Clavius, Christoph, Geometria practica

Table of figures

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          <p>
            <s xml:id="echoid-s1791" xml:space="preserve">
              <pb o="43" file="073" n="73" rhead="LIBER PRIMVS."/>
            @ur {400/1000}. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">Et in D C, {68/100}. </s>
            <s xml:id="echoid-s1793" xml:space="preserve">vnius partis rectæ AB, ſiue {63/1000}. </s>
            <s xml:id="echoid-s1794" xml:space="preserve">totius lineæ AB; </s>
            <s xml:id="echoid-s1795" xml:space="preserve">cum
              <lb/>
            quælibet centeſima particula vnius partis decimæ ſit {1/1000}. </s>
            <s xml:id="echoid-s1796" xml:space="preserve">Atque in hunc mo-
              <lb/>
            dum progredilicebit ad decimas vnius decimæ ex illis {6/10}. </s>
            <s xml:id="echoid-s1797" xml:space="preserve">quæin particula DC,
              <unsure/>
              <lb/>
            continentur. </s>
            <s xml:id="echoid-s1798" xml:space="preserve">nimirum ad fractionem à 10000. </s>
            <s xml:id="echoid-s1799" xml:space="preserve">denominatam, &</s>
            <s xml:id="echoid-s1800" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1801" xml:space="preserve">ſed ſatis mi-
              <lb/>
            hi videtur ad partes milleſimas peruenire.</s>
            <s xml:id="echoid-s1802" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1803" xml:space="preserve">
              <emph style="sc">Demonstratio</emph>
            hic eadem eſt, quæin gradibus, ac Minutis. </s>
            <s xml:id="echoid-s1804" xml:space="preserve">Eandem
              <lb/>
            enim proportionem habet recta 10. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">partium ad 1. </s>
            <s xml:id="echoid-s1806" xml:space="preserve">partem, quamrecta A E, ad
              <lb/>
            particulam D C, cum vtrobique proportio ſit decupla, ideoque permutando
              <lb/>
            erit vt recta 10. </s>
            <s xml:id="echoid-s1807" xml:space="preserve">partium ad rectam A E, ita 1. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">pars ad particulam D C. </s>
            <s xml:id="echoid-s1809" xml:space="preserve">Quamo-
              <lb/>
            brem ſicut in A E, continentur {6/10}. </s>
            <s xml:id="echoid-s1810" xml:space="preserve">rectæ A B, decem partium, & </s>
            <s xml:id="echoid-s1811" xml:space="preserve">inſuper par-
              <lb/>
            ticula F E, reſpectu vnius partis lineæ A B, decem partium, ita quoque in par-
              <lb/>
            ticula data D C, continebuntur {6/10}. </s>
            <s xml:id="echoid-s1812" xml:space="preserve">vnius partis, & </s>
            <s xml:id="echoid-s1813" xml:space="preserve">inſuper talis particula re-
              <lb/>
            ſpectu vnius decimæ qualis eſt F E, reſpectu vnius partis lineæ A B, decem par-
              <lb/>
            tium, &</s>
            <s xml:id="echoid-s1814" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1816" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            , vt vides, duabus operationibus ad milleſimas partes perueni-
              <lb/>
              <note position="right" xlink:label="note-073-01" xlink:href="note-073-01a" xml:space="preserve">Denominatio
                <lb/>
              facilis fractio-
                <lb/>
              num milleſi.
                <lb/>
              marum.</note>
            tur, ac ſi latus totum A B, in 1000. </s>
            <s xml:id="echoid-s1817" xml:space="preserve">partes ſectum eſſet, quod conſideratione
              <lb/>
            dignum eſt. </s>
            <s xml:id="echoid-s1818" xml:space="preserve">Et duo quidem numeratores decimarum eo c
              <unsure/>
            rdine poſiti, quo
              <lb/>
            inuenti ſunt, dant Numeratorem centeſimarum: </s>
            <s xml:id="echoid-s1819" xml:space="preserve">cui ſi præponatur ad ſiniſtram
              <lb/>
            numerus integrarum partium ante datam particulam exiſtentium, conflabitur
              <lb/>
            Numerator milleſimarum. </s>
            <s xml:id="echoid-s1820" xml:space="preserve">Vt in ſuperiori exemplo, quia ante datam parti-
              <lb/>
            culam D C, reperiuntur 4. </s>
            <s xml:id="echoid-s1821" xml:space="preserve">partes, inuentæque ſunt {6/10}. </s>
            <s xml:id="echoid-s1822" xml:space="preserve">& </s>
            <s xml:id="echoid-s1823" xml:space="preserve">{8/10}. </s>
            <s xml:id="echoid-s1824" xml:space="preserve">erit tota fra ctio
              <lb/>
            {468/1000}. </s>
            <s xml:id="echoid-s1825" xml:space="preserve">Sic ſi inuentæ eſſent pro aliqua particula in octaua parte, {7/10}. </s>
            <s xml:id="echoid-s1826" xml:space="preserve">{0/10}. </s>
            <s xml:id="echoid-s1827" xml:space="preserve">conſti-
              <lb/>
            tueretur fractio {870/1000}. </s>
            <s xml:id="echoid-s1828" xml:space="preserve">Item ſi in tertia parte inuentæ eſſent {0/10}. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">{7/10}. </s>
            <s xml:id="echoid-s1830" xml:space="preserve">fieret fractio
              <lb/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="38"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="39"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="40"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="41"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="42"/>
