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 |< < (322) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div24" type="section" level="1" n="14">
          <p>
            <s xml:id="echoid-s234" xml:space="preserve">
              <pb o="322" file="0022" n="22" rhead="THEOR. DE QUADRAT."/>
            ita eſt quadratum Z Y ad Λ Y quadratum. </s>
            <s xml:id="echoid-s235" xml:space="preserve">Quare & </s>
            <s xml:id="echoid-s236" xml:space="preserve">per con-
              <lb/>
            verſionem rationis, ſicut rectangulum B D E ad differenti-
              <lb/>
            am rectangulorum B D E, B P E, ita quadratum Z Y ad
              <lb/>
            differentiam quadratorum Z Y, Λ Y. </s>
            <s xml:id="echoid-s237" xml:space="preserve">Eſt autem differentia
              <lb/>
            rectangulorum B D E, B P E, æqualis rectangulo S D P,
              <lb/>
            ſicut lemmate præmiſſo demonſtratum eſt; </s>
            <s xml:id="echoid-s238" xml:space="preserve">differentia verò
              <lb/>
            quadratorum Z Y, Λ Y, æqualis quadrato Z Λ & </s>
            <s xml:id="echoid-s239" xml:space="preserve">duobus
              <lb/>
            rectangulis Z Λ Y , ſive quod idem eſt, rectangulis Z Λ
              <note symbol="3" position="left" xlink:label="note-0022-01" xlink:href="note-0022-01a" xml:space="preserve">4. lib. 2.
                <lb/>
              Elem.</note>
            Z Λ Y bis ſumptis, hoc eſt, duplo rectangulo ſub Z Λ,
              <lb/>
            X Y. </s>
            <s xml:id="echoid-s240" xml:space="preserve">Itaque ſicut eſt rectangulum B D E ad rectangulum
              <lb/>
            S D P, ita quadratum Z Y ad duplum rectangulum ſub
              <lb/>
            X Y, Z Λ. </s>
            <s xml:id="echoid-s241" xml:space="preserve">quare cum rectangulum B D E quadrato F G
              <lb/>
            æquale ſit , ideoque & </s>
            <s xml:id="echoid-s242" xml:space="preserve">quadrato Z Y, erit quoque
              <note symbol="4" position="left" xlink:label="note-0022-02" xlink:href="note-0022-02a" xml:space="preserve">Ex conſtr.</note>
            gulum S D P æquale duplo rectangulo ſub X Y, Z Λ .</s>
            <s xml:id="echoid-s243" xml:space="preserve">
              <note symbol="5" position="left" xlink:label="note-0022-03" xlink:href="note-0022-03a" xml:space="preserve">14. 5. E-
                <lb/>
              lem.</note>
            Quia verò F punctum dividit B E per medium, ſuntque
              <lb/>
            æquales B P, E S, etiam F P, F S æquales erunt, unde
              <lb/>
            additi utrique F D, erit S D æqualis toti P F D id eſt
              <lb/>
            Δ Y Ω: </s>
            <s xml:id="echoid-s244" xml:space="preserve">ſed Δ Y Ω dupla eſt lineæ V Y, quia bis continet
              <lb/>
            utramque Y Δ, Δ V in hyperbole, in ellipſi verò & </s>
            <s xml:id="echoid-s245" xml:space="preserve">circulo
              <lb/>
            bis utramque V Ω & </s>
            <s xml:id="echoid-s246" xml:space="preserve">Ω Y; </s>
            <s xml:id="echoid-s247" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s248" xml:space="preserve">S D dupla V Y, ideo-
              <lb/>
            que rectangulum S D P æquale duplo rectangulo ſub Y V,
              <lb/>
            Ω Δ. </s>
            <s xml:id="echoid-s249" xml:space="preserve">Sed idem rectangulum S D P æquale oſtenſum fuit
              <lb/>
            duplo rectangulo ſub X Y, Z Λ; </s>
            <s xml:id="echoid-s250" xml:space="preserve">ergo æquale eſt rectangu-
              <lb/>
            lum ſub Y V, Ω Δ, rectangulo ſub X Y, Z Λ. </s>
            <s xml:id="echoid-s251" xml:space="preserve">Eſt itaque
              <lb/>
            Y V ad Y X, ut Λ Z ad Ω Δ ; </s>
            <s xml:id="echoid-s252" xml:space="preserve">verùm ut Λ Z ad Ω Δ,
              <note symbol="6" position="left" xlink:label="note-0022-04" xlink:href="note-0022-04a" xml:space="preserve">16. l. 6. 6.
                <lb/>
              Elem.</note>
            eſt parallelogrammum Σ T ad R Q; </s>
            <s xml:id="echoid-s253" xml:space="preserve">itaque & </s>
            <s xml:id="echoid-s254" xml:space="preserve">Y V eſt ad
              <lb/>
            Y Χ ut parallelogrammum Σ T ad R Q parallelogr. </s>
            <s xml:id="echoid-s255" xml:space="preserve">Sunt
              <lb/>
            autem puncta X & </s>
            <s xml:id="echoid-s256" xml:space="preserve">V centra gravitatis dictorum parallelo-
              <lb/>
            grammorum; </s>
            <s xml:id="echoid-s257" xml:space="preserve">ergo magnitudinis ex utroque parallelogram-
              <lb/>
            mo compoſitæ centrum gravitatis eſt punctum Y . </s>
            <s xml:id="echoid-s258" xml:space="preserve">
              <note symbol="7" position="left" xlink:label="note-0022-05" xlink:href="note-0022-05a" xml:space="preserve">7. lib. 1.
                <lb/>
              A@chim. de
                <lb/>
              Æquip.</note>
            ratione oſtendi poteſt de reliquis omnibus parallelogrammis,
              <lb/>
            quod duorum quorumlibet oppoſitorum centrum gravitatis
              <lb/>
            eſt in linea O Ξ. </s>
            <s xml:id="echoid-s259" xml:space="preserve">Ergo totius magnitudinis quæ ex duabus
              <lb/>
            ſiguris utrimque ordinatè circumſoriptis componitur, centr.
              <lb/>
            </s>
            <s xml:id="echoid-s260" xml:space="preserve">gravitatis in eadem O Ξ reper@ri neceſſe eſt. </s>
            <s xml:id="echoid-s261" xml:space="preserve">Sed ejuſdem com-
              <lb/>
            poſitæ magnitudinis centrum gravit. </s>
            <s xml:id="echoid-s262" xml:space="preserve">eſt quoque in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum