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

Page concordance

< >
Scan Original
201 189
202 190
203 191
204 192
205 193
206 194
207 195
208 196
209 197
210 198
211 199
212 200
213 201
214 202
215 203
216 204
217 205
218 206
219 207
220 208
221 209
222 210
223 211
224 212
225 213
226 214
227 215
228 216
229 217
230 218
< >
page |< < (194) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div559" type="section" level="1" n="261">
          <p style="it">
            <s xml:id="echoid-s7875" xml:space="preserve">
              <pb o="194" file="206" n="206" rhead=""/>
            autem arcu BD, nempe complemente arcus C D, bifariam in F, ducatur ex centre
              <lb/>
            A, per
              <emph style="sc">F</emph>
            , recta A G, ſecans tangentem C
              <emph style="sc">E</emph>
            , productam in
              <emph style="sc">G</emph>
            . </s>
            <s xml:id="echoid-s7876" xml:space="preserve">Eritq́; </s>
            <s xml:id="echoid-s7877" xml:space="preserve">C
              <emph style="sc">G</emph>
            , tangens
              <lb/>
            arcus
              <emph style="sc">Cf</emph>
            , compoſiti ex dato arcu CD, & </s>
            <s xml:id="echoid-s7878" xml:space="preserve">
              <emph style="sc">Df</emph>
            , ſemiſſe complementi DB. </s>
            <s xml:id="echoid-s7879" xml:space="preserve">Dico ſe-
              <lb/>
            cantem
              <emph style="sc">Ae</emph>
            , & </s>
            <s xml:id="echoid-s7880" xml:space="preserve">tangentẽ
              <emph style="sc">Ce</emph>
            . </s>
            <s xml:id="echoid-s7881" xml:space="preserve">ſimul æquales eſſe tangenti
              <emph style="sc">Cg</emph>
            . </s>
            <s xml:id="echoid-s7882" xml:space="preserve">Quia enim anguli BAF,
              <lb/>
              <note position="left" xlink:label="note-206-01" xlink:href="note-206-01a" xml:space="preserve">27. tertij.</note>
            FAE, æquales ſunt, propter æquales arcus
              <emph style="sc">Bf</emph>
            ,
              <emph style="sc">F</emph>
            D; </s>
            <s xml:id="echoid-s7883" xml:space="preserve">& </s>
            <s xml:id="echoid-s7884" xml:space="preserve">angulo BAF, alternus
              <lb/>
              <note position="left" xlink:label="note-206-02" xlink:href="note-206-02a" xml:space="preserve">29. primi.</note>
            angulus G, æqualis eſt; </s>
            <s xml:id="echoid-s7885" xml:space="preserve">erit quoque angulus idem G, angulo
              <emph style="sc">GAe</emph>
            , æqualis Quare
              <lb/>
              <note position="left" xlink:label="note-206-03" xlink:href="note-206-03a" xml:space="preserve">6. primi.</note>
            aquales ſunt rectæ
              <emph style="sc">E</emph>
            A,
              <emph style="sc">E</emph>
            G: </s>
            <s xml:id="echoid-s7886" xml:space="preserve">at que adeo, addita communi
              <emph style="sc">E</emph>
            C, duæ A E,
              <emph style="sc">E</emph>
            C, ſimul
              <lb/>
            toti CG, æquales erunt.</s>
            <s xml:id="echoid-s7887" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div562" type="section" level="1" n="262">
          <head xml:id="echoid-head289" xml:space="preserve">THEOR. 12. PROPOS. 20.</head>
          <p>
            <s xml:id="echoid-s7888" xml:space="preserve">SECANS cuiuſuis arcus æqualis eſt tangen-
              <lb/>
              <note position="left" xlink:label="note-206-04" xlink:href="note-206-04a" xml:space="preserve">Secans cu-
                <lb/>
              iuſuis arcꝰ
                <lb/>
              quorũ duo
                <lb/>
              rú arcuum
                <lb/>
              tangentibꝰ
                <lb/>
              ſit æqualis.</note>
            ti eiuſdem, vna cum tangente ſemiſſis comple-
              <lb/>
            menti arcus eiuſdem.</s>
            <s xml:id="echoid-s7889" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7890" xml:space="preserve">IN quadrante ABC, ſit AD, ſecans, & </s>
            <s xml:id="echoid-s7891" xml:space="preserve">CD, tangens arcus CE, cuius
              <lb/>
            complementi EB, ſemiſsis ſit EF, vel FB, & </s>
            <s xml:id="echoid-s7892" xml:space="preserve">huic ſemiſsi æqualis ſit arcus
              <lb/>
            CG. </s>
            <s xml:id="echoid-s7893" xml:space="preserve">Ducta autem recta AG, & </s>
            <s xml:id="echoid-s7894" xml:space="preserve">producta, donec cum DC, protracta coeat in
              <lb/>
            H, erit CH, tangens arcus CG, qui ſemiſsis eſt complementi arcus CE.
              <lb/>
            </s>
            <s xml:id="echoid-s7895" xml:space="preserve">Dico ſecantem AD, æqualem eſſe tangenti
              <lb/>
              <figure xlink:label="fig-206-01" xlink:href="fig-206-01a" number="153">
                <image file="206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/206-01"/>
              </figure>
            CD, & </s>
            <s xml:id="echoid-s7896" xml:space="preserve">tangenti CH, ſimul, hoc eſt, toti li-
              <lb/>
            neæ DH. </s>
            <s xml:id="echoid-s7897" xml:space="preserve">Quoniam enim anguli EAF, CAG,
              <lb/>
              <note position="left" xlink:label="note-206-05" xlink:href="note-206-05a" xml:space="preserve">27. tertij.</note>
            æquales ſunt, ob æquales arcus EF, CG;
              <lb/>
            </s>
            <s xml:id="echoid-s7898" xml:space="preserve">addito communi angulo EAC, erunt toti
              <unsure/>
              <lb/>
            anguli FAC, EAH, æquales. </s>
            <s xml:id="echoid-s7899" xml:space="preserve">Rurſus quia
              <lb/>
            in triangulo rectangulo ACH, duo anguli
              <lb/>
              <note position="left" xlink:label="note-206-06" xlink:href="note-206-06a" xml:space="preserve">32. primi.</note>
            A, H, vni recto, nimirũ angulo BAC, æqua-
              <lb/>
            les ſunt; </s>
            <s xml:id="echoid-s7900" xml:space="preserve">ablatis angulis BAF, CAH, qui
              <lb/>
            propter æquales arcus BF, CG, æquales ſunt,
              <lb/>
              <note position="left" xlink:label="note-206-07" xlink:href="note-206-07a" xml:space="preserve">27. tertij.</note>
            erunt reliqui anguli FAC, & </s>
            <s xml:id="echoid-s7901" xml:space="preserve">H, æquales. </s>
            <s xml:id="echoid-s7902" xml:space="preserve">Eſt
              <lb/>
            autem angulus FAC, oſtenſus æqualis angu
              <lb/>
            lo EAH. </s>
            <s xml:id="echoid-s7903" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s7904" xml:space="preserve">angulus H, eidem angulo EAH, æqualis erit: </s>
            <s xml:id="echoid-s7905" xml:space="preserve">ac propte-
              <lb/>
            rea rectæ AD, DH, æquales erunt, hoc eſt, ſecans AD, tangentibus DC, CH,
              <lb/>
              <note position="left" xlink:label="note-206-08" xlink:href="note-206-08a" xml:space="preserve">6. primi.</note>
            æqualis erit. </s>
            <s xml:id="echoid-s7906" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s7907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7908" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s7909" xml:space="preserve">Sit rurſus AD, ſecans, & </s>
            <s xml:id="echoid-s7910" xml:space="preserve">CD, tangens arcus CE. </s>
            <s xml:id="echoid-s7911" xml:space="preserve">Dico ſecan-
              <lb/>
            tem AD, æqualem eſſe tangenti CD, vnà cum tangente ſemiſsis complemen
              <lb/>
            ti arcus EC, ſeu anguli DAC, hoc eſt, vna cum tangente ſemiſsis anguli D,
              <lb/>
            qui complementum eſt anguli DAC, cum ambo in triangulo rectágulo ACD,
              <lb/>
            vni recto ſint æquales. </s>
            <s xml:id="echoid-s7912" xml:space="preserve">Centro namque D, & </s>
            <s xml:id="echoid-s7913" xml:space="preserve">interuallo DA, arcus circuli de-
              <lb/>
              <note position="left" xlink:label="note-206-09" xlink:href="note-206-09a" xml:space="preserve">32. primi.</note>
            ſcribatur AHI, ſecans DC, productam in H, & </s>
            <s xml:id="echoid-s7914" xml:space="preserve">AC, productam in I, ducan-
              <lb/>
            turq́; </s>
            <s xml:id="echoid-s7915" xml:space="preserve">rectæ AH, HI. </s>
            <s xml:id="echoid-s7916" xml:space="preserve">Quia igitur recta DC, ex centro D, circuli AHI, edu-
              <lb/>
            cta ſecans rectam AI, ad angulos rectos, ſecat eam bifariam; </s>
            <s xml:id="echoid-s7917" xml:space="preserve">ſecabit eadem
              <lb/>
              <note position="left" xlink:label="note-206-10" xlink:href="note-206-10a" xml:space="preserve">3. tertij.</note>
            DCH, & </s>
            <s xml:id="echoid-s7918" xml:space="preserve">arcum AHI, bifariam, ex lemmate in definitionibus demonſtrato.
              <lb/>
            </s>
            <s xml:id="echoid-s7919" xml:space="preserve">Quare anguli CAH, & </s>
            <s xml:id="echoid-s7920" xml:space="preserve">I, æquales ſunt. </s>
            <s xml:id="echoid-s7921" xml:space="preserve">Quoniam autem, cum anguli D, & </s>
            <s xml:id="echoid-s7922" xml:space="preserve">I,
              <lb/>
              <note position="left" xlink:label="note-206-11" xlink:href="note-206-11a" xml:space="preserve">27. tertij.</note>
            candem habeant baſim arcum AH, & </s>
            <s xml:id="echoid-s7923" xml:space="preserve">ille ſit ad centrum D, hic vero ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum