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

Table of figures

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        <div xml:id="echoid-div784" type="section" level="1" n="454">
          <p style="it">
            <s xml:id="echoid-s9068" xml:space="preserve">
              <pb o="304" file="316" n="316" rhead=""/>
            _28._ </s>
            <s xml:id="echoid-s9069" xml:space="preserve">continuabimus eas, ponendo _
              <emph style="sc">B</emph>
            ,_ ad _C,_ vt _10._ </s>
            <s xml:id="echoid-s9070" xml:space="preserve">ad _12._ </s>
            <s xml:id="echoid-s9071" xml:space="preserve">& </s>
            <s xml:id="echoid-s9072" xml:space="preserve">_C,_ ad _A,_ vt _24._ </s>
            <s xml:id="echoid-s9073" xml:space="preserve">ad _28._ </s>
            <s xml:id="echoid-s9074" xml:space="preserve">&</s>
            <s xml:id="echoid-s9075" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9076" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9077" xml:space="preserve">_SED_ demus aliud exemplum in tertio triangulo eiuſdem figuræ, in quo ſit pro-
              <lb/>
            portio anguli _
              <emph style="sc">B</emph>
            ,_ ad angulum _C,_ vt _62._ </s>
            <s xml:id="echoid-s9078" xml:space="preserve">ad _15._ </s>
            <s xml:id="echoid-s9079" xml:space="preserve">& </s>
            <s xml:id="echoid-s9080" xml:space="preserve">proportio anguli _
              <emph style="sc">B</emph>
            ,_ ad angulum
              <lb/>
            _A,_ vt _248._ </s>
            <s xml:id="echoid-s9081" xml:space="preserve">ad _52._ </s>
            <s xml:id="echoid-s9082" xml:space="preserve">Quoniam angulus _B,_ bis fuit antecedens, hoc eſt, proportiones
              <lb/>
            datæ non ſunt continuatæ, eas continuabimus, ſtatuendo proportionem _A,_ ad _B,_ vt _52._
              <lb/>
            </s>
            <s xml:id="echoid-s9083" xml:space="preserve">ad _248._ </s>
            <s xml:id="echoid-s9084" xml:space="preserve">& </s>
            <s xml:id="echoid-s9085" xml:space="preserve">_
              <emph style="sc">B</emph>
            ,_ ad _C,_ vt _62._ </s>
            <s xml:id="echoid-s9086" xml:space="preserve">ad _15._ </s>
            <s xml:id="echoid-s9087" xml:space="preserve">Inuentis autem minimis numeris _13. </s>
            <s xml:id="echoid-s9088" xml:space="preserve">62._ </s>
            <s xml:id="echoid-s9089" xml:space="preserve">eandem
              <lb/>
            proportionem habentibus, quam anguli _A, B,_ ſiue numeri _52. </s>
            <s xml:id="echoid-s9090" xml:space="preserve">248._ </s>
            <s xml:id="echoid-s9091" xml:space="preserve">erunt duæ datæ
              <lb/>
            proportiones continuatæ in his tribus numeris minimis _13. </s>
            <s xml:id="echoid-s9092" xml:space="preserve">62. </s>
            <s xml:id="echoid-s9093" xml:space="preserve">15._ </s>
            <s xml:id="echoid-s9094" xml:space="preserve">vt conſtat. </s>
            <s xml:id="echoid-s9095" xml:space="preserve">Col-
              <lb/>
            lectis ergo ipſis in vnam ſummam _90._ </s>
            <s xml:id="echoid-s9096" xml:space="preserve">inueniemus per regulam Societatum angulos in
              <lb/>
            gradibus, vt hic apparet.</s>
            <s xml:id="echoid-s9097" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9098" xml:space="preserve">90. </s>
            <s xml:id="echoid-s9099" xml:space="preserve">180. </s>
            <s xml:id="echoid-s9100" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9101" xml:space="preserve">{13? </s>
            <s xml:id="echoid-s9102" xml:space="preserve">\\ 62? </s>
            <s xml:id="echoid-s9103" xml:space="preserve">\\ 15?</s>
            <s xml:id="echoid-s9104" xml:space="preserve">} fiunt {26. </s>
            <s xml:id="echoid-s9105" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s9106" xml:space="preserve">\\ 124. </s>
            <s xml:id="echoid-s9107" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s9108" xml:space="preserve">\\ 30. </s>
            <s xml:id="echoid-s9109" xml:space="preserve">gr.</s>
            <s xml:id="echoid-s9110" xml:space="preserve">} pro angulo {A. </s>
            <s xml:id="echoid-s9111" xml:space="preserve">\\ B. </s>
            <s xml:id="echoid-s9112" xml:space="preserve">\\ C.
              <lb/>
            </s>
            <s xml:id="echoid-s9113" xml:space="preserve">Inuentis hac ratione angulis, reperientur laterum proportiones, vt prius.</s>
            <s xml:id="echoid-s9114" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9115" xml:space="preserve">_PORRO_ in triangulo rectangulo ſatis eſt, ſi duorũ angulorum proportio detur.
              <lb/>
            </s>
            <s xml:id="echoid-s9116" xml:space="preserve">
              <note position="left" xlink:label="note-316-01" xlink:href="note-316-01a" xml:space="preserve">Quo pacto
                <lb/>
              ex propor-
                <lb/>
              tione duo-
                <lb/>
              tũ tantum
                <lb/>
              angulorũ
                <lb/>
              in triangu-
                <lb/>
              lo rectangu
                <lb/>
              lo propot
                <lb/>
              tiones late-
                <lb/>
              rum cogno
                <lb/>
              ſeantur.</note>
            Sit enim in ſecundo triangulo eiuſdem figuræ proportio anguli _A,_ ad angulum _
              <emph style="sc">B</emph>
            ,_ re-
              <lb/>
            ctum, vt _8._ </s>
            <s xml:id="echoid-s9117" xml:space="preserve">ad _18._ </s>
            <s xml:id="echoid-s9118" xml:space="preserve">Quoniam ergo rectus angulus _B,_ eſt grad. </s>
            <s xml:id="echoid-s9119" xml:space="preserve">_90._ </s>
            <s xml:id="echoid-s9120" xml:space="preserve">inueniemus per re-
              <lb/>
            gulam auream angulum _A,_ eſſe grad. </s>
            <s xml:id="echoid-s9121" xml:space="preserve">_40._ </s>
            <s xml:id="echoid-s9122" xml:space="preserve">vt hic vides.</s>
            <s xml:id="echoid-s9123" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9124" xml:space="preserve">18. </s>
            <s xml:id="echoid-s9125" xml:space="preserve">90. </s>
            <s xml:id="echoid-s9126" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9127" xml:space="preserve">8? </s>
            <s xml:id="echoid-s9128" xml:space="preserve">fiunt 40. </s>
            <s xml:id="echoid-s9129" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s9130" xml:space="preserve">pro angulo A.
              <lb/>
            </s>
            <s xml:id="echoid-s9131" xml:space="preserve">Reliquus ergo angulus _C,_ complectetur grad. </s>
            <s xml:id="echoid-s9132" xml:space="preserve">_50._ </s>
            <s xml:id="echoid-s9133" xml:space="preserve">&</s>
            <s xml:id="echoid-s9134" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9135" xml:space="preserve">Sit rurſum proportio aculi
              <lb/>
            anguli _A,_ ad angulum acutum _C,_ vt _16._ </s>
            <s xml:id="echoid-s9136" xml:space="preserve">ad _20._ </s>
            <s xml:id="echoid-s9137" xml:space="preserve">Quoniam ergo duo anguli _A, C,_ vni
              <lb/>
            recto ſunt æquales, hoc eſt, continẽt grad. </s>
            <s xml:id="echoid-s9138" xml:space="preserve">_90._ </s>
            <s xml:id="echoid-s9139" xml:space="preserve">Collectis numeris _16._ </s>
            <s xml:id="echoid-s9140" xml:space="preserve">& </s>
            <s xml:id="echoid-s9141" xml:space="preserve">_20._ </s>
            <s xml:id="echoid-s9142" xml:space="preserve">in vnam
              <lb/>
            ſummam _36._ </s>
            <s xml:id="echoid-s9143" xml:space="preserve">reperiemus per regulam Societatum vtrumq; </s>
            <s xml:id="echoid-s9144" xml:space="preserve">angulum in gradibus, vt
              <lb/>
            hic cernis.</s>
            <s xml:id="echoid-s9145" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9146" xml:space="preserve">36. </s>
            <s xml:id="echoid-s9147" xml:space="preserve">90. </s>
            <s xml:id="echoid-s9148" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s9149" xml:space="preserve">{16? </s>
            <s xml:id="echoid-s9150" xml:space="preserve">\\ 20?</s>
            <s xml:id="echoid-s9151" xml:space="preserve">} fiunt {40. </s>
            <s xml:id="echoid-s9152" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s9153" xml:space="preserve">\\ 50. </s>
            <s xml:id="echoid-s9154" xml:space="preserve">gr.</s>
            <s xml:id="echoid-s9155" xml:space="preserve">} pro angulo {A. </s>
            <s xml:id="echoid-s9156" xml:space="preserve">\\ C.
