Clavius, Christoph, Geometria practica

Table of Notes

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          <pb o="277" file="307" n="307" rhead="LIBER SEXTVS."/>
          <note position="right" xml:space="preserve">
            <lb/>
          0. # 1. # 2. # 3. # 4. # 5. # 6. # 7. # 8. # 9. # 10.&c.
            <lb/>
          1. # 2. # 4. # 8. # 16. # 32. # 64. # 128. # 256. # 512. # 1024. &c.
            <lb/>
          # Radix # Quadratus # Cubus. # Zenſizenſus # Surdeſoli- \\ dus. # Zenſicubus # B, ſurdeſo- \\ lidus. # Zenſizen- \\ zenſus # Cubicubus # Zenſurde- \\ ſolidus.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s12825" xml:space="preserve">
              <emph style="sc">Primvm</emph>
            numeri ſuperioris progreſsionis ſignificant ſpecies multiplicatio-
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            num. </s>
            <s xml:id="echoid-s12826" xml:space="preserve">Vt 2. </s>
            <s xml:id="echoid-s12827" xml:space="preserve">ſupra quadratum ſignificat, multiplicationem quadratam fieri, dum
              <lb/>
            radix bis ponitur, & </s>
            <s xml:id="echoid-s12828" xml:space="preserve">ſic multiplicatur, vt 2. </s>
            <s xml:id="echoid-s12829" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12830" xml:space="preserve">facit 4. </s>
            <s xml:id="echoid-s12831" xml:space="preserve">Sic 3. </s>
            <s xml:id="echoid-s12832" xml:space="preserve">ſignificat, multipli-
              <lb/>
            cationem cubicam fieri, dum radix ter ponitur, atque ita multiplicatur, vt 2. </s>
            <s xml:id="echoid-s12833" xml:space="preserve">2. </s>
            <s xml:id="echoid-s12834" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s12835" xml:space="preserve">facit 8. </s>
            <s xml:id="echoid-s12836" xml:space="preserve">Pari ratione 4. </s>
            <s xml:id="echoid-s12837" xml:space="preserve">oſtendit multiplicationem Zenſizenſicam: </s>
            <s xml:id="echoid-s12838" xml:space="preserve">Et 5. </s>
            <s xml:id="echoid-s12839" xml:space="preserve">ſurde-
              <lb/>
            ſolidam, &</s>
            <s xml:id="echoid-s12840" xml:space="preserve">c.</s>
            <s xml:id="echoid-s12841" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12842" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            ijdem @numeri ſignificant radicum ſpecies. </s>
            <s xml:id="echoid-s12843" xml:space="preserve">Vt 2. </s>
            <s xml:id="echoid-s12844" xml:space="preserve">ſignificat, radi-
              <lb/>
            cem quadratam producere quadratum per multiplicationem quadratam: </s>
            <s xml:id="echoid-s12845" xml:space="preserve">Et
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            3. </s>
            <s xml:id="echoid-s12846" xml:space="preserve">denotat, radicem Cubicam procreare Cubum per multiplicationem cubicam:
              <lb/>
            </s>
            <s xml:id="echoid-s12847" xml:space="preserve">Et ſic deinceps.</s>
            <s xml:id="echoid-s12848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12849" xml:space="preserve">
              <emph style="sc">In</emph>
            extra ctionibus igitur radicum obſeruanda eſt ſignatio figurarum per pũ-
              <lb/>
            cta in numero, ex quo radix aliqua extrahenda eſt, hoc modo.</s>
            <s xml:id="echoid-s12850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12851" xml:space="preserve">
              <emph style="sc">In</emph>
            extractione radicis quadratæ ſignantur omnes figuræ in Iocis imparibus,
              <lb/>
            incipiendo à dextris: </s>
            <s xml:id="echoid-s12852" xml:space="preserve">ita vt alternatim ſemper vna figura omittatur, quæ non
              <lb/>
            ſignetur.</s>
            <s xml:id="echoid-s12853" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12854" xml:space="preserve">
              <emph style="sc">In</emph>
            extractione cubica omittuntur ſemper
              <lb/>
              <note position="right" xlink:label="note-307-02" xlink:href="note-307-02a" xml:space="preserve">
                <lb/>
              Pro quadrata.
