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

Table of contents

< >
[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)
[311.] THEOR. XLII. PROP. LXVIII.
Page: 274 (88)
[312.] COROLL. I.
Page: 276 (90)
[313.] COROLL. II.
Page: 276 (90)
[314.] MONITVM.
Page: 276 (90)
[315.] DEFINITIONES. I.
Page: 278 (92)
[316.] II.
Page: 278 (92)
[317.] III.
Page: 279 (93)
[318.] IIII.
Page: 279 (93)
[319.] PROBL. XIV. PROP. LXIX.
Page: 280 (94)
[320.] SCHOLIVM I.
Page: 282 (96)
< >
page |< < (109) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div852" type="section" level="1" n="340">
          <p>
            <s xml:id="echoid-s8227" xml:space="preserve">
              <pb o="109" file="0295" n="295" rhead=""/>
            dratum A H eidem rectangulo NIO eſt æquale, cum ſit NIO
              <note symbol="a" position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">77. h.</note>
            ad A C, & </s>
            <s xml:id="echoid-s8228" xml:space="preserve">per I punctum medium baſis E G ducta, &</s>
            <s xml:id="echoid-s8229" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8230" xml:space="preserve">ergo, & </s>
            <s xml:id="echoid-s8231" xml:space="preserve">quadra-
              <lb/>
            tum M I ipſi A H, ſeu linea M I lineæ A H æqualis erit, ſed Ellipſis E M
              <lb/>
            G ad circulum A L C eſt vt rectangulum ſub G I, & </s>
            <s xml:id="echoid-s8232" xml:space="preserve">I M ad
              <note symbol="b" position="right" xlink:label="note-0295-02" xlink:href="note-0295-02a" xml:space="preserve">ex 6. Ar-
                <lb/>
              chim. de
                <lb/>
              Conoid.</note>
            ex A H, vel vt linea G I ad A H (ob communem altitudinem M I) vel
              <lb/>
            ſumptis duplis, vt E G ad A C, ergo baſis portionis ſolidę E F G, ad baſim
              <lb/>
            portionis ſolidę A B C, eſt vt E G baſis Canonis E F G, ad A C baſim Ca-
              <lb/>
            nonis A B C; </s>
            <s xml:id="echoid-s8233" xml:space="preserve">verùm vt E G ad A C, ita eſt reciprocè altitudo
              <note symbol="c" position="right" xlink:label="note-0295-03" xlink:href="note-0295-03a" xml:space="preserve">65. h.</note>
              <figure xlink:label="fig-0295-01" xlink:href="fig-0295-01a" number="240">
                <image file="0295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0295-01"/>
              </figure>
            A B C ad altitudinem Canonis E F G (cum ipſi Canones ęquales facti ſint)
              <lb/>
            atque Canonum altitudines eædem ſunt cum altitudinibus ſolidarum
              <note symbol="d" position="right" xlink:label="note-0295-04" xlink:href="note-0295-04a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            tionum, vnde baſis E M G ad baſim A L C erit reciprocè, vt altitudo ſoli-
              <lb/>
            dæ portionis A B C ad altitudinem ſolidæ E F G: </s>
            <s xml:id="echoid-s8234" xml:space="preserve">hæ autem portiones ſunt
              <lb/>
            ſolida Acuminata proportionalia, eò quod ipſarum Canones ſint
              <note symbol="e" position="right" xlink:label="note-0295-05" xlink:href="note-0295-05a" xml:space="preserve">Coroll.
                <lb/>
              70 h.</note>
            atque baſes altitudinibus ſunt reciprocæ, ergo huiuſmodi portiones ſolidæ
              <lb/>
            A B C, E F G ſunt æquales. </s>
            <s xml:id="echoid-s8235" xml:space="preserve">Quod demonſtrandum erat.</s>
            <s xml:id="echoid-s8236" xml:space="preserve"/>
          </p>
          <note symbol="f" position="right" xml:space="preserve">74. h.</note>
          <p style="it">
            <s xml:id="echoid-s8237" xml:space="preserve">Sed hoc idem, tribus proximè præcedentibus propoſitionibus omisſis,
              <lb/>
            ſuper nouo diagrammate ſic oſtendere conabimur</s>
          </p>
        </div>
        <div xml:id="echoid-div855" type="section" level="1" n="341">
          <head xml:id="echoid-head350" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s8238" xml:space="preserve">SIt Conus rectus, vt in prima figura, vel aliud quodcunque prædictorum
              <lb/>
            ſolidorum, vt in ſecunda, circa axim A B, & </s>
            <s xml:id="echoid-s8239" xml:space="preserve">ſectio per axim ſit E A
              <lb/>
            D, quæ genitrix erit dati ſolidi, à qua demptæ ſint duæ quælibet
              <note symbol="g" position="right" xlink:label="note-0295-07" xlink:href="note-0295-07a" xml:space="preserve">ex 12.
                <lb/>
              Archim.
                <lb/>
              de Co-
                <lb/>
              noid. &c.</note>
            nes planæ æquales C A D, E A F, quarum baſes ſint C D, E F, & </s>
            <s xml:id="echoid-s8240" xml:space="preserve">per ip-
              <lb/>
            ſas ducantur piana ſecantia data ſolida, & </s>
            <s xml:id="echoid-s8241" xml:space="preserve">ad ipſum planum per axem E A
              <lb/>
            D erecta, circulos, vel Ellipſes E O F, C P D deſcribentia (quarum
              <note symbol="h" position="right" xlink:label="note-0295-08" xlink:href="note-0295-08a" xml:space="preserve">ex pri-
                <lb/>
              ma primi
                <lb/>
              huius, &
                <lb/>
              ex 13. 14.
                <lb/>
              15. Arch.
                <lb/>
              de Co-
                <lb/>
              noid. &c.</note>
            iores axes in Cono, Conoide Parabolico, Hyperbolico, & </s>
            <s xml:id="echoid-s8242" xml:space="preserve">Sphæroide </s>
          </p>
        </div>
      </text>
    </echo>
Impressum