            {307/1000}. </s>
            <s xml:id="echoid-s1831" xml:space="preserve">& </s>
            <s xml:id="echoid-s1832" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s1833" xml:space="preserve">Quod ſirecta A B, id eſt, latus vtriuſque vmbræ diui-
              <lb/>
            deretur in 100. </s>
            <s xml:id="echoid-s1834" xml:space="preserve">partes, reperientur partes milleſimæ vnica operatione; </s>
            <s xml:id="echoid-s1835" xml:space="preserve">ſi nimi-
              <lb/>
            rum particula data in vna centeſima decuplaretur: </s>
            <s xml:id="echoid-s1836" xml:space="preserve">quia tunc intelligerentur ſin-
              <lb/>
            gulæ centeſimę in denas particulas ſub diuiſæ. </s>
            <s xml:id="echoid-s1837" xml:space="preserve">Sed quia particula data in cen-
              <lb/>
            teſima aliqua parte perparua eſt, vt vix circino capi poſsit, accipiemus eam cũ
              <lb/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="38"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="39"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="40"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="41"/>
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            vna centeſima, vel duabus, & </s>
            <s xml:id="echoid-s1838" xml:space="preserve">ex decuplo abijciemus 10. </s>
            <s xml:id="echoid-s1839" xml:space="preserve">vel 20. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">centeſimas, vt
              <lb/>
            reliquę centeſimæ exhibeant decimas vnius centeſimę. </s>
            <s xml:id="echoid-s1841" xml:space="preserve">Eadem ratione, quan-
              <lb/>
            do data particula in linea 10. </s>
            <s xml:id="echoid-s1842" xml:space="preserve">partium eſt perpuſilla accipienda erit reliqua parti-
              <lb/>
            cula maior decies. </s>
            <s xml:id="echoid-s1843" xml:space="preserve">Nam reliqua pars rectę AB, à B, vſque ad finem illius par-
              <lb/>
            ticulę decuplę dabit numerum decimarum in propoſita minore particula, &</s>
            <s xml:id="echoid-s1844" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s1845" xml:space="preserve">Hac ratione, ſi particulam CH, decuples, in cides in punctum K Ergo ſegmẽ-
              <lb/>
            tum B K, dabit {6/10}. </s>
            <s xml:id="echoid-s1846" xml:space="preserve">& </s>
            <s xml:id="echoid-s1847" xml:space="preserve">inſuper particulam DK, vt ſupra; </s>
            <s xml:id="echoid-s1848" xml:space="preserve">cum DK, particulę FE,
              <lb/>
            ſit ęqualis. </s>
            <s xml:id="echoid-s1849" xml:space="preserve">Ratio huius reieſt, quod ambę particulę DC, CH, decuplatę con-
              <lb/>
            ficere debeanttotam A B, vt conſtat.</s>
            <s xml:id="echoid-s1850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1851" xml:space="preserve">
              <emph style="sc">Ad</emph>
            Maiorem quo que commo ditatem pro inueſtigandis partibus decimis,
              <lb/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="38"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="39"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="40"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="41"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="42"/>
            hoc eſt, pro decuplanda particula propoſita, conſtrui poterit circinus dupli-
              <lb/>
            cis aperturę, in quo ſcilicet crura producta ſe mutuo interſecent, at que vna a-
              <lb/>
            pertura alterius ſit ſemper decupla, inſtar circini, quo linea duas in partes ęqua-
              <lb/>
            les diuidi ſolet. </s>
            <s xml:id="echoid-s1852" xml:space="preserve">Ita enim fiet, vt accepta per minorem aperturam particula ab-
              <lb/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="38"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="39"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="40"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="41"/>
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            ſciſſa, particula maior exhibeat eam particulam decies ſumptam, vt non opus
              <lb/>
            ſit toties circinum circumducere: </s>
            <s xml:id="echoid-s1853" xml:space="preserve">qua quidem in re facile error committi
              <lb/>
            poteſt, quiillo circino, ſi recte fabricatus ſit, facilius vitatur. </s>
            <s xml:id="echoid-s1854" xml:space="preserve">Sed ſine hoc
              <lb/>
            circino, idem fieri poteſt per inſtrumentum partium, quod capite pręceden-
              <lb/>
            ti conſtruximus. </s>
            <s xml:id="echoid-s1855" xml:space="preserve">Nam ſi particula data circino capiatur, & </s>
            <s xml:id="echoid-s1856" xml:space="preserve">ſumma diligentia ei
              <lb/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="38"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="39"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="40"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="41"/>
              <handwritten xlink:label="hd-073-1" xlink:href="hd-073-1a" number="42"/>
            </s>
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