Clavius, Christoph, Geometria practica

Table of Notes

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          <p>
            <s xml:id="echoid-s6554" xml:space="preserve">
              <pb o="164" file="194" n="194" rhead="GEOMETR. PRACT."/>
            quæad huncnumerum 9 {547/1208}. </s>
            <s xml:id="echoid-s6555" xml:space="preserve">reducetur, ſi numerator per denominatorem
              <lb/>
            diuidatur: </s>
            <s xml:id="echoid-s6556" xml:space="preserve">atque tanta eſt fermè perpendicularis DC, nimirum 9 {547/1208}. </s>
            <s xml:id="echoid-s6557" xml:space="preserve">Sic et-
              <lb/>
            iam ſi differentia 2 {3/8}. </s>
            <s xml:id="echoid-s6558" xml:space="preserve">inter ſegmentum B C, 17 {5/8}. </s>
            <s xml:id="echoid-s6559" xml:space="preserve">& </s>
            <s xml:id="echoid-s6560" xml:space="preserve">latus B D, 20. </s>
            <s xml:id="echoid-s6561" xml:space="preserve">multiplice-
              <lb/>
            tur per 37 {5/8}. </s>
            <s xml:id="echoid-s6562" xml:space="preserve">ſummam eiuſdem ſegmenti B C, & </s>
            <s xml:id="echoid-s6563" xml:space="preserve">latus B D: </s>
            <s xml:id="echoid-s6564" xml:space="preserve">gignetur idem
              <lb/>
            numerus, qui prius, {5719/64}. </s>
            <s xml:id="echoid-s6565" xml:space="preserve">hoc eſt, 89 {23/64}. </s>
            <s xml:id="echoid-s6566" xml:space="preserve">cuius radix quadrata paulo ma-
              <lb/>
            ior eſt, quam 9 {547/1208}. </s>
            <s xml:id="echoid-s6567" xml:space="preserve">velutiprius. </s>
            <s xml:id="echoid-s6568" xml:space="preserve">Atque hęcratio ſatis expedita eſt.</s>
            <s xml:id="echoid-s6569" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6570" xml:space="preserve">A
              <emph style="sc">LTER.</emph>
            Quoniam quadratum rectę A B, in priori triangulo A B
              <note symbol="a" position="left" xlink:label="note-194-01" xlink:href="note-194-01a" xml:space="preserve">47. primi.</note>
            æquale eſt duobus quadratis rectarum A D, B D: </s>
            <s xml:id="echoid-s6571" xml:space="preserve">ſi quadratum 36. </s>
            <s xml:id="echoid-s6572" xml:space="preserve">ſegmen-
              <lb/>
            ti B D, tollatur ex 100. </s>
            <s xml:id="echoid-s6573" xml:space="preserve">quadrato lateris adiacentis A B, relinquetur quadra-
              <lb/>
            tum 64. </s>
            <s xml:id="echoid-s6574" xml:space="preserve">perpendicularis A D. </s>
            <s xml:id="echoid-s6575" xml:space="preserve">Radix ergo eius quadrata 8. </s>
            <s xml:id="echoid-s6576" xml:space="preserve">erit magnitudo per-
              <lb/>
            pendicula@is A D, vt ſupra. </s>
            <s xml:id="echoid-s6577" xml:space="preserve">Similiter ſi quadratum 225. </s>
            <s xml:id="echoid-s6578" xml:space="preserve">ſegmenti C D, dema-
              <lb/>
            tur ex 289. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">quadrato lateris adiacentis A C, reliquum fiet qudratum 64. </s>
            <s xml:id="echoid-s6580" xml:space="preserve">per-
              <lb/>
            pendicularis A D, cuius radix 8. </s>
            <s xml:id="echoid-s6581" xml:space="preserve">magnitudo erit perpendicularis A D, vt
              <lb/>
            prius.</s>
            <s xml:id="echoid-s6582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6583" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo verò poſteriori A B D, ſi quadratum 31 {45
              <unsure/>
            /64}. </s>
            <s xml:id="echoid-s6584" xml:space="preserve">ſegmenti AC, 5 {5/8}.
              <lb/>
            </s>
            <s xml:id="echoid-s6585" xml:space="preserve">ſubtrahatur ex 121. </s>
            <s xml:id="echoid-s6586" xml:space="preserve">quadrato lateris adiacentis A D, 11. </s>
            <s xml:id="echoid-s6587" xml:space="preserve">remanebit quadratum
              <lb/>
            89 {23/64}. </s>
            <s xml:id="echoid-s6588" xml:space="preserve">perpendicularis DC, cuius radix eſt paulò maior quam 9 {547/1208}. </s>
            <s xml:id="echoid-s6589" xml:space="preserve">vt ſupra. </s>
            <s xml:id="echoid-s6590" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-194-02" xlink:href="note-194-02a" xml:space="preserve">Quæ via in-
                <lb/>
              ueſtigandæ
                <lb/>
              perpendicu-
                <lb/>
              laris ſit expe-
                <lb/>
              ditior.</note>
            Sic etiam ſi quadratum 310 {41/64}. </s>
            <s xml:id="echoid-s6591" xml:space="preserve">ſegmenti B C, 17 {5/8}. </s>
            <s xml:id="echoid-s6592" xml:space="preserve">ſubtrahatur à quadrato 400.
              <lb/>
            </s>
            <s xml:id="echoid-s6593" xml:space="preserve">lateris adiacentis B D, 20. </s>
            <s xml:id="echoid-s6594" xml:space="preserve">remanebitrurſus quadratum 89 {23/64}. </s>
            <s xml:id="echoid-s6595" xml:space="preserve">perpendicularis
              <lb/>
            DC, cuiusradix paulo maior eſt quam 9 {547/1208}. </s>
            <s xml:id="echoid-s6596" xml:space="preserve">vt ſupra. </s>
            <s xml:id="echoid-s6597" xml:space="preserve">Verum priorratio ma-
              <lb/>
            gis expedita videtur, quanquam alij poſteri@rem hanc viam tradant.</s>
            <s xml:id="echoid-s6598" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6599" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo porro æquilatero perpendicularis hoc alio modo inuenie-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s6600" xml:space="preserve"> Quoniam quadratum lateris ſeſquitertium eſt quadrati
              <note position="left" xlink:label="note-194-03" xlink:href="note-194-03a" xml:space="preserve">12. quarti
                <lb/>
              decimi.</note>
            ris: </s>
            <s xml:id="echoid-s6601" xml:space="preserve">ſi fiat vt 4. </s>
            <s xml:id="echoid-s6602" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s6603" xml:space="preserve">ita quadratum lateris ad aliud, proueniet quadratum per-
              <lb/>
            pendicularis. </s>
            <s xml:id="echoid-s6604" xml:space="preserve">Radix ergo huius quadrati notam exhibebit perpendicularem.
              <lb/>
            </s>
            <s xml:id="echoid-s6605" xml:space="preserve">Vtſi latus eſt 10. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">& </s>
            <s xml:id="echoid-s6607" xml:space="preserve">fiat vt 4. </s>
            <s xml:id="echoid-s6608" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s6609" xml:space="preserve">ita 100. </s>
            <s xml:id="echoid-s6610" xml:space="preserve">quadratum lateris ad aliud gignetur
              <lb/>
            quadratum perpendicularis 75. </s>
            <s xml:id="echoid-s6611" xml:space="preserve">cuius radix 8 {11/17}. </s>
            <s xml:id="echoid-s6612" xml:space="preserve">proximè erit perpendicula-
              <lb/>
            ris quæſita.</s>
            <s xml:id="echoid-s6613" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6614" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            inuentis ſegmentis baſis à perpendiculari factis, perpendicu-
              <lb/>
            laris ipſa per ſinusita fiet cognita in priori triangulo. </s>
            <s xml:id="echoid-s6615" xml:space="preserve">Fiat vt 10. </s>
            <s xml:id="echoid-s6616" xml:space="preserve">latus A B, re-
              <lb/>
            cto angulo oppoſitum ad ſinum totum rectianguli D; </s>
            <s xml:id="echoid-s6617" xml:space="preserve">ita 6. </s>
            <s xml:id="echoid-s6618" xml:space="preserve">ſegmentum B D,
              <lb/>
            ad aliud; </s>
            <s xml:id="echoid-s6619" xml:space="preserve">produceturque ſinus anguli oppoſiti B A D, 60000. </s>
            <s xml:id="echoid-s6620" xml:space="preserve">Ergo angulus
              <lb/>
            B A D, erit grad. </s>
            <s xml:id="echoid-s6621" xml:space="preserve">36. </s>
            <s xml:id="echoid-s6622" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6623" xml:space="preserve">52. </s>
            <s xml:id="echoid-s6624" xml:space="preserve">ac proinde angulus B, eius complementum erit
              <lb/>
            grad. </s>
            <s xml:id="echoid-s6625" xml:space="preserve">53. </s>
            <s xml:id="echoid-s6626" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s6627" xml:space="preserve">8. </s>
            <s xml:id="echoid-s6628" xml:space="preserve">Siergo rurſus fiat, vt ſinustotus ad 10. </s>
            <s xml:id="echoid-s6629" xml:space="preserve">latus A B: </s>
            <s xml:id="echoid-s6630" xml:space="preserve">ita 80003.
              <lb/>
            </s>
            <s xml:id="echoid-s6631" xml:space="preserve">ſinus anguli B A D, ad aliud, procreabitur latus A D, hoc eſt, perpendicula-
              <lb/>
            ris 8 {30/100000}. </s>
            <s xml:id="echoid-s6632" xml:space="preserve">fermè, quæ paulo maior eſt, quam 8. </s>
            <s xml:id="echoid-s6633" xml:space="preserve">ſupra inuenta. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">quod di-
              <lb/>
            ſcrimen oritur exeo, quodſinus nonſunt omnino tales, qualesin tabula deſcri-
              <lb/>
            buntur: </s>
            <s xml:id="echoid-s6635" xml:space="preserve">quodcamen in menſuratione camporumnon inducit ſenſibilem ad-
              <lb/>
            modumerrorem.</s>
            <s xml:id="echoid-s6636" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6637" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            ſi in priori triangulo A B C, perpendicularis A D, 8. </s>
            <s xml:id="echoid-s6638" xml:space="preserve">ducatur in
              <lb/>
              <note position="left" xlink:label="note-194-04" xlink:href="note-194-04a" xml:space="preserve">Area prioris
                <lb/>
              trianguli
                <lb/>
              ABC.</note>
            10 {1/2}. </s>
            <s xml:id="echoid-s6639" xml:space="preserve">ſemiſem baſis BC, vel 4. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">ſemiſsis perpendicularis AD, in 21. </s>
            <s xml:id="echoid-s6641" xml:space="preserve">totam baſem,
              <lb/>
            procreabitur area trianguli ABC, 84. </s>
            <s xml:id="echoid-s6642" xml:space="preserve">Quę etiam producetur, ſi tota perpendi-
              <lb/>
            culari@ 8. </s>
            <s xml:id="echoid-s6643" xml:space="preserve">in totam baſem 21. </s>
            <s xml:id="echoid-s6644" xml:space="preserve">multiplicetur, & </s>
            <s xml:id="echoid-s6645" xml:space="preserve">producti numeri 168. </s>
            <s xml:id="echoid-s6646" xml:space="preserve">ſemiſsis ac-
              <lb/>
            cipi@tur 84.</s>
            <s xml:id="echoid-s6647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6648" xml:space="preserve">
              <emph style="sc">Item</emph>
            in poſteriori triangulo ABD, ſi perpendicularis DC, 9 {547/1208}. </s>
            <s xml:id="echoid-s6649" xml:space="preserve">ducatur
              <lb/>
              <note position="left" xlink:label="note-194-05" xlink:href="note-194-05a" xml:space="preserve">Area poſte-
                <lb/>
              rioris trian-
                <lb/>
              guli ABD.</note>
            i@ 6. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">ſemiſſem baſis AB, vel ſemiſsis perpendicularis, nimirum {11419/2416}. </s>
            <s xml:id="echoid-s6651" xml:space="preserve"/>
          </p>
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