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              68719476736
                <lb/>
              . . . . . .
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              Pro cubica
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              68719476736
                <lb/>
              . . . .
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              Zenſizenſica.
                <lb/>
              68719476736
                <lb/>
              . . .
                <lb/>
              Pro ſurdeſolida.
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              68719476736
                <lb/>
              . . .
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              </note>
            duæ figuræ. </s>
            <s xml:id="echoid-s12855" xml:space="preserve">In Zenſizenſica tres. </s>
            <s xml:id="echoid-s12856" xml:space="preserve">In ſurdeſolida
              <lb/>
              <note position="right" xlink:label="note-307-03" xlink:href="note-307-03a" xml:space="preserve">Quo modo fi-
                <lb/>
              guræ per pun-
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              cta ſignentur.</note>
            quatuor. </s>
            <s xml:id="echoid-s12857" xml:space="preserve">Et ſic deinceps in infinitum. </s>
            <s xml:id="echoid-s12858" xml:space="preserve">Vtin ap-
              <lb/>
            poſitis exemplis vides.</s>
            <s xml:id="echoid-s12859" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12860" xml:space="preserve">
              <emph style="sc">Respondent</emph>
            autem hæ ſignationes me-
              <lb/>
            dijs proportionalibus. </s>
            <s xml:id="echoid-s12861" xml:space="preserve">Vt quoniam inter duos
              <lb/>
            quadratos cadit vnus medius, ideo in extractio-
              <lb/>
            ne ra dicis quadratę omittitur ſemper vnafigu-
              <lb/>
            ra: </s>
            <s xml:id="echoid-s12862" xml:space="preserve">Inter duos verò Cubos cadunt duo medij,
              <lb/>
            idcirco omittuntur ſemper duæ figuræ, & </s>
            <s xml:id="echoid-s12863" xml:space="preserve">ſic de
              <lb/>
            cæteris.</s>
            <s xml:id="echoid-s12864" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12865" xml:space="preserve">
              <emph style="sc">Pro</emph>
            qualibet autem ſpecie radicis extrahẽ-
              <lb/>
            dę inſeruiunt quidam numeri peculiares: </s>
            <s xml:id="echoid-s12866" xml:space="preserve">qui per
              <lb/>
            ſequentem tabulam inueniuntur, quæ hoc mo-
              <lb/>
            dò conſtruitur. </s>
            <s xml:id="echoid-s12867" xml:space="preserve">Prima columna continet ſeriem
              <lb/>
            naturalẽ numerorũ. </s>
            <s xml:id="echoid-s12868" xml:space="preserve">Ex hac colũna naſcit ſecũ-
              <lb/>
            da: </s>
            <s xml:id="echoid-s12869" xml:space="preserve">tertia ex ſecũda: </s>
            <s xml:id="echoid-s12870" xml:space="preserve">& </s>
            <s xml:id="echoid-s12871" xml:space="preserve">quarta ex tertia, hoc mo-
              <lb/>
            do. </s>
            <s xml:id="echoid-s12872" xml:space="preserve">Relictis duab. </s>
            <s xml:id="echoid-s12873" xml:space="preserve">cellulis primæ colũnæ, repetit
              <lb/>
            numerus tertiæ cellulæ in ſecunda columna. </s>
            <s xml:id="echoid-s12874" xml:space="preserve">De-
              <lb/>
            inde ex additione duorum numerorum, id eſt, ex
              <lb/>
            tertio primæ columnæ, & </s>
            <s xml:id="echoid-s12875" xml:space="preserve">primo ſecundæ columnæ, fit ſecundus numerus ſe-
              <lb/>
            cundæ columnæ. </s>
            <s xml:id="echoid-s12876" xml:space="preserve">Eodem modo ex ſecundo numero ſecundæ columnæ, & </s>
            <s xml:id="echoid-s12877" xml:space="preserve">ex
              <lb/>
            eius collaterali conficitur tertius ſecundæ columnæ: </s>
            <s xml:id="echoid-s12878" xml:space="preserve">Atque ex tertio numero
              <lb/>
            ſecundæ columnę, & </s>
            <s xml:id="echoid-s12879" xml:space="preserve">ex eius collaterali fit quartus eiuſdem ſecundę </s>
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