Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s17326" xml:space="preserve">
              <pb o="367" file="395" n="395" rhead="LIBER OCTAVVS."/>
            quadratum æquale eſt rectangulo ſub AD, AB, quo diuiſo per AB, altitudinem
              <lb/>
            montis, prodibit in Quotiente recta A D; </s>
            <s xml:id="echoid-s17327" xml:space="preserve">ex qua ſi dematur altitudo montis
              <lb/>
            A B, nota relinquetur diameter terræ BD. </s>
            <s xml:id="echoid-s17328" xml:space="preserve"> Ac proinde circumferentia B C
              <note symbol="a" position="right" xlink:label="note-395-01" xlink:href="note-395-01a" xml:space="preserve">coroll. 2. de
                <lb/>
              Dimens. cir-
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              culi lib. 4. hu-
                <lb/>
              i{us}.</note>
            cognita fiet.</s>
            <s xml:id="echoid-s17329" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17330" xml:space="preserve">
              <emph style="sc">Sed</emph>
            quia in hac ratione metiendi ambitus terreſtris aſſumitur, arcum B C,
              <lb/>
            à linea recta non diſferre. </s>
            <s xml:id="echoid-s17331" xml:space="preserve">quod verum non eſt, quando mons tam altus eſt, vt
              <lb/>
            ſpacium 200. </s>
            <s xml:id="echoid-s17332" xml:space="preserve">vel 300. </s>
            <s xml:id="echoid-s17333" xml:space="preserve">milliariorum cerni poſsit, quod tunc arcus BC, iuxta am-
              <lb/>
            bitum à Ptolomæo poſitum contineat grad. </s>
            <s xml:id="echoid-s17334" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17335" xml:space="preserve">min. </s>
            <s xml:id="echoid-s17336" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17337" xml:space="preserve">vel grad. </s>
            <s xml:id="echoid-s17338" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17339" xml:space="preserve">min. </s>
            <s xml:id="echoid-s17340" xml:space="preserve">48. </s>
            <s xml:id="echoid-s17341" xml:space="preserve">Ac
              <lb/>
            proinde non rectè linea tangens A C, ex lateribus A B, BC, colligitur. </s>
            <s xml:id="echoid-s17342" xml:space="preserve">Adde
              <lb/>
            quod per ptoblemata lib. </s>
            <s xml:id="echoid-s17343" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17344" xml:space="preserve">& </s>
            <s xml:id="echoid-s17345" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17346" xml:space="preserve">citata inuenitur perpendicularis BE, in plano,
              <lb/>
            ad quod mons eſt ad angulos rectos: </s>
            <s xml:id="echoid-s17347" xml:space="preserve">Redigemus rationem hanc ad meliorem
              <lb/>
            formam multis viis hoc modo. </s>
            <s xml:id="echoid-s17348" xml:space="preserve">Deprehenſo angulo A, per Quadrantem, vel
              <lb/>
            Quadratum, quando radius viſualis per dioptram circulum terræ tangit. </s>
            <s xml:id="echoid-s17349" xml:space="preserve">Quod
              <lb/>
            tum denique certiſsimè fiet, cum per dioptram conſpicitur Sol, aut alia ſtella,
              <lb/>
            quando oritur, vel occidit. </s>
            <s xml:id="echoid-s17350" xml:space="preserve">Deprehenſo, inquam, angulo A, inuenienda erit
              <lb/>
            perpendicularis BE, per problemata paulò ante citata. </s>
            <s xml:id="echoid-s17351" xml:space="preserve"> Etrecta AE, ex
              <note symbol="b" position="right" xlink:label="note-395-02" xlink:href="note-395-02a" xml:space="preserve">47. primi.</note>
            A B, B E. </s>
            <s xml:id="echoid-s17352" xml:space="preserve">Si enim ad A E, adiicietur BE, hoc eſt, EC, quæ ipſi BE, æqualis
              <note symbol="c" position="right" xlink:label="note-395-03" xlink:href="note-395-03a" xml:space="preserve">2. coroll. 36.
                <lb/>
              tertii.</note>
            nota fiet tota tangens AC, ex qua, vt ſupra dictum eſt, & </s>
            <s xml:id="echoid-s17353" xml:space="preserve">diameter terræ BD, & </s>
            <s xml:id="echoid-s17354" xml:space="preserve">
              <lb/>
            circumferentia inueſtigabitur. </s>
            <s xml:id="echoid-s17355" xml:space="preserve">Quin etiam cognito angulo A, ac proinde & </s>
            <s xml:id="echoid-s17356" xml:space="preserve">eius
              <lb/>
            complemento E, reperietur tam latus B E, quam baſis A E,
              <note symbol="d" position="right" xlink:label="note-395-04" xlink:href="note-395-04a" xml:space="preserve">4. triang.
