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

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            <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>
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