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

Page concordance

< >
Scan Original
151 424
152 425
153 426
154 427
155 428
156 429
157 430
158 431
159 432
160 433
161 434
162 435
163 436
164 437
165 438
166 439
167 440
168 441
169 442
170 443
171 444
172 445
173 446
174 447
175 448
176 449
177 450
178
179
180
< >
page |< < (448) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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>
        </div>
        <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>
            <s xml:id="echoid-s3768" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum