Clavius, Christoph, Geometria practica

Table of Notes

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          <p>
            <s xml:id="echoid-s1704" xml:space="preserve">
              <pb o="42" file="072" n="72" rhead="GEOMETR. PRACT."/>
            tria autem Min. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">in 4. </s>
            <s xml:id="echoid-s1706" xml:space="preserve">gradu, ſi tres particulæ transferantur, & </s>
            <s xml:id="echoid-s1707" xml:space="preserve">ſic decæteris.</s>
            <s xml:id="echoid-s1708" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1709" xml:space="preserve">
              <emph style="sc">Pari</emph>
            ratione, ſi quis deſideret quotlibet gradus, ac Minuta, inquirenda
              <lb/>
            prius erit particula Minutorum, quæ deſiderantur, eaque ad gradus propoſitos
              <lb/>
            adijcienda. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">Quod ſi particula minutorum inuentorum tam exigua fuerit, vt
              <lb/>
            circino vix accipi poſsit, accipienda ea erit vnà cum 1. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">gradu: </s>
            <s xml:id="echoid-s1712" xml:space="preserve">& </s>
            <s xml:id="echoid-s1713" xml:space="preserve">hic arcus ex 1.
              <lb/>
            </s>
            <s xml:id="echoid-s1714" xml:space="preserve">gradu & </s>
            <s xml:id="echoid-s1715" xml:space="preserve">particula conflatus adijciendus ad numerum graduum propoſitum
              <lb/>
            minus vno. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">Vt ſi velit quis grad. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">89. </s>
            <s xml:id="echoid-s1718" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">59. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">Inuenienda prius erunt 59. </s>
            <s xml:id="echoid-s1721" xml:space="preserve">Mi-
              <lb/>
            nuta. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">quod fiet, ſi 59. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">particulæ arcus X Y, in Quadrantem B C, transferantur. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">
              <lb/>
            Nam particula in 60. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">gradu complectetur 59. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s1727" xml:space="preserve">vt dictum eſt. </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Siigitur arcus
              <lb/>
            ex illa particula, & </s>
            <s xml:id="echoid-s1729" xml:space="preserve">1. </s>
            <s xml:id="echoid-s1730" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">conflatus adijciatur ad arcum 88. </s>
            <s xml:id="echoid-s1732" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">conficietur
              <lb/>
            arcus grad. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">89. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s1736" xml:space="preserve">59. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">Eademque ratio eſt de cæteris. </s>
            <s xml:id="echoid-s1738" xml:space="preserve">Accipientur autem in ar-
              <lb/>
            cu XY, particulæ 59. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">ſi vnus pes circini in puncto 50. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">ſtatuatur, & </s>
            <s xml:id="echoid-s1741" xml:space="preserve">alter in nona
              <lb/>
            particula primæ partis ſextæ totius arcus XY, verſus X. </s>
            <s xml:id="echoid-s1742" xml:space="preserve">Ita accipientur quoque
              <lb/>
            particulæ 49. </s>
            <s xml:id="echoid-s1743" xml:space="preserve">48. </s>
            <s xml:id="echoid-s1744" xml:space="preserve">39. </s>
            <s xml:id="echoid-s1745" xml:space="preserve">34. </s>
            <s xml:id="echoid-s1746" xml:space="preserve">&</s>
            <s xml:id="echoid-s1747" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1748" xml:space="preserve">vt perſpicuum eſt.</s>
            <s xml:id="echoid-s1749" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1750" xml:space="preserve">
              <emph style="sc">Iam</emph>
            vero ſi Minutanonin Quadrante BC, ſed in maiori, minoriue accipien-
              <lb/>
            da ſint, inquirenda ea erunt in Quadrante B C, beneficio arcus X Y, vt docui-
              <lb/>
            mus; </s>
            <s xml:id="echoid-s1751" xml:space="preserve">Deinde arcuiinter C, & </s>
            <s xml:id="echoid-s1752" xml:space="preserve">finem particulæ inuentæ auferendus ex Quadrã-
              <lb/>
            te propoſito arcus ſimilis. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">quod fiet, ſi ille Quadrans ex centro A, deſcribatur,
              <lb/>
            rectaque ex A, per finem particulæ in B C, inuentæ educatur, &</s>
            <s xml:id="echoid-s1754" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1755" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1756" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">
              <emph style="sc">Qvæ</emph>
            Num. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1759" xml:space="preserve">præcedenti diximus, perbelle etiam quadrant in lineas
              <lb/>
              <note position="left" xlink:label="note-072-01" xlink:href="note-072-01a" xml:space="preserve">Quo pactore-
                <lb/>
              peri
                <unsure/>
              atur fra-
                <lb/>
              ctio cuiuſque
                <lb/>
              particulæ in
                <lb/>
              parte qualibet
                <lb/>
              lineæ rectæ in
                <lb/>
              part{es} æqual{es}
                <lb/>
              diuiſæ.</note>
            rectas. </s>
            <s xml:id="echoid-s1760" xml:space="preserve">Nam eadem ratione cognoſcemus, ſi linea recta in quotuis partes æqua-
              <lb/>
            les ſecetur, quantam fractionem quælibet particula vnius partis contineat: </s>
            <s xml:id="echoid-s1761" xml:space="preserve">Et
              <lb/>
            viciſsim quo pacto ex vna parte abſcindenda ſit quæcun que fractio propoſita.
              <lb/>
            </s>
            <s xml:id="echoid-s1762" xml:space="preserve">Quæ res incredibile eſt, quantam vtilitatem cum alijs rebus Geometricis, tum
              <lb/>
            ver ò maxime Dimenſionibus, quæ per ſcalam altimetram fieri ſolent, afferat, vt
              <lb/>
            lib. </s>
            <s xml:id="echoid-s1763" xml:space="preserve">3. </s>
            <s xml:id="echoid-s1764" xml:space="preserve">cum de Quadrato Geometrico, vbiſcalæ altimetræ vſus apparebit, perſpi-
              <lb/>
            cuum erit. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">Sit enim recta linea A B, vt ad pedem Quadrantis ſuperioris vides,
              <lb/>
            ſecta in 10. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">partes æquales. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">(In totenim partes libet tam vmbiam rectam, quam
              <lb/>
              <handwritten xlink:label="hd-072-1" xlink:href="hd-072-1a" number="37"/>
            verſam ſcalæ altimetræ diſtribuere: </s>
            <s xml:id="echoid-s1768" xml:space="preserve">quamuis ab alijs vtraque in 12. </s>
            <s xml:id="echoid-s1769" xml:space="preserve">diuidatur:
              <lb/>
            </s>
            <s xml:id="echoid-s1770" xml:space="preserve">quod per illam diuiſionem facilius Dimenſiones perficiantur, vt ſuo loco pate-
              <lb/>
            bit. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Magis tamen probarem, ſi vtrumque vmbræ latus in 100. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">partes ſecare-
              <lb/>
            tur, ſi id magnitudo inſtrumenti commode permittit) propoſitumque ſit, quot
              <lb/>
            partes decimas contineat particula D C, partis quintæ. </s>
            <s xml:id="echoid-s1773" xml:space="preserve">Beneficio circini ſum-
              <lb/>
            pta paiticula D C, decupletur ab A, vſque ad E. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">Et quoniamin A E, continen-
              <lb/>
            tur ſex partes totius lineæ A B, continebit propterea particula D C. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">{6/10}. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">vnius
              <lb/>
            partis decimæ, hoceſt, {6/100}. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">totius lineæ. </s>
            <s xml:id="echoid-s1778" xml:space="preserve">Ita vt ſirecta A B, diuiſa cogitetur in
              <lb/>
            100. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">partes, tribuendo ſingulis decimis partibus denas particulas, ſegmentum
              <lb/>
            A C, comprehendat {46/100}. </s>
            <s xml:id="echoid-s1780" xml:space="preserve">Quia vero vltra {6/10}. </s>
            <s xml:id="echoid-s1781" xml:space="preserve">ſupereſt adhuc particula F E,
              <lb/>
            vnius decimæ, ſi ea rurſum decupletur ab A, vſque ad G, reperientur in A G,
              <lb/>
            octo partes totius lineæ A B. </s>
            <s xml:id="echoid-s1782" xml:space="preserve">Continet ergo particula F E, {8/10}. </s>
            <s xml:id="echoid-s1783" xml:space="preserve">vnius decimæ,
              <lb/>
            hoc eſt, propoſita particula D C, vltra {6/10}. </s>
            <s xml:id="echoid-s1784" xml:space="preserve">vnius partis rectæ A B, continet in
              <lb/>
            ſuper {8/10}, vnius decimæ, (vnius inquam decimæ ex illis {6/10}. </s>
            <s xml:id="echoid-s1785" xml:space="preserve">quas in particula
              <lb/>
            D C, diximus comprehendi) nimirum {8/100}. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">vnius partis. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">ſi ſingulæ partes deci-
              <lb/>
            mærectæ A B, diuiſæ eſſent in 100. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">particulas; </s>
            <s xml:id="echoid-s1789" xml:space="preserve">atque adeo, ſi recta A B, ſecta
              <lb/>
            intelligatur in 1000. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">partes, tribuendo ſingulis decimis partibus centenas par-
              <lb/>
            ticulas ſegmentum A C, complectetur {468/1000}. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">quippe cum in A D, </s>
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