Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Page concordance

< >
Scan Original
21 321
22 322
23 323
24 324
25
26
27
28 325
29 326
30
31
32
33 327
34 328
35
36
37
38 329
39 330
40 331
41 332
42 333
43 334
44 335
45 336
46 337
47 338
48 339
49 340
50
< >
page |< < (325) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div31" type="section" level="1" n="16">
          <p>
            <s xml:id="echoid-s321" xml:space="preserve">
              <pb o="325" file="0027" n="28" rhead="HYPERB. ELLIPS. ET CIRC."/>
            tione A B C punctum L. </s>
            <s xml:id="echoid-s322" xml:space="preserve">Dico igitur portionem ad inſcri-
              <lb/>
            ptum ſibi triangulum A B C eam habere rationem quam duæ
              <lb/>
            tertiæ E D ad F L. </s>
            <s xml:id="echoid-s323" xml:space="preserve">Conſtituatur enim ut ſupra triangulus
              <lb/>
            K F H, cujus nimirum baſis K H ſit baſi A C æqualis & </s>
            <s xml:id="echoid-s324" xml:space="preserve">
              <lb/>
            parallela, & </s>
            <s xml:id="echoid-s325" xml:space="preserve">F G quæ à vertice ad mediam baſin pertingit
              <lb/>
            poſſit rectangulum B D E: </s>
            <s xml:id="echoid-s326" xml:space="preserve">& </s>
            <s xml:id="echoid-s327" xml:space="preserve">centrum gravitatis trianguli
              <lb/>
            K F H ſit M punctum, ſumptâ ſcilicet F M æquali duabus
              <lb/>
              <note symbol="1" position="right" xlink:label="note-0027-01" xlink:href="note-0027-01a" xml:space="preserve">14. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquip.</note>
            tertiis lineæ F G .</s>
            <s xml:id="echoid-s328" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s329" xml:space="preserve">Triangulus igitur K F H eſt ad triangulum A B C, ut
              <lb/>
            F G ad B D; </s>
            <s xml:id="echoid-s330" xml:space="preserve">ut autem F G ad B D, ſic eſt E D ad F G,
              <lb/>
            quia quadratum F G æquale eſt B D E rectangulo; </s>
            <s xml:id="echoid-s331" xml:space="preserve">& </s>
            <s xml:id="echoid-s332" xml:space="preserve">ut
              <lb/>
            E D ad F G, ſic ſunt duæ tertiæ E D ad duas tertias F G,
              <lb/>
            id eſt, ad F M. </s>
            <s xml:id="echoid-s333" xml:space="preserve">Ergo triangulus K F H ad triangulum A B C,
              <lb/>
            ſicut duæ tertiæ E D ad F M. </s>
            <s xml:id="echoid-s334" xml:space="preserve">Portio autem A B C eſt ad
              <lb/>
            triangulum K F H, ut F M ad F L , quoniam
              <note symbol="2" position="right" xlink:label="note-0027-02" xlink:href="note-0027-02a" xml:space="preserve">7. lib. 1.
                <lb/>
              Archim. de
                <lb/>
              Æquipond.</note>
            brium eorum eſt in F , & </s>
            <s xml:id="echoid-s335" xml:space="preserve">centra gravitatis ſingulorum
              <note symbol="3" position="right" xlink:label="note-0027-03" xlink:href="note-0027-03a" xml:space="preserve">Theor. 5. h.</note>
            cta L & </s>
            <s xml:id="echoid-s336" xml:space="preserve">M; </s>
            <s xml:id="echoid-s337" xml:space="preserve">Ergo ex æquali in proportione perturbata,
              <lb/>
            erit portio A B C ad A B C triangulum, ſicut duæ tertiæ
              <lb/>
            E D ad F L .</s>
            <s xml:id="echoid-s338" xml:space="preserve"/>
          </p>
          <note symbol="4" position="right" xml:space="preserve">23. lib. 5.
            <lb/>
          Elem.</note>
          <p>
            <s xml:id="echoid-s339" xml:space="preserve">Sit nunc portio A B C dimidiâ figurâ major. </s>
            <s xml:id="echoid-s340" xml:space="preserve">Dico eam
              <lb/>
              <note position="right" xlink:label="note-0027-05" xlink:href="note-0027-05a" xml:space="preserve">TAB. XXXVI.
                <lb/>
              Fig. 1. 2.</note>
            rurſus ad inſcriptum triangulum eam habere rationem, quam
              <lb/>
            duæ tertiæ E D ad F L.</s>
            <s xml:id="echoid-s341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s342" xml:space="preserve">Ponatur enim portionis reliquæ A E C centrum gravitatis
              <lb/>
            H punctum, & </s>
            <s xml:id="echoid-s343" xml:space="preserve">jungantur A E, E C. </s>
            <s xml:id="echoid-s344" xml:space="preserve">Igitur per ea quæ jam
              <lb/>
            oſtendimus, erit portio A E C ad A E C triangulum, ut
              <lb/>
            duæ tertiæ B D ad F H; </s>
            <s xml:id="echoid-s345" xml:space="preserve">verùm ut triangulus A E C ad
              <lb/>
            triangulum A B C, ſic eſt E D ad B D, ſive duæ tertiæ
              <lb/>
            E D ad duas tertias B D; </s>
            <s xml:id="echoid-s346" xml:space="preserve">ex æquali igitur in proportione
              <lb/>
            perturbata, erit ſicut portio A E C ad triangulum A B C,
              <lb/>
            ita duæ tertiæ E D ad F H . </s>
            <s xml:id="echoid-s347" xml:space="preserve">Sed ut portio A B C
              <note symbol="5" position="right" xlink:label="note-0027-06" xlink:href="note-0027-06a" xml:space="preserve">23. lib. 5.
                <lb/>
              Elem.</note>
            A E C portionem, ita eſt F H ad F L , quoniam
              <note symbol="6" position="right" xlink:label="note-0027-07" xlink:href="note-0027-07a" xml:space="preserve">8. lib. 1.
                <lb/>
              Arch. de
                <lb/>
              Æquipond.</note>
            figuræ centrum gravitatis eſt F, centraque dictarum portio-
              <lb/>
            num L & </s>
            <s xml:id="echoid-s348" xml:space="preserve">H; </s>
            <s xml:id="echoid-s349" xml:space="preserve">Ergo iterum ex æquali in proportione per-
              <lb/>
            turbata, erit portio A B C ad A B C triangulum, ut duæ
              <lb/>
            tertiæ E D ad F L. </s>
            <s xml:id="echoid-s350" xml:space="preserve">Omnis igitur Ellipſis vel circuli portio
              <lb/>
            &</s>
            <s xml:id="echoid-s351" xml:space="preserve">c. </s>
            <s xml:id="echoid-s352" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s353" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum