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

Table of contents

< >
[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)
[321.] COROLL. I.
Page: 282 (96)
[322.] SCHOLIVM II.
Page: 282 (96)
[323.] COROLL. II.
Page: 282 (96)
[324.] SCHOLIVM III.
Page: 283 (97)
[325.] COROLL. III.
Page: 283 (97)
[326.] THEOR. XLIII. PROP. LXX.
Page: 284 (98)
[327.] COROLL.
Page: 286 (100)
[328.] THEOR. XLIV. PROP. LXXI.
Page: 286 (100)
[329.] COROLL.
Page: 287 (101)
[330.] THEOR. XLV. PROP. LXXII.
Page: 288 (102)
[331.] SCHOLIVM.
Page: 288 (102)
[332.] THEOR. XLVI. PROP. LXXIII.
Page: 288 (102)
[333.] THEOR. XLVII. PROP. LXXIV.
Page: 288 (102)
[334.] MONITVM.
Page: 290 (104)
[335.] LEMMA XIV. PROP. LXXV.
Page: 290 (104)
[336.] SCHOLIVM.
Page: 291 (105)
[337.] LEMMA XV. PROP. LXXVI.
Page: 292 (106)
[338.] THEOR. XLVIII. PROP. LXXVII.
Page: 292 (106)
[339.] MONITVM.
Page: 293 (107)
[340.] THEOR. IL. PROP. LXXVIII.
Page: 294 (108)
< >
page |< < (108) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div851" type="section" level="1" n="339">
          <p style="it">
            <s xml:id="echoid-s8205" xml:space="preserve">
              <pb o="108" file="0294" n="294" rhead=""/>
            vel Conoidis, ſiue Sphær
              <unsure/>
            æ, aut Sphæroidis portiones inter ſe æquales eſ-
              <lb/>
            ſent: </s>
            <s xml:id="echoid-s8206" xml:space="preserve">vnde mox venit nobis in animum perpendendi, an illæ inter ſe
              <lb/>
            æqualitatem ſortirentur, quarum portiones planæ genitricium ſectionum
              <lb/>
            ad plana baſium erectæ, nempe quarum recti Canones inter ſe pariter
              <lb/>
            æquales eſſent, prout æquales inſpexeramus in Conoide Paraboli co, ex
              <lb/>
            25. </s>
            <s xml:id="echoid-s8207" xml:space="preserve">Archimedis in libro de Conoid. </s>
            <s xml:id="echoid-s8208" xml:space="preserve">& </s>
            <s xml:id="echoid-s8209" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s8210" xml:space="preserve">Res quidem ex cogi-
              <lb/>
            tatione ſuccesſit, tunc enim in ſequentem vniuerſalem demonſtr ationem
              <lb/>
            incidimus, cuius, atque ſuperioris quadrageſimæ propoſitionis, ſolæ enun-
              <lb/>
            ciationes, cum præſtantisſimis Geometris, Galileo, ac Torricellio com-
              <lb/>
            municatæ, tantos Viros, meruerunt habere laudatores.</s>
            <s xml:id="echoid-s8211" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div852" type="section" level="1" n="340">
          <head xml:id="echoid-head349" xml:space="preserve">THEOR. IL. PROP. LXXVIII.</head>
          <p>
            <s xml:id="echoid-s8212" xml:space="preserve">Solidæ portiones eiuſdem Coni recti, vel Conoidis Parabo-
              <lb/>
            lici, aut Hyperbolici, ſiue Sphæræ, aut Sphæroidis oblongi,
              <lb/>
            vel prolati, quarum recti Canones ſint æquales, inter ſe quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s8213" xml:space="preserve">æquales ſunt.</s>
            <s xml:id="echoid-s8214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8215" xml:space="preserve">ESto Coni recti, vt in prima figura, vel Conoidis Parabolici, aut Hy-
              <lb/>
            perbolici, ſiue Sphæræ, aut Sphæroidis oblongi, vel prolati, vt in ſe-
              <lb/>
            cunda, quorum axis B D, quælibet ſectio per axem A B C, quæ erit
              <note symbol="a" position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">12. Ar-
                <lb/>
              chim. de
                <lb/>
              Conoid.</note>
            trix dati ſolidi, à qua demantur duæ æquales portiones planæ A B C, E F
              <lb/>
            G (hoc autem fieri poſſe manifeſtum iam eſt) quarum baſes ſint A C,
              <note symbol="b" position="left" xlink:label="note-0294-02" xlink:href="note-0294-02a" xml:space="preserve">ex 40. &
                <lb/>
              ex 75. h.</note>
            G bifariam ſectæ in H, I, & </s>
            <s xml:id="echoid-s8216" xml:space="preserve">ipſarum altera A C ſit axi perpendicularis,
              <lb/>
            altera verò vtcunque inclinata; </s>
            <s xml:id="echoid-s8217" xml:space="preserve">& </s>
            <s xml:id="echoid-s8218" xml:space="preserve">per eas concipiantur duci plana A L C,
              <lb/>
            E M G ad planum per axem A B C erecta, auferentia portiones ſolidas A
              <lb/>
            B C, E F G, quarum recti Canones erunt ipſæ portiones planæ A B C, E
              <lb/>
            F G: </s>
            <s xml:id="echoid-s8219" xml:space="preserve">patet ſectionem A L C circulum eſſe, cuius diameter A C,
              <note symbol="c" position="left" xlink:label="note-0294-03" xlink:href="note-0294-03a" xml:space="preserve">ex 1. pri-
                <lb/>
              mihuius,
                <lb/>
              & ex 12.
                <lb/>
              13. 14. 15.
                <lb/>
              Archim.
                <lb/>
              de Co-
                <lb/>
              noid. &c.</note>
            H, atque E M G eſſe Ellipſim, cuius axis maior, in Cono, vel in Conoide
              <lb/>
            Parabolico, aut Hyperbolico, atque in Sphæroide oblongo, erit ipſa baſis
              <lb/>
            E G, ſed in prolato erit minor axis, vbique autem centrum I. </s>
            <s xml:id="echoid-s8220" xml:space="preserve">Dico
              <note symbol="d" position="left" xlink:label="note-0294-04" xlink:href="note-0294-04a" xml:space="preserve">ibidem.</note>
            iuſmodi ſolidas portiones A B C, E F G inter ſe æquales eſſe.</s>
            <s xml:id="echoid-s8221" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8222" xml:space="preserve">Secetur iterum datum ſolidum A B C, plano per punctum I tranſeunte,
              <lb/>
            & </s>
            <s xml:id="echoid-s8223" xml:space="preserve">ad axem B D erecto, ſiue plano A L C æquidiſtanti, quod in ſolido
              <lb/>
            efficiet pariter circulum N M O, cuius centrum P in axe, & </s>
            <s xml:id="echoid-s8224" xml:space="preserve">diameter
              <note symbol="e" position="left" xlink:label="note-0294-05" xlink:href="note-0294-05a" xml:space="preserve">12. ibid.</note>
            O, quæ ipſi A C æquidiſtabit, communis autem ſectio recti plani N
              <note symbol="f" position="left" xlink:label="note-0294-06" xlink:href="note-0294-06a" xml:space="preserve">16. Vnd.
                <lb/>
              Elem.</note>
            O, cum alio plano E M G, erit recta M I, quæ quidem recta erit ad
              <note symbol="g" position="left" xlink:label="note-0294-07" xlink:href="note-0294-07a" xml:space="preserve">3. ibid.</note>
              <note symbol="h" position="left" xlink:label="note-0294-08" xlink:href="note-0294-08a" xml:space="preserve">19. ibid.</note>
            num per axem A B C (cum ea ſit communis ſectio duorum planorum ad
              <lb/>
            idem planum per axem erectorum) ideoque tùm ad circuli diametrum N
              <lb/>
            O, tum ad E G axem Ellipſis, erit perpendicularis, & </s>
            <s xml:id="echoid-s8225" xml:space="preserve">in Cono, aut Co-
              <lb/>
            noide, vel Sphæroide oblongo erit ſemi- axis minor, in prolato verò ſemi-
              <lb/>
            axis maior. </s>
            <s xml:id="echoid-s8226" xml:space="preserve">Et quoniam M I ad diametrum N O ſemi - circuli N M O eſt
              <lb/>
            perpendicularis, erit quadratum M I ęquale rectangulo NIO, ſed & </s>
            <s xml:id="echoid-s8227" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum