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

Page concordance

< >
Scan Original
241 229
242 230
243 231
244 232
245 233
246 234
247 235
248 236
249 237
250 238
251 239
252 240
253 241
254 242
255 243
256
257
258 246
259 247
260 248
261 249
262 250
263 251
264 252
265 253
266 254
267 255
268 256
269 257
270 258
< >
page |< < (326) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div868" type="section" level="1" n="468">
          <p>
            <s xml:id="echoid-s10450" xml:space="preserve">
              <pb o="326" file="338" n="338" rhead=""/>
            13. </s>
            <s xml:id="echoid-s10451" xml:space="preserve">dat AB, ſinum totum partium 100000. </s>
            <s xml:id="echoid-s10452" xml:space="preserve">quid dabit BD, 5? </s>
            <s xml:id="echoid-s10453" xml:space="preserve">inueniemusq́
              <lb/>
            ſinum BD, 38461. </s>
            <s xml:id="echoid-s10454" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s10455" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AB. # AB. # BD. # # BD.
            <lb/>
          13. # 100000. # 5? # fit. # 38461.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10456" xml:space="preserve">Ex tabula ergo ſinuum dabitur angulus BAD,
              <lb/>
              <figure xlink:label="fig-338-01" xlink:href="fig-338-01a" number="183">
                <image file="338-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/338-01"/>
              </figure>
            grad. </s>
            <s xml:id="echoid-s10457" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10458" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10459" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10460" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s10461" xml:space="preserve">adeo eius complementum
              <lb/>
            B, grad. </s>
            <s xml:id="echoid-s10462" xml:space="preserve">67. </s>
            <s xml:id="echoid-s10463" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10464" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10465" xml:space="preserve">qui eſt vnus angulorum quę-
              <lb/>
            ſitorum. </s>
            <s xml:id="echoid-s10466" xml:space="preserve">Rurſus, quia poſito AC, ſinu toto, CD,
              <lb/>
            ſinus eſt anguli CAD, dicemus iterum per regu-
              <lb/>
            lam auream. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">Si AC, 20. </s>
            <s xml:id="echoid-s10468" xml:space="preserve">dat AC, 100000. </s>
            <s xml:id="echoid-s10469" xml:space="preserve">ſinum
              <lb/>
            totum, quid dabit CD, 16? </s>
            <s xml:id="echoid-s10470" xml:space="preserve">Inueniemuſq; </s>
            <s xml:id="echoid-s10471" xml:space="preserve">ſinum
              <lb/>
            CD, 80000. </s>
            <s xml:id="echoid-s10472" xml:space="preserve">Vt hic patet.</s>
            <s xml:id="echoid-s10473" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          AC. # AC. # CD. # # CD.
            <lb/>
          20. # 100000. # 16? # fit # 80000.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10474" xml:space="preserve">Qui ſinus in tabula ſinuum monſtrat angulum
              <lb/>
            CAD, grad. </s>
            <s xml:id="echoid-s10475" xml:space="preserve">53. </s>
            <s xml:id="echoid-s10476" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10477" xml:space="preserve">8. </s>
            <s xml:id="echoid-s10478" xml:space="preserve">ac proinde eius comple-
              <lb/>
            mentum C, erit grad. </s>
            <s xml:id="echoid-s10479" xml:space="preserve">36. </s>
            <s xml:id="echoid-s10480" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10481" xml:space="preserve">52. </s>
            <s xml:id="echoid-s10482" xml:space="preserve">qui eſt vnus
              <lb/>
            etiam angulorum quæſitorum. </s>
            <s xml:id="echoid-s10483" xml:space="preserve">Quòd ſi duo an-
              <lb/>
            guli duorum ſinuum inuentorum, nempe grad. </s>
            <s xml:id="echoid-s10484" xml:space="preserve">22. </s>
            <s xml:id="echoid-s10485" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10486" xml:space="preserve">37. </s>
            <s xml:id="echoid-s10487" xml:space="preserve">& </s>
            <s xml:id="echoid-s10488" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s10489" xml:space="preserve">53. </s>
            <s xml:id="echoid-s10490" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s10491" xml:space="preserve">
              <note position="left" xlink:label="note-338-03" xlink:href="note-338-03a" xml:space="preserve">Praxis.</note>
            8. </s>
            <s xml:id="echoid-s10492" xml:space="preserve">ſimul componantur, fiet tertius angulus BAC, grad. </s>
            <s xml:id="echoid-s10493" xml:space="preserve">75. </s>
            <s xml:id="echoid-s10494" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10495" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10496" xml:space="preserve">Vel cer-
              <lb/>
            te ſi ſumma duorum angulorum B, C, inuentorum ex grad. </s>
            <s xml:id="echoid-s10497" xml:space="preserve">180. </s>
            <s xml:id="echoid-s10498" xml:space="preserve">auferatur,
              <lb/>
            reliquus fiet tertius angulus BAC, grad. </s>
            <s xml:id="echoid-s10499" xml:space="preserve">75. </s>
            <s xml:id="echoid-s10500" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s10501" xml:space="preserve">45.</s>
            <s xml:id="echoid-s10502" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10503" xml:space="preserve">ITAQVE, (vt totam praxim complectamur) ſi fiat, vt maximum
              <lb/>
            latus (in quod perpendicularis ducta eſt) ad ſummam aliorum duorum,
              <lb/>
            ita differentia eorundem duorum ad aliud, reperietur numerus, qui ex
              <lb/>
            maximo latere ſubductus relinquet numerum, cuius ſemiſſis dabit minus
              <lb/>
            ſegmentum baſis, hoc autem ex baſi detractum relinquet maius ſegmen-
              <lb/>
            tum, vt conſtat ex ſecunda praxi propoſ. </s>
            <s xml:id="echoid-s10504" xml:space="preserve">9. </s>
            <s xml:id="echoid-s10505" xml:space="preserve">Quòd ſi rurſum fiat, vt mi-
              <lb/>
            nimum latus ad ſinum totum, ita ſegmentum baſis minus ad aliud, inue-
              <lb/>
            nietur ſinus, cuius arcus complementum dabit angulum ſupra baſim me-
              <lb/>
            dio lateri oppoſitum. </s>
            <s xml:id="echoid-s10506" xml:space="preserve">Deinde ſi rurſum fiat, vt medium latus ad ſinum
              <lb/>
            totum, ita maius ſegmentum baſis ad aliud, reperietur ſinus, cuius ar-
              <lb/>
            cus complementum dabit angulum ſupra baſim minimo lateri oppoſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s10507" xml:space="preserve">Tertius vero angulus maximo lateri oppoſitus conflabitur ex duobus il-
              <lb/>
            lis arcubus duorum ſinuum inuentorum: </s>
            <s xml:id="echoid-s10508" xml:space="preserve">vel certè relinquetur poſt de-
              <lb/>
            tractionem duorum angulorum inuentorum ex duobus rectis.</s>
            <s xml:id="echoid-s10509" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10510" xml:space="preserve">RVRSVS in poſteriori triangulo datum ſit latus AB, 11. </s>
            <s xml:id="echoid-s10511" xml:space="preserve">AC, 13. </s>
            <s xml:id="echoid-s10512" xml:space="preserve">& </s>
            <s xml:id="echoid-s10513" xml:space="preserve">
              <lb/>
            BC, 20. </s>
            <s xml:id="echoid-s10514" xml:space="preserve">Demiſſa in maximum latus BC, perpendiculari AD, inuenietur
              <lb/>
            ſegmentum BD, 8 {4/5}. </s>
            <s xml:id="echoid-s10515" xml:space="preserve">at CD, 11{@/5}. </s>
            <s xml:id="echoid-s10516" xml:space="preserve">vt hic apparet ſecundum praxim poſte-
              <lb/>
            riorem propoſ. </s>
            <s xml:id="echoid-s10517" xml:space="preserve">9.</s>
            <s xml:id="echoid-s10518" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          BC. # AB. AB. # Differ. inter # AB, AC.
            <lb/>
          20. # 24. # 2? # fit # 2 {2/5}.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s10519" xml:space="preserve">Hic numerus ex baſe 20. </s>
            <s xml:id="echoid-s10520" xml:space="preserve">ablatus relinquit 17 {3/5}. </s>
            <s xml:id="echoid-s10521" xml:space="preserve">cuius ſemiſsis 8 {4/5}. </s>
            <s xml:id="echoid-s10522" xml:space="preserve">dat ſeg-
              <lb/>
            mentum minus BD. </s>
            <s xml:id="echoid-s10523" xml:space="preserve">Ergo maius CD, erit 11 {1/5}. </s>
            <s xml:id="echoid-s10524" xml:space="preserve">Hinc inuenietur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum