E F erunt re- ctæ M N, O P ipſis A C, D
              <lb/>
              <note symbol="h" position="left" xlink:label="note-0284-08" xlink:href="note-0284-08a" xml:space="preserve">16. ib.</note>
            F parallelæ, & </s>
            <s xml:id="echoid-s7945" xml:space="preserve">earundem ſi- milium ſectionum homologæ
              <lb/>
            diametri.</s>
            <s xml:id="echoid-s7946" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7947" xml:space="preserve">Iam cum ſit G B ad B I, vt
              <lb/>
            H E ad E L, ob conſtructio-
              <lb/>
            nem, ſitque in prima figura A
              <lb/>
            C ad M N, vt G B ad B I; </s>
            <s xml:id="echoid-s7948" xml:space="preserve">& </s>
            <s xml:id="echoid-s7949" xml:space="preserve">
              <lb/>
            D F ad O P, vt H E ad E L (cum Canones A B C, D E F ſint triangula)
              <lb/>
            erit A C ad M N vt D F ad O P, & </s>
            <s xml:id="echoid-s7950" xml:space="preserve">quadratum A C ad M N, vt
              <lb/>
            quadratum D F ad O P. </s>
            <s xml:id="echoid-s7951" xml:space="preserve">In ſecunda verò eſt quadratum A C ad M N, vt
              <lb/>
            re cta G B ad B I (cum Canon A B C ſit portio Parabolæ) vel vt recta H
              <lb/>
              <note symbol="i" position="left" xlink:label="note-0284-09" xlink:href="note-0284-09a" xml:space="preserve">Coroll.
                <lb/>
              7. Arch.
                <lb/>
              ibid.</note>
            E ad E L, per conſtructionem, vel vt quadratum D E ad O P: </s>
            <s xml:id="echoid-s7952" xml:space="preserve">eſt ergo in
              <lb/>
            vtraque ſigura, vt quadratum A C ad M N, vel vt circulus, aut </s>
          </p>
        </div>
      </text>
    </echo>
Impressum