                <lb/>
              rectil.</note>
            bus ex lib. </s>
            <s xml:id="echoid-s17357" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17358" xml:space="preserve">& </s>
            <s xml:id="echoid-s17359" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17360" xml:space="preserve">citatis, &</s>
            <s xml:id="echoid-s17361" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17363" xml:space="preserve">
              <emph style="sc">Vel</emph>
            ſic agemus. </s>
            <s xml:id="echoid-s17364" xml:space="preserve">Cognito per dioptram angulo A, cognitus etiam erit (du-
              <lb/>
              <note symbol="e" position="right" xlink:label="note-395-05" xlink:href="note-395-05a" xml:space="preserve">5. triang. re-
                <lb/>
              ctil.</note>
            cta recta F C, quæ ad A C, perpendicularis erit) angulus F, eius complemen- tum in centro. </s>
            <s xml:id="echoid-s17365" xml:space="preserve">Quia verò ducta recta FE, duo latera EC, CF, duobus lateribus
              <lb/>
              <note symbol="f" position="right" xlink:label="note-395-06" xlink:href="note-395-06a" xml:space="preserve">18. tertii.</note>
            E B, BF, æqualia ſunt, comprehenduntque angulos æquales, nemperectos:
              <lb/>
            </s>
            <s xml:id="echoid-s17366" xml:space="preserve"> erunt anguli ad F, æquales. </s>
            <s xml:id="echoid-s17367" xml:space="preserve">Cum ergo totus angulus B F C, cognitus ſit,
              <note symbol="g" position="right" xlink:label="note-395-07" xlink:href="note-395-07a" xml:space="preserve">4. primi.</note>
            proximè diximus; </s>
            <s xml:id="echoid-s17368" xml:space="preserve">cognitus etiam erit BFE, tanquam ſemiſsis ipſius: </s>
            <s xml:id="echoid-s17369" xml:space="preserve">ac proin-
              <lb/>
            de & </s>
            <s xml:id="echoid-s17370" xml:space="preserve">eius complementum B E F, notum erit. </s>
            <s xml:id="echoid-s17371" xml:space="preserve">Igitur in triangulo ABE, ex an-
              <lb/>
            gulis A, E, & </s>
            <s xml:id="echoid-s17372" xml:space="preserve">latere AE, reperietur BE, in partibus altitudinis montis A B,
              <note symbol="h" position="right" xlink:label="note-395-08" xlink:href="note-395-08a" xml:space="preserve">4. rectang.
                <lb/>
              rectil.</note>
            tæ. </s>
            <s xml:id="echoid-s17373" xml:space="preserve">Atque eodem modo in triangulo B E F, ex angulis E, F, & </s>
            <s xml:id="echoid-s17374" xml:space="preserve">latere BE, cog-
              <lb/>
            noſcetur ſemidiameter B F, in partibus lateris BE, hoc eſt, in partibus altitudinis
              <lb/>
            montis A B; </s>
            <s xml:id="echoid-s17375" xml:space="preserve">ideoque & </s>
            <s xml:id="echoid-s17376" xml:space="preserve">tota diameter B D, nota fiet, & </s>
            <s xml:id="echoid-s17377" xml:space="preserve">ex hac ambitus terræ.
              <lb/>
            </s>
            <s xml:id="echoid-s17378" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17379" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17380" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            hoc etiam modo idem aſſequemur. </s>
            <s xml:id="echoid-s17381" xml:space="preserve">Cognito per dioptram an-
              <lb/>
            gulo A, quando radius viſualis terram contingit, cognitus etiam erit angulus
              <lb/>
            A F C, eius complementum. </s>
            <s xml:id="echoid-s17382" xml:space="preserve">Ergo huius anguli ſecans AF, cognita erit in parti-
              <lb/>
            busſinus totius FC. </s>
            <s xml:id="echoid-s17383" xml:space="preserve">Ex qua ſecante, ſi dematur ſinus BF, nota relinquetur alti-
              <lb/>
            tudo montis AB, in partibus ſinus totius BF. </s>
            <s xml:id="echoid-s17384" xml:space="preserve">Si igitur fiat, vt altitudo montis
              <lb/>
            AB, nota in partibus ſinus totius ad eandem A B, notam in data menſura, ita ſi-
              <lb/>
            nus totus BF, ad aliud; </s>
            <s xml:id="echoid-s17385" xml:space="preserve">proueniet ſemidiameter BF, nota in partibus altitudinis
              <lb/>
            montis, &</s>
            <s xml:id="echoid-s17386" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17387" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1068" type="section" level="1" n="383">
          <head xml:id="echoid-head410" xml:space="preserve">PROBL. 21. PROPOS. 35.</head>
          <p>
            <s xml:id="echoid-s17388" xml:space="preserve">PRISMATI cuicunque Cylindrum æqualem, & </s>
            <s xml:id="echoid-s17389" xml:space="preserve">Pyramidi Conum
              <lb/>
            æqualem: </s>
            <s xml:id="echoid-s17390" xml:space="preserve">Ac viciſsim Cylindro Priſma æquale, & </s>
            <s xml:id="echoid-s17391" xml:space="preserve">Cono æqualem
              <lb/>
            Pyramidem conſtituere.</s>
            <s xml:id="echoid-s17392" xml:space="preserve"/>
          </p>
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