Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

Page concordance

< >
Scan Original
171 159
172 160
173 161
174 162
175 163
176 164
177 165
178 166
179 167
180 168
181 169
182 170
183 171
184 172
185 173
186 174
187 175
188 176
189 177
190 178
191 179
192 180
193 181
194 182
195 183
196 184
197 185
198 186
199 187
200 188
< >
page |< < (175) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div476" type="section" level="1" n="240">
          <p style="it">
            <s xml:id="echoid-s6540" xml:space="preserve">
              <pb o="175" file="187" n="187" rhead=""/>
            recta gradus _20._ </s>
            <s xml:id="echoid-s6541" xml:space="preserve">
              <de:unknown code="022"/>
            . </s>
            <s xml:id="echoid-s6542" xml:space="preserve">_Q_uot autem gradus complectatur arcus _VC_, indicabit quadrans
              <lb/>
            in _90_. </s>
            <s xml:id="echoid-s6543" xml:space="preserve">gradus diuiſus.</s>
            <s xml:id="echoid-s6544" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6545" xml:space="preserve">_EODEM_ pacto omnia alia problemata _G_eometrice per ſinus abſoluemus, etiamſi
              <lb/>
            ſinubus verſis vti oportuerit aliquando, qui quidem eadem facilitate exdatis arcu-
              <lb/>
            bus inueniuntur, & </s>
            <s xml:id="echoid-s6546" xml:space="preserve">exipſis arcus, qua ſinus rectos, & </s>
            <s xml:id="echoid-s6547" xml:space="preserve">ſinus complemẽtorum reperi-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s6548" xml:space="preserve">_S_i enim arcus datus minor eſt quadrante, vt _AG;_ </s>
            <s xml:id="echoid-s6549" xml:space="preserve">ducta _GS_. </s>
            <s xml:id="echoid-s6550" xml:space="preserve">ad _AE_, perpendi-
              <lb/>
            culari, erit _AS_ ſinus verſus arcus _AG_. </s>
            <s xml:id="echoid-s6551" xml:space="preserve">_S_i vero datus arcus quadrante maior eſt, vt
              <lb/>
            _AV;_ </s>
            <s xml:id="echoid-s6552" xml:space="preserve">ducta _VT_, ad _EC_, perpendiculari, erit _AT_, ſinus verſus arcus _AV_, vt ex
              <lb/>
            definitione manifeſtum eſt.</s>
            <s xml:id="echoid-s6553" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6554" xml:space="preserve">_SED_ iam ad inquiſitionem chordarum _G_eometricam aggrediamur, ex quibus
              <lb/>
            rurſum ſinuum tabulam facili negotio componemus.</s>
            <s xml:id="echoid-s6555" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div492" type="section" level="1" n="241">
          <head xml:id="echoid-head268" xml:space="preserve">THEOR. 7. PROPOS. 10.</head>
          <p>
            <s xml:id="echoid-s6556" xml:space="preserve">IN circulo ſumptis duobus arcubus inæqua-
              <lb/>
              <note position="right" xlink:label="note-187-01" xlink:href="note-187-01a" xml:space="preserve">Maior eſt
                <lb/>
              proportio
                <lb/>
              maioris ar-
                <lb/>
              cꝰ in circu-
                <lb/>
              lo ad arcũ
                <lb/>
              minorẽ, q̃
                <lb/>
              chordæ ma
                <lb/>
              ioris arcus
                <lb/>
              ad chordã
                <lb/>
              minoris.</note>
            libus, quorum maioris chorda maior ſit, quam
              <lb/>
            chorda minoris; </s>
            <s xml:id="echoid-s6557" xml:space="preserve">maior eſt proportio arcus maio-
              <lb/>
            ris ad minorem, quam chordæ arcus maioris ad
              <lb/>
            chordam minoris arcus.</s>
            <s xml:id="echoid-s6558" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6559" xml:space="preserve">IN circulo ABCD, ſint inęquales arcus AB,
              <emph style="sc">Bc</emph>
            ; </s>
            <s xml:id="echoid-s6560" xml:space="preserve">ille maior, hic vero minor:
              <lb/>
            </s>
            <s xml:id="echoid-s6561" xml:space="preserve">quorum chordæ AB, BC; </s>
            <s xml:id="echoid-s6562" xml:space="preserve">illa maior, hæc vero minor. </s>
            <s xml:id="echoid-s6563" xml:space="preserve">Dico maiorem eſſe
              <lb/>
            proportionem arcus AB, ad arcum BC, quam chordæ AB, ad chordam BC. </s>
            <s xml:id="echoid-s6564" xml:space="preserve">
              <lb/>
            Contineant enim chordæ AB, BC, angulum ABC, ita vt arcus ſint conti-
              <lb/>
            nuati, minoreſq; </s>
            <s xml:id="echoid-s6565" xml:space="preserve">ſint tota circunferentia. </s>
            <s xml:id="echoid-s6566" xml:space="preserve">Nam ſi toti circunferentiæ forent
              <lb/>
            æquales, eſſet eadem chorda vtriuſq; </s>
            <s xml:id="echoid-s6567" xml:space="preserve">arcus: </s>
            <s xml:id="echoid-s6568" xml:space="preserve">ſi vero totam circunferentiam
              <lb/>
            excederent, eſſet chorda arcus minoris maior, quam maioris, vt patet in ſe-
              <lb/>
              <figure xlink:label="fig-187-01" xlink:href="fig-187-01a" number="137">
                <image file="187-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/187-01"/>
              </figure>
            cunda figura, ſi minor arcus foret BAI. </s>
            <s xml:id="echoid-s6569" xml:space="preserve">Angulus porrò ABC, bifariam ſe-
              <lb/>
              <note position="right" xlink:label="note-187-02" xlink:href="note-187-02a" xml:space="preserve">9. primi.</note>
            cetur recta BD, connectãturq́; </s>
            <s xml:id="echoid-s6570" xml:space="preserve">rectæ AC, AD, CD, quarum AC, rectam BD,
              <lb/>
            ſecet in E. </s>
            <s xml:id="echoid-s6571" xml:space="preserve">Erunt autem rectæ AD, CD, æquales, propter arcus AD, CD,
              <lb/>
              <note position="right" xlink:label="note-187-03" xlink:href="note-187-03a" xml:space="preserve">29. tertij.</note>
            qui ſubten ſiangulis ABD, CBD, ex conſtructione æqualibus æqualesinter
              <lb/>
              <note position="right" xlink:label="note-187-04" xlink:href="note-187-04a" xml:space="preserve">26. tertij.</note>
            ſe ſunt. </s>
            <s xml:id="echoid-s6572" xml:space="preserve">Et quoniam in triangulo ABC, recta BE, angulum ABC, bifariam
              <lb/>
            ſecat; </s>
            <s xml:id="echoid-s6573" xml:space="preserve">erit, vt AB, ad BC, ita AE, ad EC: </s>
            <s xml:id="echoid-s6574" xml:space="preserve">Eſt autem recta AB, maior, quam
              <lb/>
              <note position="right" xlink:label="note-187-05" xlink:href="note-187-05a" xml:space="preserve">3. fextia</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum