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

Page concordance

< >
Scan Original
161 149
162 150
163 151
164 152
165 153
166 154
167 155
168 156
169 157
170 158
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
< >
page |< < (301) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div779" type="section" level="1" n="453">
          <p>
            <s xml:id="echoid-s8825" xml:space="preserve">
              <pb o="301" file="313" n="313" rhead=""/>
            rint, vel alter eorũ obtuſus: </s>
            <s xml:id="echoid-s8826" xml:space="preserve">erit in triangulo rectangulo ABD, vt latus AB,
              <lb/>
            ad latus AD, ita ſinus anguli recti D, ad ſinum anguli B, vt ſupra eſt demon-
              <lb/>
            ſtratum: </s>
            <s xml:id="echoid-s8827" xml:space="preserve">Item in triangulo rectangulo ADC, vt latus AD, ad latus AC, ita
              <lb/>
            ſinus anguli C, ad ſinum anguli recti D. </s>
            <s xml:id="echoid-s8828" xml:space="preserve">Ex æqualitate ergo, & </s>
            <s xml:id="echoid-s8829" xml:space="preserve">perturbata
              <lb/>
            proportione erit, vt latus AB, ad latus AC, ita ſinus anguli C, (Habẽt enim
              <lb/>
            duo anguli ad C, in obtuſangulo triangulo eundem ſinum, vt in tractatione
              <lb/>
            ſinuum oſtendimus. </s>
            <s xml:id="echoid-s8830" xml:space="preserve">ad ſinum anguli B, vt in formula ſuprapoſita apparet: </s>
            <s xml:id="echoid-s8831" xml:space="preserve">Et
              <lb/>
            conuertendo quoq;</s>
            <s xml:id="echoid-s8832" xml:space="preserve">, vt latus AC, ad latus AB, ita ſinus anguli B, ad ſinum
              <lb/>
            anguli C. </s>
            <s xml:id="echoid-s8833" xml:space="preserve">Eodem modo concludemus eſſe, vt latus AB, ad latus BC, ita ſi-
              <lb/>
            num anguli C, ad ſinum anguli BAC: </s>
            <s xml:id="echoid-s8834" xml:space="preserve">Vel vt latus BC, ad latus AB, ita ſi-
              <lb/>
            num anguli BAC, ad ſinum anguli C, &</s>
            <s xml:id="echoid-s8835" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8836" xml:space="preserve">Quocirca in omni triangulo re-
              <lb/>
            ctilineo latera quæuis duo eandem proportionem habent, quam ſinus angu-
              <lb/>
            lorum illis oppoſitorum. </s>
            <s xml:id="echoid-s8837" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s8838" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div784" type="section" level="1" n="454">
          <head xml:id="echoid-head486" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Qua rŏne
            <lb/>
          ex @@ibꝰ vel
            <lb/>
          duobusan-
            <lb/>
          gulis notis
            <lb/>
          cuiuſuis
            <lb/>
          triãguli co-
            <lb/>
          gnoſcantur
            <lb/>
          propottio-
            <lb/>
          nes laterũ.</note>
          <p style="it">
            <s xml:id="echoid-s8839" xml:space="preserve">_EX_ hac propoſ facile colligemus proportiones laterum cuiuſuis trianguli recti-
              <lb/>
            linei, cuius omnes anguli cogniti ſint, vel duo tantum Sint entm omnes anguli in
              <lb/>
            triangulo _ABC,_ noti. </s>
            <s xml:id="echoid-s8840" xml:space="preserve">Dico proportiones laterum notas eſſe. </s>
            <s xml:id="echoid-s8841" xml:space="preserve">Cum enim eadem
              <lb/>
            ſit proportio lateris _AB,_ ad latus
              <lb/>
              <figure xlink:label="fig-313-01" xlink:href="fig-313-01a" number="163">
                <image file="313-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/313-01"/>
              </figure>
            _AC,_ quæ ſinus anguli _C,_ ad ſinum
              <lb/>
            anguli _B;_ </s>
            <s xml:id="echoid-s8842" xml:space="preserve">ſint autem ſinus angulorũ
              <lb/>
              <note position="right" xlink:label="note-313-02" xlink:href="note-313-02a" xml:space="preserve">@.huius.</note>
            _C, B,_ notorum cogniti ex tabula ſi-
              <lb/>
            nuum; </s>
            <s xml:id="echoid-s8843" xml:space="preserve">nota erit proportio lateris _AB,_
              <lb/>
            ad latus _AC,_ &</s>
            <s xml:id="echoid-s8844" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8845" xml:space="preserve">Exempli cauſa,
              <lb/>
            ponatur in primo triangulo angulus
              <lb/>
            _C,_ grad. </s>
            <s xml:id="echoid-s8846" xml:space="preserve">_60. </s>
            <s xml:id="echoid-s8847" xml:space="preserve">B,_ grad. </s>
            <s xml:id="echoid-s8848" xml:space="preserve">_50. </s>
            <s xml:id="echoid-s8849" xml:space="preserve">& </s>
            <s xml:id="echoid-s8850" xml:space="preserve">A,_
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8851" xml:space="preserve">_70._ </s>
            <s xml:id="echoid-s8852" xml:space="preserve">Horum ſinus ſunt _86602._
              <lb/>
            </s>
            <s xml:id="echoid-s8853" xml:space="preserve">_76604. </s>
            <s xml:id="echoid-s8854" xml:space="preserve">93969._ </s>
            <s xml:id="echoid-s8855" xml:space="preserve">Eſt ergo proportio
              <lb/>
            _AB,_ ad _AC,_ eadem, quæ _86602._ </s>
            <s xml:id="echoid-s8856" xml:space="preserve">ad _76604._ </s>
            <s xml:id="echoid-s8857" xml:space="preserve">& </s>
            <s xml:id="echoid-s8858" xml:space="preserve">_AB,_ ad _BC,_ eadem, quæ _86602._ </s>
            <s xml:id="echoid-s8859" xml:space="preserve">
              <lb/>
            ad _93969._ </s>
            <s xml:id="echoid-s8860" xml:space="preserve">& </s>
            <s xml:id="echoid-s8861" xml:space="preserve">_AC,_ ad _BC,_ eadem, quæ _76604._ </s>
            <s xml:id="echoid-s8862" xml:space="preserve">ad _93969._ </s>
            <s xml:id="echoid-s8863" xml:space="preserve">In triangulo vero ſecun
              <lb/>
            do ponatur angulus _B,_ rectus, ac proinde grad. </s>
            <s xml:id="echoid-s8864" xml:space="preserve">_90. </s>
            <s xml:id="echoid-s8865" xml:space="preserve">C,_ grad. </s>
            <s xml:id="echoid-s8866" xml:space="preserve">_50._ </s>
            <s xml:id="echoid-s8867" xml:space="preserve">& </s>
            <s xml:id="echoid-s8868" xml:space="preserve">_A,_ grad _40._ </s>
            <s xml:id="echoid-s8869" xml:space="preserve">
              <lb/>
            Horum ſinus ſunt _100000. </s>
            <s xml:id="echoid-s8870" xml:space="preserve">76604. </s>
            <s xml:id="echoid-s8871" xml:space="preserve">64278._ </s>
            <s xml:id="echoid-s8872" xml:space="preserve">Eritigitur _AB,_ ad _AC,_ vt _76604._ </s>
            <s xml:id="echoid-s8873" xml:space="preserve">ad
              <lb/>
            _100000._ </s>
            <s xml:id="echoid-s8874" xml:space="preserve">& </s>
            <s xml:id="echoid-s8875" xml:space="preserve">_AB,_ ad _BC,_ vt _76604._ </s>
            <s xml:id="echoid-s8876" xml:space="preserve">ad _64278._ </s>
            <s xml:id="echoid-s8877" xml:space="preserve">& </s>
            <s xml:id="echoid-s8878" xml:space="preserve">_AC,_ ad _BC,_ vt _100000._ </s>
            <s xml:id="echoid-s8879" xml:space="preserve">ad
              <lb/>
            _64278._ </s>
            <s xml:id="echoid-s8880" xml:space="preserve">In triangulo deniq; </s>
            <s xml:id="echoid-s8881" xml:space="preserve">tertio ſtatuatur angulus _B,_ obtuſus & </s>
            <s xml:id="echoid-s8882" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s8883" xml:space="preserve">_124 C,_
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8884" xml:space="preserve">_30_ & </s>
            <s xml:id="echoid-s8885" xml:space="preserve">_A,_ grad _26_ Horum ſinus ſunt (ſi pro ſinu anguli obtuſi accipiatur ſi-
              <lb/>
            nus complementi ipſius vſq; </s>
            <s xml:id="echoid-s8886" xml:space="preserve">ad grad. </s>
            <s xml:id="echoid-s8887" xml:space="preserve">_180_ nempe ſinus grad _56._) </s>
            <s xml:id="echoid-s8888" xml:space="preserve">_82903. </s>
            <s xml:id="echoid-s8889" xml:space="preserve">50000._ </s>
            <s xml:id="echoid-s8890" xml:space="preserve">
              <lb/>
            _43837_ Quare erit _AB,_ ad _AC,_ vt _50000._ </s>
            <s xml:id="echoid-s8891" xml:space="preserve">ad _82903._ </s>
            <s xml:id="echoid-s8892" xml:space="preserve">& </s>
            <s xml:id="echoid-s8893" xml:space="preserve">_AB,_ ad _BC,_ vt _50000._ </s>
            <s xml:id="echoid-s8894" xml:space="preserve">
              <lb/>
            ad _43837._ </s>
            <s xml:id="echoid-s8895" xml:space="preserve">& </s>
            <s xml:id="echoid-s8896" xml:space="preserve">_AC,_ ad _BC,_ vt _82903._ </s>
            <s xml:id="echoid-s8897" xml:space="preserve">ad _43837._</s>
            <s xml:id="echoid-s8898" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8899" xml:space="preserve">IT AQVE vt facile pro@ortiones laterum habeantur, ſatis eſt, ſila-
              <lb/>
              <note position="right" xlink:label="note-313-03" xlink:href="note-313-03a" xml:space="preserve">Praxis.</note>
            teribus ſinus angulorum oppoſitorum aſcribantur: </s>
            <s xml:id="echoid-s8900" xml:space="preserve">propterea quòd late-
              <lb/>
            ra eandem proportionem habent, quam oppoſitorum angulorum ſinus, vt
              <lb/>
            demonſtratum eſt.</s>
            <s xml:id="echoid-s8901" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8902" xml:space="preserve">_QVOD_ ſi duo tantum anguli cogniti ſint, erit reliquus tertius quoq; </s>
            <s xml:id="echoid-s8903" xml:space="preserve">notus.
              <lb/>
            </s>
            <s xml:id="echoid-s8904" xml:space="preserve">Quare, vt prius, laterum proportiones cognoſcentur.</s>
            <s xml:id="echoid-s8905" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8906" xml:space="preserve">_POSSVMVS_ eaſdem proportiones laterum cognoſcere ex angulis datis, ſine
              <lb/>
            auxilio antecedentis propoſ. </s>
            <s xml:id="echoid-s8907" xml:space="preserve">hoc modo. </s>
            <s xml:id="echoid-s8908" xml:space="preserve">Circa datum triangulum _ABC,_ deſcriba-
              <lb/>
              <note position="right" xlink:label="note-313-04" xlink:href="note-313-04a" xml:space="preserve">5. quarti.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum