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

Table of contents

< >
[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)
[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)
< >
page |< < (153) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div975" type="section" level="1" n="395">
          <p>
            <s xml:id="echoid-s9434" xml:space="preserve">
              <pb o="153" file="0339" n="339" rhead=""/>
            prop. </s>
            <s xml:id="echoid-s9435" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9436" xml:space="preserve">huius) ipſum erit minus aggregato extremarum poſt B F, F C; </s>
            <s xml:id="echoid-s9437" xml:space="preserve">qua-
              <lb/>
            re primum aggregatum, ad rectam B C minorem habebit rationem, quam
              <lb/>
            ſecundum aggregatum ad eandem B C, ſed primum ad B C eſt vt
              <note symbol="*" position="right" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">8. App.</note>
              <figure xlink:label="fig-0339-01" xlink:href="fig-0339-01a" number="270">
                <image file="0339-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0339-01"/>
              </figure>
            gatum triangulorum A E B, D E C ad triã-
              <lb/>
            gulum A C B, & </s>
            <s xml:id="echoid-s9438" xml:space="preserve">ſecundum ad eandem B
              <lb/>
            C eſt vt aggregatum triangulorum A F B,
              <lb/>
            G F C ad idem trian gulum A C B, quare
              <lb/>
            aggregatum A E B, D E C ad triangulum
              <lb/>
            A C B minorem habebit rationem quàm
              <lb/>
            aggregatum A F B, G F C ad idem trian-
              <lb/>
            gulum A C B, vnde aggregatum ex A E
              <lb/>
            B, D E C minus erit aggregato ex A F B,
              <lb/>
            G F C, ac propterea aggregatum triangu-
              <lb/>
            lorum ad punctum E erit _MINIMVM_.
              <lb/>
            </s>
            <s xml:id="echoid-s9439" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s9440" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div977" type="section" level="1" n="396">
          <head xml:id="echoid-head407" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s9441" xml:space="preserve">HInc, cum ſit vt ſubduplum ad ſubduplum, ita duplum ad duplum, ſi
              <lb/>
            compleantur parallelogramma B H, C I, ipſorum aggregatum erit
              <lb/>
            _MINIMVM_, &</s>
            <s xml:id="echoid-s9442" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9443" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div978" type="section" level="1" n="397">
          <head xml:id="echoid-head408" xml:space="preserve">PROBL. IV. PROP. X.</head>
          <p>
            <s xml:id="echoid-s9444" xml:space="preserve">Ijſdem poſitis, ac in præcedenti. </s>
            <s xml:id="echoid-s9445" xml:space="preserve">Si datum ſit in linea B C,
              <lb/>
            quodlibet aliud punctum F inter inuentum punctum E, & </s>
            <s xml:id="echoid-s9446" xml:space="preserve">extre-
              <lb/>
            mum B, & </s>
            <s xml:id="echoid-s9447" xml:space="preserve">oporteat aliud in ipſa punctum aſſignare, quæ ſimul
              <lb/>
            exhibeant aggregata triangulorum ad verticem inter ſe æqualia.</s>
            <s xml:id="echoid-s9448" xml:space="preserve"/>
          </p>
          <figure number="271">
            <image file="0339-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0339-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s9449" xml:space="preserve">ERigatur B G perpendicularis, & </s>
            <s xml:id="echoid-s9450" xml:space="preserve">æqualis ipſi B C, iungatur G C, & </s>
            <s xml:id="echoid-s9451" xml:space="preserve">
              <lb/>
            per F agatur F H æquidiſtans B G, & </s>
            <s xml:id="echoid-s9452" xml:space="preserve">fiat vt B F ad F H, ita F H ad
              <lb/>
            aliam F I, & </s>
            <s xml:id="echoid-s9453" xml:space="preserve">circa diametrum B I circulus deſcribatur rectam G C ſecans
              <lb/>
            in H, & </s>
            <s xml:id="echoid-s9454" xml:space="preserve">L, & </s>
            <s xml:id="echoid-s9455" xml:space="preserve">ex L ducatur L M parallela ad G B; </s>
            <s xml:id="echoid-s9456" xml:space="preserve">dico punctum M eſſe
              <lb/>
            quæſitum, hoc eſt ſi producantur A F, A M rectam C D ſecantes in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum