Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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        <div xml:id="echoid-div205" type="section" level="1" n="99">
          <pb o="448" file="0166" n="175" rhead="VERA CIRCULI."/>
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        <div xml:id="echoid-div206" type="section" level="1" n="100">
          <head xml:id="echoid-head136" xml:space="preserve">PROP. XXX. PROBLEMA.</head>
          <head xml:id="echoid-head137" style="it" xml:space="preserve">Ex dato ſinu invenire arcum.</head>
          <p>
            <s xml:id="echoid-s3746" xml:space="preserve">Sit arcus circuli A E deſcriptus ex centro B. </s>
            <s xml:id="echoid-s3747" xml:space="preserve">hujus arcus da-
              <lb/>
              <note position="left" xlink:label="note-0166-01" xlink:href="note-0166-01a" xml:space="preserve">TAB. XLIII.
                <lb/>
              fig. 5.</note>
            tur radius nempe A B & </s>
            <s xml:id="echoid-s3748" xml:space="preserve">ſinus nempe A D: </s>
            <s xml:id="echoid-s3749" xml:space="preserve">oportet in-
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            venire quam proportionem habetipſe arcusad integram circuli
              <lb/>
            circunferentiam. </s>
            <s xml:id="echoid-s3750" xml:space="preserve">ſit arcus chorda A E & </s>
            <s xml:id="echoid-s3751" xml:space="preserve">ejus ſemiſſis tan-
              <lb/>
            gens A C vel C E. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">ex quadrato radii A B auferatur quadra-
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            tum ſinus A D & </s>
            <s xml:id="echoid-s3753" xml:space="preserve">relinquetur quadratum ſinus complementi
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            B D, datur igitur B D; </s>
            <s xml:id="echoid-s3754" xml:space="preserve">& </s>
            <s xml:id="echoid-s3755" xml:space="preserve">ideo datur area trianguli rectanguli
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            A B D; </s>
            <s xml:id="echoid-s3756" xml:space="preserve">datur quoque area trianguli A B E nempe rectangu-
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            lum ſinus dati A D in ſemiſſem radii B E. </s>
            <s xml:id="echoid-s3757" xml:space="preserve">deinde fiat ut ſumma
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            triangulorum A B D, A B E, ad triangulum A B E ita duplum
              <lb/>
            trianguli A B E ad trapezium A B E C, ut conſtat ex hujus
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            5. </s>
            <s xml:id="echoid-s3758" xml:space="preserve">& </s>
            <s xml:id="echoid-s3759" xml:space="preserve">ex dato triangulo inſcripto A B E & </s>
            <s xml:id="echoid-s3760" xml:space="preserve">trapezio circum-
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            ſcripto A B E C, inveniatur per præcedentem ſector ipſe
              <lb/>
            A B E, qui ad circulum integrum datum quæſitam habet pro-
              <lb/>
            portionem arcus A E ad totam circumferentiam, quam inve-
              <lb/>
            nire oportuit.</s>
            <s xml:id="echoid-s3761" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div208" type="section" level="1" n="101">
          <head xml:id="echoid-head138" xml:space="preserve">PROP. XXXI. PROBLEMA.</head>
          <head xml:id="echoid-head139" style="it" xml:space="preserve">Ex dato arcu invenire ſinum.</head>
          <p>
            <s xml:id="echoid-s3762" xml:space="preserve">Ex dato arcu manifeſtum eſt dari ſectoris aream; </s>
            <s xml:id="echoid-s3763" xml:space="preserve">hoc igitur
              <lb/>
              <note position="left" xlink:label="note-0166-02" xlink:href="note-0166-02a" xml:space="preserve">TAB. XLIII.
                <lb/>
              fig. 5.</note>
            ſectore dato conſideretur ex quot notis arithmeticis con-
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            ſtet ſinus totus: </s>
            <s xml:id="echoid-s3764" xml:space="preserve">deinde ſumatur ſectoris dati talis pars ali-
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            quota nempe ſector A B E, ut trianguli inſcripti A B E & </s>
            <s xml:id="echoid-s3765" xml:space="preserve">
              <lb/>
            trapezii circumſcripti A B E C toties multiplicia, quoties ſe-
              <lb/>
            ctor datus multiplex eſt ſectoris A B E, concordent in totno-
              <lb/>
            tis arithmeticis quot continet radix quadrata ſinus totius; </s>
            <s xml:id="echoid-s3766" xml:space="preserve">hoc
              <lb/>
            enim facile fieri poteſt ex ſpeculatione tabellæ hujus 29: </s>
            <s xml:id="echoid-s3767" xml:space="preserve">non
              <lb/>
            enim requiritur in hoc praxis præciſa, nam nihil refertetiam-
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            ſi in magnis radiis diſcrepantia ſit notarum aliquot. </s>
            <s xml:id="echoid-s3768" xml:space="preserve"/>
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