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

Table of figures

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[91] Pag. 506.TAB. XLV.Fig. 1.C F D B
[92] Fig. 2.C B A E F
[93] Fig. 3.B b F f H c
[94] Fig. 4.C D B A E F G H
[95] Fig. 5.C b d D B E F G f g e
[96] Fig. 6.B G A C D
[Figure 97]
[Figure 98]
[Figure 99]
[Figure 100]
[Figure 101]
[Figure 102]
[103] Pag. 520.TAB. XLVI.Fig. 1.D C E A X F K V O I L T α M N
[104] Fig. 3.Δ A Φ G F N E M I D H L B C K O P Q Σ R T V X Y Z S Γ Δ Θ @
[105] Fig. 5.C B A D E
[106] Fig. 4.H C L E B A D F K G
[107] Fig. 6.L G C F M A H B E I D K
[108] Fig. 2.G C H B A Y L X P K V Q I O S R F D E N
[Figure 109]
[Figure 110]
[Figure 111]
[Figure 112]
[113] Pag. 542.Fig. 1.♃
[114] Fig. 2.♃
[115] Fig. 3.♂
[116] Fig. 5.25 Mart. 1655. * a b *
[117] Fig. 7.26 Mart. * a b *
[118] Fig. 4.
[119] Fig. 6.
[120] Pag. 550.TAB. XLV III.Fig. 1.* a * b 27. Mart. 1655.
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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."/>
        </div>
        <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-
              <lb/>
            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-
              <lb/>
            tum ſinus A D & </s>
            <s xml:id="echoid-s3753" xml:space="preserve">relinquetur quadratum ſinus complementi
              <lb/>
            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
              <lb/>
            A B D; </s>
            <s xml:id="echoid-s3756" xml:space="preserve">datur quoque area trianguli A B E nempe rectangu-
              <lb/>
            lum ſinus dati A D in ſemiſſem radii B E. </s>
            <s xml:id="echoid-s3757" xml:space="preserve">deinde fiat ut ſumma
              <lb/>
            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
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            ſtet ſinus totus: </s>
            <s xml:id="echoid-s3764" xml:space="preserve">deinde ſumatur ſectoris dati talis pars ali-
              <lb/>
            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-
              <lb/>
            ſi in magnis radiis diſcrepantia ſit notarum aliquot. </s>
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