              <lb/>
            </s>
            <s xml:id="echoid-s9157" xml:space="preserve">Iuuentis autem angulis hac ratione, notæ fient laterum proportiones, vt prius.</s>
            <s xml:id="echoid-s9158" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quo pacto
            <lb/>
          ex propor-
            <lb/>
          tione vtriuſ
            <lb/>
          uis angulo
            <lb/>
          rum æqua-
            <lb/>
          lium ad ter
            <lb/>
          tium angu
            <lb/>
          lum in triã
            <lb/>
          gulo Iſoſce
            <lb/>
          le inueniã-
            <lb/>
          cur laterũ
            <lb/>
          proportio-
            <lb/>
          nes.</note>
          <p style="it">
            <s xml:id="echoid-s9159" xml:space="preserve">_EODEM_ modo in triangulo Iſoſcele ſatis eſt, ſi proportio vtriuslibet æqualium
              <lb/>
            angulorum ad tertium angulum cognoſcatur, aut tertij anguli ad vtrumlibet angu-
              <lb/>
              <figure xlink:label="fig-316-01" xlink:href="fig-316-01a" number="166">
                <image file="316-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/316-01"/>
              </figure>
            lorum æqualium. </s>
            <s xml:id="echoid-s9160" xml:space="preserve">Nam ſi in triangulo Iſoſcele _
              <emph style="sc">Ab</emph>
            C,_ cu-
              <lb/>
            ius duo latera _AB, AC,_ æqualia ſunt, cognita ſit propor-
              <lb/>
            tio anguli _
              <emph style="sc">B</emph>
            ,_ ad angulum _A,_ nempe eadem, quæ _10._ </s>
            <s xml:id="echoid-s9161" xml:space="preserve">ad _16._
              <lb/>
            </s>
            <s xml:id="echoid-s9162" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s9163" xml:space="preserve">proportio anguli _C,_ @ad angulum _A,_ vt _10._ </s>
            <s xml:id="echoid-s9164" xml:space="preserve">ad _16._ </s>
            <s xml:id="echoid-s9165" xml:space="preserve">
              <lb/>
            Quare duæ proportiones notæ erunt, quas continuabimus,
              <lb/>
            ſi dicamus proportionem _
              <emph style="sc">A</emph>
            ,_ ad _
              <emph style="sc">B</emph>
            ,_ eſſe, vt _16._ </s>
            <s xml:id="echoid-s9166" xml:space="preserve">ad _10._ </s>
            <s xml:id="echoid-s9167" xml:space="preserve">& </s>
            <s xml:id="echoid-s9168" xml:space="preserve">_B,_
              <lb/>
            ad _C,_ vt _10._ </s>
            <s xml:id="echoid-s9169" xml:space="preserve">ad _10._ </s>
            <s xml:id="echoid-s9170" xml:space="preserve">Ex quibus inuenietur angulus _A,_ grad. </s>
            <s xml:id="echoid-s9171" xml:space="preserve">
              <lb/>
            _80._ </s>
            <s xml:id="echoid-s9172" xml:space="preserve">& </s>
            <s xml:id="echoid-s9173" xml:space="preserve">vterq; </s>
            <s xml:id="echoid-s9174" xml:space="preserve">_
              <emph style="sc">B</emph>
            , C,_ grad. </s>
            <s xml:id="echoid-s9175" xml:space="preserve">_50._ </s>
            <s xml:id="echoid-s9176" xml:space="preserve">per ea, quæ iam demonſtra-
              <lb/>
            ta ſunt.</s>
            <s xml:id="echoid-s9177" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9178" xml:space="preserve">_
              <emph style="sc">De</emph>
            _ æquilatero triangulo non eſt, quòd quicquam præcipiamus, cum in eo late-
              <lb/>
            @a babeant æqualitatis proportionem.</s>
            <s xml:id="echoid-s9179" xml:space="preserve"/>
          </p>
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    </echo>
Impressum