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 |< < (314) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div820" type="section" level="1" n="460">
          <p>
            <s xml:id="echoid-s9780" xml:space="preserve">
              <pb o="314" file="326" n="326" rhead=""/>
            quadrato rectæ EG, æqualia ſunt, ſi ea in vnam ſummam colligamus, fiet qua-
              <lb/>
            dratum rectæ EG, 2698720744. </s>
            <s xml:id="echoid-s9781" xml:space="preserve">cuius radix quadrata dabit EG, partium
              <lb/>
            51949. </s>
            <s xml:id="echoid-s9782" xml:space="preserve">Cum autem, poſito ſinu toto EG, recta HG, ſinus ſit anguli HEG,
              <lb/>
            vt in ſinuum defin. </s>
            <s xml:id="echoid-s9783" xml:space="preserve">diximus, dicemus rurſum. </s>
            <s xml:id="echoid-s9784" xml:space="preserve">Si EG, inuenta partium 51949.
              <lb/>
            </s>
            <s xml:id="echoid-s9785" xml:space="preserve">dat EG, ſinum totum partium 100000. </s>
            <s xml:id="echoid-s9786" xml:space="preserve">quid dabit HG, inuenta partium
              <lb/>
            30210? </s>
            <s xml:id="echoid-s9787" xml:space="preserve">inueniemusque HG, ſinum anguli HEG, partiũ 58153. </s>
            <s xml:id="echoid-s9788" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s9789" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">
            <lb/>
          EG. # EG. # HG. # # HG.
            <lb/>
          51949. # 100000. # 30210? # ſit. # 58153.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s9790" xml:space="preserve">Ex ſinuum ergo tabula dabitur angulus HEG, ſiue arcus AF, grad. </s>
            <s xml:id="echoid-s9791" xml:space="preserve">35. </s>
            <s xml:id="echoid-s9792" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s9793" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9794" xml:space="preserve">qui additus ſemiſsi AB, grad. </s>
            <s xml:id="echoid-s9795" xml:space="preserve">65. </s>
            <s xml:id="echoid-s9796" xml:space="preserve">exhibebit maiorem arcum BF, ideoq́ue
              <lb/>
            & </s>
            <s xml:id="echoid-s9797" xml:space="preserve">angulum BEF, grad. </s>
            <s xml:id="echoid-s9798" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9799" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9800" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9801" xml:space="preserve">ablatus vero ex ſemiſſe AD, reliquum
              <lb/>
            faciet arcum minorem FD, atque adeo & </s>
            <s xml:id="echoid-s9802" xml:space="preserve">angulum FED, grad. </s>
            <s xml:id="echoid-s9803" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9804" xml:space="preserve">Min.</s>
            <s xml:id="echoid-s9805" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9806" xml:space="preserve">
              <lb/>
            vt prius.</s>
            <s xml:id="echoid-s9807" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9808" xml:space="preserve">QVOCIRCA, quando aggregatum duorum arcuum, vel angulo-
              <lb/>
              <note position="left" xlink:label="note-326-02" xlink:href="note-326-02a" xml:space="preserve">Praxis.</note>
            rum minus eſt, quam grad. </s>
            <s xml:id="echoid-s9809" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9810" xml:space="preserve">Si fiat, vt ſemiſſis aggregati terminorum
              <lb/>
            proportionis datæ ad ſinum ſemiſſis aggregatiarcuum, angulorumve, ita
              <lb/>
            differentia inter ſemiſſem aggregati terminorum datæ proportionis, & </s>
            <s xml:id="echoid-s9811" xml:space="preserve">
              <lb/>
            alterutrum terminorum, ad aliud, inuenietur numerus; </s>
            <s xml:id="echoid-s9812" xml:space="preserve">cuius quadr atum
              <lb/>
            ſi adiungatur quadrato ſinus complementi ſemiſſis aggregati arcuum, ſeu
              <lb/>
            angulorum; </s>
            <s xml:id="echoid-s9813" xml:space="preserve">Et tandem fiat, vt compoſiti buius numeri radix quadrata
              <lb/>
            ad ſinum totum, it a numerus per auream regulam nuper inuẽtus ad aliud,
              <lb/>
            producetur ſinus anguli, ſiue arcus, quo vter angulus, arcusve quæſitus
              <lb/>
            ab eorundem aggregati ſemiſſe differt. </s>
            <s xml:id="echoid-s9814" xml:space="preserve">Additus ergo arcus, ſiue angulus
              <lb/>
            buius ſinus inuenti ad ſemiſſem aggregati dati, dabit maiorem arcum, vel
              <lb/>
            angulum; </s>
            <s xml:id="echoid-s9815" xml:space="preserve">ablatus vero ex eadem ſemiſſe relinquet minorem arcum, ſiu@
              <lb/>
            angulum. </s>
            <s xml:id="echoid-s9816" xml:space="preserve">Sed priores duæ viæ longe ſunt expeditiores; </s>
            <s xml:id="echoid-s9817" xml:space="preserve">vt perſpicuum eſt</s>
          </p>
          <p>
            <s xml:id="echoid-s9818" xml:space="preserve">DETVR deinde aggregatum arcuum BC, CD, quorum ſinguli ſemicit
              <lb/>
              <note position="left" xlink:label="note-326-03" xlink:href="note-326-03a" xml:space="preserve">Quádo ag-
                <lb/>
              gregatũ ar
                <lb/>
              cuũ, vel an
                <lb/>
              gulorũ ma
                <lb/>
              ius eſt, quá
                <lb/>
              grad.180.</note>
            culo quoq; </s>
            <s xml:id="echoid-s9819" xml:space="preserve">ſint minores, vel angulorum BEC, CED, at aggregatum tam
              <lb/>
            arcuum, quam angulorum ſuperet grad. </s>
            <s xml:id="echoid-s9820" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9821" xml:space="preserve">nempe detur grad. </s>
            <s xml:id="echoid-s9822" xml:space="preserve">230. </s>
            <s xml:id="echoid-s9823" xml:space="preserve">Detut
              <lb/>
            item proportio ſinus arcus BC, vel anguli BEC, ad ſinum arcus CD, vel an-
              <lb/>
            guli CED, eadem, quæ 10. </s>
            <s xml:id="echoid-s9824" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9825" xml:space="preserve">Oportet ex his vtrumq; </s>
            <s xml:id="echoid-s9826" xml:space="preserve">arcum BC, CD, vel
              <lb/>
            vtrumq; </s>
            <s xml:id="echoid-s9827" xml:space="preserve">angulum BEC, CED, elicere. </s>
            <s xml:id="echoid-s9828" xml:space="preserve">Ducta diametro CF, & </s>
            <s xml:id="echoid-s9829" xml:space="preserve">detracto da-
              <lb/>
            to aggregato ex integro circulo, hoc eſt, ex grad. </s>
            <s xml:id="echoid-s9830" xml:space="preserve">360. </s>
            <s xml:id="echoid-s9831" xml:space="preserve">reliquum erit aggrega-
              <lb/>
            tum arcuum BF, FD, vel angulorum BEF, FED, grad. </s>
            <s xml:id="echoid-s9832" xml:space="preserve">130. </s>
            <s xml:id="echoid-s9833" xml:space="preserve">minus, quam
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9834" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9835" xml:space="preserve">Et quoniam arcus BC, BF, eundem ſinuum habent, necnon & </s>
            <s xml:id="echoid-s9836" xml:space="preserve">ar-
              <lb/>
            cus CD, FD, vt in deſin. </s>
            <s xml:id="echoid-s9837" xml:space="preserve">ſinuum diximus, data quoq; </s>
            <s xml:id="echoid-s9838" xml:space="preserve">erit proportio ſinuum
              <lb/>
            arcuum BF, FD, vel angulorum BEF, FED, eadem, quæ 10. </s>
            <s xml:id="echoid-s9839" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s9840" xml:space="preserve">Quam
              <lb/>
            ob rem, vt iam demonſtratum eſt, inueniemus arcus BF, FD, vel angulos
              <lb/>
            BEF, FED, grad. </s>
            <s xml:id="echoid-s9841" xml:space="preserve">100. </s>
            <s xml:id="echoid-s9842" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9843" xml:space="preserve">34. </s>
            <s xml:id="echoid-s9844" xml:space="preserve">& </s>
            <s xml:id="echoid-s9845" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9846" xml:space="preserve">29. </s>
            <s xml:id="echoid-s9847" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9848" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9849" xml:space="preserve">qui ex ſemicirculo, hoc
              <lb/>
            eſt, ex grad. </s>
            <s xml:id="echoid-s9850" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9851" xml:space="preserve">ſublati relinquent arcus BC, CD, vel angulos BEC, CED,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s9852" xml:space="preserve">79. </s>
            <s xml:id="echoid-s9853" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9854" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9855" xml:space="preserve">& </s>
            <s xml:id="echoid-s9856" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9857" xml:space="preserve">150. </s>
            <s xml:id="echoid-s9858" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s9859" xml:space="preserve">34.</s>
            <s xml:id="echoid-s9860" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9861" xml:space="preserve">QVANDO ergo aggregatum duorum arcuum, ſeu angulorum ma-
              <lb/>
              <note position="left" xlink:label="note-326-04" xlink:href="note-326-04a" xml:space="preserve">Praxis.</note>
            ius eſt, quam grad. </s>
            <s xml:id="echoid-s9862" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9863" xml:space="preserve">Si illud ex grad. </s>
            <s xml:id="echoid-s9864" xml:space="preserve">360. </s>
            <s xml:id="echoid-s9865" xml:space="preserve">auferamus, remanebit
              <lb/>
            aggregatum aliorum duorum arcuum, vel angulorum minus, quam grad.</s>
            <s xml:id="echoid-s9866" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum