Clavius, Christoph, Geometria practica

Table of Notes

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            <s xml:id="echoid-s1856" xml:space="preserve">
              <pb o="44" file="074" n="74" rhead="GEOMETR. PRACT."/>
            ſumatur in inſtrumento interuallum inter 10. </s>
            <s xml:id="echoid-s1857" xml:space="preserve">& </s>
            <s xml:id="echoid-s1858" xml:space="preserve">10. </s>
            <s xml:id="echoid-s1859" xml:space="preserve">æquale, erit interuallum in-
              <lb/>
            ter 100. </s>
            <s xml:id="echoid-s1860" xml:space="preserve">& </s>
            <s xml:id="echoid-s1861" xml:space="preserve">100. </s>
            <s xml:id="echoid-s1862" xml:space="preserve">datæ particulæ decuplum.</s>
            <s xml:id="echoid-s1863" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1864" xml:space="preserve">15. </s>
            <s xml:id="echoid-s1865" xml:space="preserve">
              <emph style="sc">Iam</emph>
            vero ſi viciſsim ex qualibet parte rectæ A B, auferendæ ſint quot-
              <lb/>
              <note position="left" xlink:label="note-074-01" xlink:href="note-074-01a" xml:space="preserve">Quo modo ex
                <lb/>
              data linea au-
                <lb/>
              ferendæ ſint
                <lb/>
              quotcunque
                <lb/>
              part{es} decim æ
                <lb/>
              velaliæ part{es}.</note>
            cunque decimæ partes vnius, diuidendum erit ſegmentum continens numerum
              <lb/>
            partium decimarum in 10. </s>
            <s xml:id="echoid-s1866" xml:space="preserve">pattes æquales. </s>
            <s xml:id="echoid-s1867" xml:space="preserve">Nam vna pars decima huius ſegmen-
              <lb/>
            ti continebit decimas partes quæſitas. </s>
            <s xml:id="echoid-s1868" xml:space="preserve">Vt ſi cupiat quis {7/10}, diuidendum erit
              <lb/>
            ſegmentum rectæ A B, includens 7. </s>
            <s xml:id="echoid-s1869" xml:space="preserve">partes, in 10. </s>
            <s xml:id="echoid-s1870" xml:space="preserve">particulas. </s>
            <s xml:id="echoid-s1871" xml:space="preserve">Quælibet namq;
              <lb/>
            </s>
            <s xml:id="echoid-s1872" xml:space="preserve">harum comprehendet {7/10}. </s>
            <s xml:id="echoid-s1873" xml:space="preserve">vnius partis rectæ A B. </s>
            <s xml:id="echoid-s1874" xml:space="preserve">Eademq; </s>
            <s xml:id="echoid-s1875" xml:space="preserve">ratio eſt de cæteris. </s>
            <s xml:id="echoid-s1876" xml:space="preserve">
              <lb/>
            Sed commodius hunc vſum nobis præſtabit inſtrumentum partium ſupra con-
              <lb/>
              <handwritten xlink:label="hd-074-1" xlink:href="hd-074-1a" number="43"/>
            ſtructum. </s>
            <s xml:id="echoid-s1877" xml:space="preserve">Eius enim beneficio ex quauis recta abſcindemus non ſolum quot-
              <lb/>
            cunque decimas, ſed etiam centeſimas, decimas nonas, nonageſimas octauas,
              <lb/>
            & </s>
            <s xml:id="echoid-s1878" xml:space="preserve">ſic deinceps, vſque ad dimidiatam partem. </s>
            <s xml:id="echoid-s1879" xml:space="preserve">Nam ſi velimus {3/100}. </s>
            <s xml:id="echoid-s1880" xml:space="preserve">alicuius
              <lb/>
            lineæ, capiemus ei lineæ interuallum inter 100. </s>
            <s xml:id="echoid-s1881" xml:space="preserve">& </s>
            <s xml:id="echoid-s1882" xml:space="preserve">100. </s>
            <s xml:id="echoid-s1883" xml:space="preserve">æquale. </s>
            <s xml:id="echoid-s1884" xml:space="preserve">Circinus nam-
              <lb/>
            que extenſus inter 3. </s>
            <s xml:id="echoid-s1885" xml:space="preserve">& </s>
            <s xml:id="echoid-s1886" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1887" xml:space="preserve">dabit {3/100}. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">quæſitas. </s>
            <s xml:id="echoid-s1889" xml:space="preserve">Ita quo que circini pedes inter
              <lb/>
            50. </s>
            <s xml:id="echoid-s1890" xml:space="preserve">& </s>
            <s xml:id="echoid-s1891" xml:space="preserve">50. </s>
            <s xml:id="echoid-s1892" xml:space="preserve">dabunt {50/100}. </s>
            <s xml:id="echoid-s1893" xml:space="preserve">id eſt, {1/2}. </s>
            <s xml:id="echoid-s1894" xml:space="preserve">Rurſus pedes circini inter 20, & </s>
            <s xml:id="echoid-s1895" xml:space="preserve">20. </s>
            <s xml:id="echoid-s1896" xml:space="preserve">dabunt
              <lb/>
            {20/100}. </s>
            <s xml:id="echoid-s1897" xml:space="preserve">hoc eſt, {1/5}. </s>
            <s xml:id="echoid-s1898" xml:space="preserve">& </s>
            <s xml:id="echoid-s1899" xml:space="preserve">ſic de cæteris, vt fuſius in vſu prædicti inſtrumenti partium
              <lb/>
            cap. </s>
            <s xml:id="echoid-s1900" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1901" xml:space="preserve">expoſuimus.</s>
            <s xml:id="echoid-s1902" xml:space="preserve"/>
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        <div xml:id="echoid-div68" type="section" level="1" n="20">
          <head xml:id="echoid-head23" xml:space="preserve">PROBLEMATA VARIA TRIANGV-
            <lb/>
          lorum rectilineorum.
            <lb/>
            <emph style="sc">Capvt</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s1903" xml:space="preserve">TERTIO loco præmiſſuros nos polliciti ſumus varia problema-
              <lb/>
            ta triangulorum rectilineorum, vt & </s>
            <s xml:id="echoid-s1904" xml:space="preserve">latera eorum atque anguli
              <lb/>
            ex quibuſdam datis, & </s>
            <s xml:id="echoid-s1905" xml:space="preserve">cognitis promptè, atque expeditè, cum id
              <lb/>
            res poſtulauerit, poſsint erui: </s>
            <s xml:id="echoid-s1906" xml:space="preserve">quod hoc tertio capite exequemur.
              <lb/>
            </s>
            <s xml:id="echoid-s1907" xml:space="preserve">Prioriautem loco de triangulis rectangulis: </s>
            <s xml:id="echoid-s1908" xml:space="preserve">poſteriori vero de ob-
              <lb/>
            liquangulis agemus. </s>
            <s xml:id="echoid-s1909" xml:space="preserve">In margine porrò adſcripſimus propoſitiones noſtri
              <lb/>
            tractatus triangulorum rectilineorum, in Theodoſio noſtro editi, in quibus
              <lb/>
            problemata hæc demonſtrantur, vt ſtudioſi intelligant, vnde eorum demon-
              <lb/>
            ſtrationes, quando libuerit, petere debeant.</s>
            <s xml:id="echoid-s1910" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div69" type="section" level="1" n="21">
          <head xml:id="echoid-head24" xml:space="preserve">TRIANGVLORVM RECTILINEORVM RECTAN-
            <lb/>
          gulorum problemata.
            <lb/>
          I. PROPORTIONES LATERVM</head>
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            <s xml:id="echoid-s1911" xml:space="preserve">Ex datis omnibus angulis cuiuſuis trianguli patefacere.</s>
            <s xml:id="echoid-s1912" xml:space="preserve"/>
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          <note position="left" xml:space="preserve">1. Triang. re-
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          ctil.</note>
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            <s xml:id="echoid-s1913" xml:space="preserve">Singulis laterib{us} adſcribantur ſin{us} angulorum oppoſitorum. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">Latera enim eaſ-
              <lb/>
            dem proportion{es} habent, quæ inter ſin{us} angulorum laterib{us} oppoſitorum reperiuntur.</s>
            <s xml:id="echoid-s1915" xml:space="preserve"/>
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