Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div113" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s4952" xml:space="preserve">
              <pb o="78" file="0096" n="96" rhead=""/>
            ceſcit ex eo, quod earum omnium ad ſe proportiones in eodem ubique
              <lb/>
            modo fundantur in una ratione I ad R. </s>
            <s xml:id="echoid-s4953" xml:space="preserve">verbis, & </s>
            <s xml:id="echoid-s4954" xml:space="preserve">Schematis effin-
              <lb/>
            gendis parco. </s>
            <s xml:id="echoid-s4955" xml:space="preserve">Pro ſequentibus hæc adjungo _Lemmatia._</s>
            <s xml:id="echoid-s4956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4957" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s4958" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4959" xml:space="preserve">Sint tria quanta A, B, C (quorum maximum A) ſe dein-
              <lb/>
            ceps æqualiter excedentia; </s>
            <s xml:id="echoid-s4960" xml:space="preserve">ſint etiam altera totidem M, N, O; </s>
            <s xml:id="echoid-s4961" xml:space="preserve">& </s>
            <s xml:id="echoid-s4962" xml:space="preserve">
              <lb/>
            ſit A. </s>
            <s xml:id="echoid-s4963" xml:space="preserve">B:</s>
            <s xml:id="echoid-s4964" xml:space="preserve">: MN; </s>
            <s xml:id="echoid-s4965" xml:space="preserve">ac B, C:</s>
            <s xml:id="echoid-s4966" xml:space="preserve">: N, O; </s>
            <s xml:id="echoid-s4967" xml:space="preserve">dico fore quoque tria M, N,
              <lb/>
            O in ratione continua _Aritbmetica._ </s>
            <s xml:id="echoid-s4968" xml:space="preserve">Nam ob A. </s>
            <s xml:id="echoid-s4969" xml:space="preserve">B:</s>
            <s xml:id="echoid-s4970" xml:space="preserve">: M. </s>
            <s xml:id="echoid-s4971" xml:space="preserve">N. </s>
            <s xml:id="echoid-s4972" xml:space="preserve">erit
              <lb/>
            diviſim A-B. </s>
            <s xml:id="echoid-s4973" xml:space="preserve">B:</s>
            <s xml:id="echoid-s4974" xml:space="preserve">: M-N. </s>
            <s xml:id="echoid-s4975" xml:space="preserve">N. </s>
            <s xml:id="echoid-s4976" xml:space="preserve">item ob B. </s>
            <s xml:id="echoid-s4977" xml:space="preserve">C:</s>
            <s xml:id="echoid-s4978" xml:space="preserve">: N. </s>
            <s xml:id="echoid-s4979" xml:space="preserve">O. </s>
            <s xml:id="echoid-s4980" xml:space="preserve">erit per
              <lb/>
            rationis converſionem B. </s>
            <s xml:id="echoid-s4981" xml:space="preserve">B-C:</s>
            <s xml:id="echoid-s4982" xml:space="preserve">: N. </s>
            <s xml:id="echoid-s4983" xml:space="preserve">N-O. </s>
            <s xml:id="echoid-s4984" xml:space="preserve">ergò erit ex æquo
              <lb/>
            A-B. </s>
            <s xml:id="echoid-s4985" xml:space="preserve">B-C:</s>
            <s xml:id="echoid-s4986" xml:space="preserve">: M-N. </s>
            <s xml:id="echoid-s4987" xml:space="preserve">N-O. </s>
            <s xml:id="echoid-s4988" xml:space="preserve">itaque cùm ſit ex Hypotheſi
              <lb/>
            A-B = B-C; </s>
            <s xml:id="echoid-s4989" xml:space="preserve">erit etiam M-N = N-O: </s>
            <s xml:id="echoid-s4990" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4991" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4992" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4993" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4994" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s4995" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4996" xml:space="preserve">In circuli quadrante ZQ trium arcuum ZG, ZH, ZI
              <lb/>
            Sinus recti F α, F β, F γ æqualiter creſcant (ut nempe ſit αβ = βγ)
              <lb/>
            dico fore Gα-Hβ&</s>
            <s xml:id="echoid-s4997" xml:space="preserve">lt;</s>
            <s xml:id="echoid-s4998" xml:space="preserve">Hβ-Iγ.</s>
            <s xml:id="echoid-s4999" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 115.</note>
          <p>
            <s xml:id="echoid-s5000" xml:space="preserve">Nam ducatur ſubtenſa GI ipſam Hβ ſecans, in X; </s>
            <s xml:id="echoid-s5001" xml:space="preserve">& </s>
            <s xml:id="echoid-s5002" xml:space="preserve">ſint XR,
              <lb/>
            IS ad FQ parallelæ patet ipſas GR, XS æquari hoc eſt fore
              <lb/>
            Gα-Xβ = Xβ-Iγ; </s>
            <s xml:id="echoid-s5003" xml:space="preserve">unde liquidum eſt eſſe Gα-Hβ&</s>
            <s xml:id="echoid-s5004" xml:space="preserve">lt;</s>
            <s xml:id="echoid-s5005" xml:space="preserve">Hβ
              <lb/>
            -Iγ: </s>
            <s xml:id="echoid-s5006" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5007" xml:space="preserve">E. </s>
            <s xml:id="echoid-s5008" xml:space="preserve">D.</s>
            <s xml:id="echoid-s5009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5010" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s5011" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5012" xml:space="preserve">Sunto concentrici bini circulorum quadrantes FZ X,
              <lb/>
            F ζ ξ; </s>
            <s xml:id="echoid-s5013" xml:space="preserve">& </s>
            <s xml:id="echoid-s5014" xml:space="preserve">ad FZ parallela ducatur recta quævis LG γ; </s>
            <s xml:id="echoid-s5015" xml:space="preserve">circulos inter-
              <lb/>
            ſecans punctis G, γ; </s>
            <s xml:id="echoid-s5016" xml:space="preserve">dico fore FZ - LG &</s>
            <s xml:id="echoid-s5017" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s5018" xml:space="preserve">Fζ-Lγ.</s>
            <s xml:id="echoid-s5019" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 116.</note>
          <p>
            <s xml:id="echoid-s5020" xml:space="preserve">Nam connexa FG circulum ζ γξ producta ſecet in T; </s>
            <s xml:id="echoid-s5021" xml:space="preserve">connectan-
              <lb/>
            túrque ſubtenſæ ZG, ζ T (hæc ipſam L γ ſecans in S) Patétque jam
              <lb/>
            rectas ZG, ζ T parallelas eſſe; </s>
            <s xml:id="echoid-s5022" xml:space="preserve">adeóque quadrangulum ZGSζ fore
              <lb/>
            parallelogrammum; </s>
            <s xml:id="echoid-s5023" xml:space="preserve">unde GS = Z ζ; </s>
            <s xml:id="echoid-s5024" xml:space="preserve">adeóque F ζ - LS = FZ
              <lb/>
            - LG. </s>
            <s xml:id="echoid-s5025" xml:space="preserve">ergo F ζ- L γ&</s>
            <s xml:id="echoid-s5026" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s5027" xml:space="preserve">FZ - LG: </s>
            <s xml:id="echoid-s5028" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5029" xml:space="preserve">E. </s>
            <s xml:id="echoid-s5030" xml:space="preserve">D.</s>
            <s xml:id="echoid-s5031" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5032" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s5033" xml:space="preserve">Sint jam tres radii paralleli MN, QR, VX, à ſe diſtantes
              <lb/>
            æqualiter (hoc eſt ut ductis N v, Rρ, Xξ ad axem AC perpendicu-
              <lb/>
            laribus ſit Xξ-Rρ = Rρ-Nv) & </s>
            <s xml:id="echoid-s5034" xml:space="preserve">ipſorum refracti cum axe
              <lb/>
            conveniant punctis K, L, O; </s>
            <s xml:id="echoid-s5035" xml:space="preserve">erit obliquiorum concurſibus interjectum
              <lb/>
              <note position="left" xlink:label="note-0096-03" xlink:href="note-0096-03a" xml:space="preserve">Fig. 117.</note>
            ſpatium OL majus ſpatio LK, quod à rectiorum occurſibus conti-
              <lb/>
            netur.</s>
            <s xml:id="echoid-s5036" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5037" xml:space="preserve">Nam ducantur NC, RC, XC circulo refractario occurrentes
              <lb/>
            punctis G, H, I; </s>
            <s xml:id="echoid-s5038" xml:space="preserve">& </s>
            <s xml:id="echoid-s5039" xml:space="preserve">ad has à refractarii centro F ducantur perpendi-
              <lb/>
            culares F α, F β, F γ; </s>
            <s xml:id="echoid-s5040" xml:space="preserve">& </s>
            <s xml:id="echoid-s5041" xml:space="preserve">quoniam triangula CXξ, CFγ ſimilia
              <lb/>
            ſunt; </s>
            <s xml:id="echoid-s5042" xml:space="preserve">erit Xξ. </s>
            <s xml:id="echoid-s5043" xml:space="preserve">CX:</s>
            <s xml:id="echoid-s5044" xml:space="preserve">: Fγ. </s>
            <s xml:id="echoid-s5045" xml:space="preserve">CF. </s>
            <s xml:id="echoid-s5046" xml:space="preserve">item ſimili de cauſa, eſt CR (CX).</s>
            <s xml:id="echoid-s5047" xml:space="preserve"/>
          </p>
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