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

Table of Notes

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              <pb o="383" file="0095" n="101" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            utriuſque I G, G H ad ſexcuplam I G cum noncupla G H:
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            <s xml:id="echoid-s1869" xml:space="preserve">vel ſumptis horum trientibus ut decem tertiæ duarum ſimul
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            G I, G H ad duplam G I cum tripla G H. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">Eſt autem ea-
              <lb/>
            dem ratio linearum G I ad G H, hoc eſt, B A ad A M,
              <lb/>
            quæ B D ad D N, propter ſimiles triangulos B A M,
              <lb/>
            B D N. </s>
            <s xml:id="echoid-s1871" xml:space="preserve">Ergo etiam O H ad H I, ut {10/3} utriuſque ſimul
              <lb/>
            B D, D N ad duplam B D cum tripla D N; </s>
            <s xml:id="echoid-s1872" xml:space="preserve">hoc eſt, ut
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            {10/3} N C ad diametrum E C cum tripla D N. </s>
            <s xml:id="echoid-s1873" xml:space="preserve">Hac autem ra-
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            tione minor eſt ratio portionis A E B ad A E B triangulum .</s>
            <s xml:id="echoid-s1874" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">per præced.</note>
            Ergo dictæ portionis ad dictum triang. </s>
            <s xml:id="echoid-s1875" xml:space="preserve">minor quoque ratio
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            quam O H ad H I, hoc eſt, quam trianguli O H L ad
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            triangulum I H L. </s>
            <s xml:id="echoid-s1876" xml:space="preserve">Triangulum autem I H L æquale eſt tri-
              <lb/>
            angulo A E B. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">Quod ſic oſtenditur. </s>
            <s xml:id="echoid-s1878" xml:space="preserve">Triangulum enim
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            G H L æquale eſt triangulo D A B, quoniam baſes & </s>
            <s xml:id="echoid-s1879" xml:space="preserve">alti-
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            tudines reciprocè æquales habent. </s>
            <s xml:id="echoid-s1880" xml:space="preserve">Similique ratione quo-
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            niam G I æqualis eſt rectæ A B, erit triangulum G I L æ-
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            quale duobus ſimul triangulis D A E, D B E, hoc eſt,
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            quadrilatero D A E B. </s>
            <s xml:id="echoid-s1881" xml:space="preserve">Itaque triangulum H I L triangulo
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            A E B æquari neceſſe eſt, quod dicebamus. </s>
            <s xml:id="echoid-s1882" xml:space="preserve">Habebit itaque
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            portio A E B ad triangulum ſibi inſcriptum A E B mino-
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            rem quoque rationem quam triangulum O H L ad idem tri-
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            angulum A E B. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">Quamobrem triangulum O H L portione
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            A E B majus erit. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">Et totum proinde triangulum O G L
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            majus ſectore D A E B. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">Altitudo autem trianguli G L O
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            æqualis eſt radio D B. </s>
            <s xml:id="echoid-s1886" xml:space="preserve">Ergo baſis G O major erit arcu A B.
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            </s>
            <s xml:id="echoid-s1887" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s1888" xml:space="preserve"/>
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            <s xml:id="echoid-s1889" xml:space="preserve">Ex his autem manifeſtum eſt de tota quoque circumferen-
              <lb/>
            tia pronunciari poſſe, quod, Si circulo inſcribantur polygona
              <lb/>
            duo æquilatera, quorum alterum alterius ſit duplo laterum nu-
              <lb/>
            mero, & </s>
            <s xml:id="echoid-s1890" xml:space="preserve">differentiæ perimetrorum triens perimetro polygoni
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            majoris adjungatur, compoſita ex his circuli circumferentiâ mi-
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            nor erit. </s>
            <s xml:id="echoid-s1891" xml:space="preserve">Eidem vero majori perimetro ſi linea addatur quæ
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            ad dictum differentiæ trientem ſeſe habeat, ſicut quadrupla
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            perimetri majoris juncta perimetro minori, ad duplam ma-
              <lb/>
            joris cum tripla minoris, compoſita circumferentiam circuli ex-
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            cedet.</s>
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