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

Table of figures

< >
[Figure 171]
Page: 323
[Figure 172]
Page: 324
[Figure 173]
Page: 327
[Figure 174]
Page: 328
[Figure 175]
Page: 330
[Figure 176]
Page: 331
[Figure 177]
Page: 332
[Figure 178]
Page: 333
[Figure 179]
Page: 334
[Figure 180]
Page: 335
[Figure 181]
Page: 336
[Figure 182]
Page: 337
[Figure 183]
Page: 338
[Figure 184]
Page: 339
[Figure 185]
Page: 340
[Figure 186]
Page: 341
[Figure 187]
Page: 342
[Figure 188]
Page: 342
[Figure 189]
Page: 343
[Figure 190]
Page: 344
[Figure 191]
Page: 344
[Figure 192]
Page: 346
[Figure 193]
Page: 346
[Figure 194]
Page: 349
[Figure 195]
Page: 351
[Figure 196]
Page: 370
[Figure 197]
Page: 371
[Figure 198]
Page: 371
[Figure 199]
Page: 372
[Figure 200]
Page: 372
< >
page |< < (329) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div878" type="section" level="1" n="470">
          <p style="it">
            <s xml:id="echoid-s10681" xml:space="preserve">
              <pb o="329" file="341" n="341" rhead=""/>
            hoc eſt, terminorum proportionis ſinuum angulorum reliquorum, & </s>
            <s xml:id="echoid-s10682" xml:space="preserve">al-
              <lb/>
            terum laterum, ſiue terminorum proportionis, ad aliud, reperietur tan-
              <lb/>
            gens anguli, qui cum ſemiſſe ſummæ reliquorum angulorum componet ma-
              <lb/>
            iorem angulum, qui nimirum maiori lateri dato opponitur: </s>
            <s xml:id="echoid-s10683" xml:space="preserve">idem verò ex
              <lb/>
            eadem ſemiſſe dictæ ſummæ detractus relinquet angulum minorem mino-
              <lb/>
            ri lateri dato oppoſitum; </s>
            <s xml:id="echoid-s10684" xml:space="preserve">vt perſpicuum eſt ex praxi priore propoſ. </s>
            <s xml:id="echoid-s10685" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s10686" xml:space="preserve">Quòd ſi rurſus fiat, vt ſinus vtriuſuis angulorum inuentorum ad ſinum
              <lb/>
            anguli in principio dati, ita latus inuento angulo, qui acceptus fuerit in
              <lb/>
            regula aurea, oppoſitum ad aliud, inuenietur tertium latus. </s>
            <s xml:id="echoid-s10687" xml:space="preserve">Et ad maio-
              <lb/>
            rem perſpicuit atem proponemus aliud exemplam.</s>
            <s xml:id="echoid-s10688" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10689" xml:space="preserve">SINT in triangulo ABC, data duo latera AB, AC, 22. </s>
            <s xml:id="echoid-s10690" xml:space="preserve">& </s>
            <s xml:id="echoid-s10691" xml:space="preserve">31. </s>
            <s xml:id="echoid-s10692" xml:space="preserve">vnà cum
              <lb/>
              <figure xlink:label="fig-341-01" xlink:href="fig-341-01a" number="186">
                <image file="341-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/341-01"/>
              </figure>
            angulo A, grad. </s>
            <s xml:id="echoid-s10693" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10694" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10695" xml:space="preserve">42. </s>
            <s xml:id="echoid-s10696" xml:space="preserve">Hicangulus ablatus ex
              <lb/>
            grad. </s>
            <s xml:id="echoid-s10697" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10698" xml:space="preserve">reliqua fiet ſumma angulorum B, C, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s10699" xml:space="preserve">156. </s>
            <s xml:id="echoid-s10700" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10701" xml:space="preserve">18. </s>
            <s xml:id="echoid-s10702" xml:space="preserve">Si ergo fiat, vt 26 {1/2}. </s>
            <s xml:id="echoid-s10703" xml:space="preserve">ſemiſsis laterum
              <lb/>
            AB, AC, id eſt, terminorum proportionis ſinuum
              <lb/>
            angulorum B, C, ad 476595. </s>
            <s xml:id="echoid-s10704" xml:space="preserve">tangentem ſemiſsis ſum-
              <lb/>
            mæ angulorum B, C, hoc eſt, ad tangentem grad. </s>
            <s xml:id="echoid-s10705" xml:space="preserve">78. </s>
            <s xml:id="echoid-s10706" xml:space="preserve">
              <lb/>
            Min. </s>
            <s xml:id="echoid-s10707" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10708" xml:space="preserve">ita 4 {1/2}. </s>
            <s xml:id="echoid-s10709" xml:space="preserve">differentia inter ſemiſſem ſummæ la-
              <lb/>
            terũ AB, AC, vel terminorũ laterum, ſeu terminorum,
              <lb/>
            ad aliud, reperietur tangens 80931. </s>
            <s xml:id="echoid-s10710" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s10711" xml:space="preserve">38. </s>
            <s xml:id="echoid-s10712" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10713" xml:space="preserve">59. </s>
            <s xml:id="echoid-s10714" xml:space="preserve">additus ad
              <lb/>
            grad. </s>
            <s xml:id="echoid-s10715" xml:space="preserve">78. </s>
            <s xml:id="echoid-s10716" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10717" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10718" xml:space="preserve">nempe ad ſemiſſem ſummæ angulorum B, C, conſtituet an-
              <lb/>
            gulum maiorem B, maiori lateri dato AC, oppoſitum grad. </s>
            <s xml:id="echoid-s10719" xml:space="preserve">117. </s>
            <s xml:id="echoid-s10720" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10721" xml:space="preserve">8. </s>
            <s xml:id="echoid-s10722" xml:space="preserve">Idem
              <lb/>
            vero arcus grad. </s>
            <s xml:id="echoid-s10723" xml:space="preserve">38. </s>
            <s xml:id="echoid-s10724" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10725" xml:space="preserve">59. </s>
            <s xml:id="echoid-s10726" xml:space="preserve">ex eadem ſemiſſe ſummæ angulorum B, C, id
              <lb/>
            eſt, ex grad. </s>
            <s xml:id="echoid-s10727" xml:space="preserve">78. </s>
            <s xml:id="echoid-s10728" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10729" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10730" xml:space="preserve">detractus relinquet minorem angulum C, minori la-
              <lb/>
            teri dato AB, oppoſitum grad. </s>
            <s xml:id="echoid-s10731" xml:space="preserve">39. </s>
            <s xml:id="echoid-s10732" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10733" xml:space="preserve">10. </s>
            <s xml:id="echoid-s10734" xml:space="preserve">Operationem aureæ regulæ
              <lb/>
            hic vides.</s>
            <s xml:id="echoid-s10735" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          26 {1/2}. # 476595. # 4 {1/2}? # fit # 80931.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10736" xml:space="preserve">Quòd ſi iam fiat, vt 63158. </s>
            <s xml:id="echoid-s10737" xml:space="preserve">ſinus anguli C, ad 40195. </s>
            <s xml:id="echoid-s10738" xml:space="preserve">ſinum anguli A, ita la-
              <lb/>
            tus AB, 22. </s>
            <s xml:id="echoid-s10739" xml:space="preserve">ad aliud: </s>
            <s xml:id="echoid-s10740" xml:space="preserve">Vel vt 88995. </s>
            <s xml:id="echoid-s10741" xml:space="preserve">ſinus anguli B, ad 40195. </s>
            <s xml:id="echoid-s10742" xml:space="preserve">ſinum anguli
              <lb/>
            A, ita latus AC, 31. </s>
            <s xml:id="echoid-s10743" xml:space="preserve">ad aliud, inuenietur latus BC, 14. </s>
            <s xml:id="echoid-s10744" xml:space="preserve">ferè. </s>
            <s xml:id="echoid-s10745" xml:space="preserve">vt hic cernis.</s>
            <s xml:id="echoid-s10746" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          C. # A. # # AB. # # BC.
            <lb/>
          63158. # 40195. # # 22? # ſit # 14 ferè
            <lb/>
          # # Vel
            <lb/>
          B. # A. # # AC. # # BC.
            <lb/>
          88995. # 40195. # # 31? # fit # 14. ferè.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10747" xml:space="preserve">SI vti nolis tangentibus, vſurpanda erit poſterior praxis propoſ. </s>
            <s xml:id="echoid-s10748" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10749" xml:space="preserve">in in-
              <lb/>
            uentione angulorum B, C.</s>
            <s xml:id="echoid-s10750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10751" xml:space="preserve">IAM ſi proportio laterum AB, AC, data ſit, vna cum angulo A, ab ipſis
              <lb/>
              <note position="right" xlink:label="note-341-03" xlink:href="note-341-03a" xml:space="preserve">Quando la
                <lb/>
              terum pro-
                <lb/>
              portio data
                <lb/>
              eſt.</note>
            comprehenſo, aſcribemus dictis lateribus numeros proportionis, ac ſi in ipſis
              <lb/>
            data eſſent, problemaq́ abſoluemus, vt prius.</s>
            <s xml:id="echoid-s10752" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10753" xml:space="preserve">HOC etiam problema abſolui poteſt ſine auxilio propoſ. </s>
            <s xml:id="echoid-s10754" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10755" xml:space="preserve">hoc modo.
              <lb/>
            </s>
            <s xml:id="echoid-s10756" xml:space="preserve">
              <note position="right" xlink:label="note-341-04" xlink:href="note-341-04a" xml:space="preserve">Alia demõ
                <lb/>
              ſtratio pro-
                <lb/>
              blematis ſi-
                <lb/>
              ne ppoſ.6.</note>
            In triangulo ABC, detur latus AB, 29. </s>
            <s xml:id="echoid-s10757" xml:space="preserve">AC, 24. </s>
            <s xml:id="echoid-s10758" xml:space="preserve">& </s>
            <s xml:id="echoid-s10759" xml:space="preserve">angulus A, primùm acutus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s10760" xml:space="preserve">38. </s>
            <s xml:id="echoid-s10761" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10762" xml:space="preserve">16. </s>
            <s xml:id="echoid-s10763" xml:space="preserve">Ducatur ad maius latus A B, ab angulo oppoſito C, per-
              <lb/>
            pendicularis CD: </s>
            <s xml:id="echoid-s10764" xml:space="preserve">quæ neceſſario intra triangulum cadet. </s>
            <s xml:id="echoid-s10765" xml:space="preserve">Cum enim </s>
          </p>
        </div>
      </text>
    </echo>
Impressum