Clavius, Christoph, Geometria practica

Table of handwritten notes

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              <pb o="276" file="306" n="306" rhead="GEOMETR. PRACT."/>
            altera D, contentum, cubo rectæ E, æquale eſſe. </s>
            <s xml:id="echoid-s12790" xml:space="preserve"> Quoniam enim
              <note symbol="a" position="left" xlink:label="note-306-01" xlink:href="note-306-01a" xml:space="preserve">coroll 20.
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              ſexti.</note>
            rectæ A, ad quadratum rectæ E proportionem habet, quam A, ad F, id eſt, quam
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            E, ad D, recipro cabuntur baſes cum altitudinibus, cum baſis parallelepipedi
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            ſit quadratum rectæ A, & </s>
            <s xml:id="echoid-s12791" xml:space="preserve">eiuſdem altitudo recta D: </s>
            <s xml:id="echoid-s12792" xml:space="preserve">cubi autem baſis quadra-
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            tum rectæ E, & </s>
            <s xml:id="echoid-s12793" xml:space="preserve">altitudo ipſamet recta E. </s>
            <s xml:id="echoid-s12794" xml:space="preserve"> Igitur æqualia erunt
              <note symbol="b" position="left" xlink:label="note-306-02" xlink:href="note-306-02a" xml:space="preserve">34. vnde-
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              cimi.</note>
            dum, & </s>
            <s xml:id="echoid-s12795" xml:space="preserve">cubus. </s>
            <s xml:id="echoid-s12796" xml:space="preserve">Eadem ratione erit parallelepipedum ſub quadrato extremæ
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            D, & </s>
            <s xml:id="echoid-s12797" xml:space="preserve">ſub altera extrema A, contentum æquale cubo rectæ F. </s>
            <s xml:id="echoid-s12798" xml:space="preserve"> Nam cum ſit,
              <note symbol="c" position="left" xlink:label="note-306-03" xlink:href="note-306-03a" xml:space="preserve">coroll. 20.
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              ſexti.</note>
            quadratum rectæ D, ad quadratum rectæ F, id eſt, vt baſis dicti parallelepipe-
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            di ad baſem dicti cubi, ita D, ad E, hoc eſt, ita F, ad A, hoc eſt, ita altitudo cubi,
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            ad altitudinem parallelepipedi; </s>
            <s xml:id="echoid-s12799" xml:space="preserve">reciprocabuntur quo que baſes cum altitudi-
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            nibus: </s>
            <s xml:id="echoid-s12800" xml:space="preserve"> ideo que æqualia erunt parallelepipedum, & </s>
            <s xml:id="echoid-s12801" xml:space="preserve">cubus. </s>
            <s xml:id="echoid-s12802" xml:space="preserve">quod
              <note symbol="d" position="left" xlink:label="note-306-04" xlink:href="note-306-04a" xml:space="preserve">34. vnde-
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              cimi.</note>
            propoſitum.</s>
            <s xml:id="echoid-s12803" xml:space="preserve"/>
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              <emph style="sc">Qvia</emph>
            verò in noſtra Arithmetica practica ſolum radicis quadratæ extra-
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            ctionem explicauimus, operæ me pretium facturum puto, radicis cubicæ extra-
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            ctionem hoc loco, quamuis fortaſſe alieno, inſerere: </s>
            <s xml:id="echoid-s12805" xml:space="preserve">quando quidem ea neceſ-
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            ſaria omninò eſt, vt problema hoc 13. </s>
            <s xml:id="echoid-s12806" xml:space="preserve">ad opus poſsit deduci. </s>
            <s xml:id="echoid-s12807" xml:space="preserve">Hoc autem ef-
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            ficiam, ſi præſcribam artem quandam generalem, qua cuiuſcunque generis ra-
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            dicem extrahere poſsimus, ex libro eximij cuiuſdam Arithmetici Germani de-
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            promptam fermè totam: </s>
            <s xml:id="echoid-s12808" xml:space="preserve">quod quidem ſtudioſo Lectorinon iniucundum, aut
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            ingratum fore confido.</s>
            <s xml:id="echoid-s12809" xml:space="preserve"/>
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        <div xml:id="echoid-div794" type="section" level="1" n="274">
          <head xml:id="echoid-head299" xml:space="preserve">PROBL. 14. PROPOS. 19.</head>
          <head xml:id="echoid-head300" xml:space="preserve">RADICEM cuiuslibet generis extrahere.</head>
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              <emph style="sc">Extractio</emph>
            radicis eſt inuentio numeri ex propoſito numero, qui mul-
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              <note position="left" xlink:label="note-306-05" xlink:href="note-306-05a" xml:space="preserve">Extractio ra-
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              dicis quid.</note>
            tiplicatione aliqua in ſe numerum propoſitum producat. </s>
            <s xml:id="echoid-s12811" xml:space="preserve">Vt extractio qua-
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            dratæ radicis eſt inuentio numeri ex numero quadrato, qui quadratè mul-
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            tiplicatus ipſum producat: </s>
            <s xml:id="echoid-s12812" xml:space="preserve">Et extractio radicis cubicæ, eſt inuentio nume-
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            ri, qui in ſe ductus cubicè producat cubum propoſitum, &</s>
            <s xml:id="echoid-s12813" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12814" xml:space="preserve">Quid autem
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            ſit multiplicare numerum quadratè, aut cubicè, aut alio modo, mox expli-
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            cabo.</s>
            <s xml:id="echoid-s12815" xml:space="preserve"/>
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              <emph style="sc">Qvemadmodvm</emph>
            igitur infinitæ ſunt ſpecies multiplicationum nume-
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              <note position="left" xlink:label="note-306-06" xlink:href="note-306-06a" xml:space="preserve">Infinitæ ſpe-
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              ci{es}
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              radicum.</note>
            rorumin ſe, vt ſtatim dicam, ex quibus oriuntur numeri quadrati; </s>
            <s xml:id="echoid-s12817" xml:space="preserve">& </s>
            <s xml:id="echoid-s12818" xml:space="preserve">ſolidi, vt
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            cubi, Zenficenſi, Surdeſolidi, &</s>
            <s xml:id="echoid-s12819" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12820" xml:space="preserve">qui à Iunioribus nonnullis in Algebra ex-
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            plicari ſolent: </s>
            <s xml:id="echoid-s12821" xml:space="preserve">ſic etiam infinitæ ſunt radicum ſpecies iuxta varias numerorum
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            appellationes, qui conſurgunt ex varia radicum multiplicatione. </s>
            <s xml:id="echoid-s12822" xml:space="preserve">Quæ omnia
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            pulchrè nobis repræſentat naturalis numerorum progreſsio, inſeruiens
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            progreſsionibus Geometricis ab vnitate incipienti-
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            bus: </s>
            <s xml:id="echoid-s12823" xml:space="preserve">vt hic.</s>
            <s xml:id="echoid-s12824" xml:space="preserve"/>
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