Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div794" type="section" level="1" n="274">
          <p>
            <s xml:id="echoid-s12879" xml:space="preserve">
              <pb o="278" file="308" n="308" rhead="GEOMETR. PRACT."/>
              <note position="left" xlink:label="note-308-02" xlink:href="note-308-02a" xml:space="preserve">Conſtructio
                <lb/>
              tabulæ miri-
                <lb/>
              ficæ.</note>
              <note position="left" xlink:label="note-308-02" xlink:href="note-308-02a" xml:space="preserve">Conſtructio
                <lb/>
              tabulæ miri-
                <lb/>
              ficæ.</note>
            2
              <lb/>
            3 # 3
              <lb/>
            4 # 6
              <lb/>
            5 # 10 # 10
              <lb/>
            6 # 15 # 20
              <lb/>
            7 # 21 # 35 # 35
              <lb/>
            8 # 28 # 56 # 70
              <lb/>
            9 # 36 # 84 # 126 # 126
              <lb/>
            10 # 45 # 120 # 210 # 252
              <lb/>
            11 # 55 # 165 # 330 # 462 # 462
              <lb/>
            12 # 66 # 220 # 495 # 792 # 924
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            13 # 78 # 286 # 715 # 1287 # 1716 # 1716
              <lb/>
            14 # 91 # 364 # 100 # 2002 # 3003 # 3432
              <lb/>
            15 # 105 # 455 # 1365 # 3003 # 5005 # 6435 # 6435
              <lb/>
            16 # 120 # 560 # 1820 # 4368 # 8008 # 11440 # 12870
              <lb/>
            17 # 136 # 680 # 2380 # 6188 # 12376 # 16448 # 24310 # 24310
              <lb/>
            & </s>
            <s xml:id="echoid-s12880" xml:space="preserve">ſic deinceps. </s>
            <s xml:id="echoid-s12881" xml:space="preserve">Continentur autem in ſecunda columna omnes numeri trian-
              <lb/>
            gulares. </s>
            <s xml:id="echoid-s12882" xml:space="preserve">Non aliter tertia columna ex ſecunda oritur, & </s>
            <s xml:id="echoid-s12883" xml:space="preserve">quarta ex tertia,
              <lb/>
            &</s>
            <s xml:id="echoid-s12884" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12885" xml:space="preserve">Semper enim in qualibet columna relinquũtur duæ primæ cellu@æ, & </s>
            <s xml:id="echoid-s12886" xml:space="preserve">nu-
              <lb/>
            merus tertiæ cellulæ repetitur pro primo numero ſequentis columnæ: </s>
            <s xml:id="echoid-s12887" xml:space="preserve">atque ex
              <lb/>
            additione eius numeri cum collaterali præcedentis columnæ conflatur ſecun-
              <lb/>
            dus numerus, &</s>
            <s xml:id="echoid-s12888" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s12889" xml:space="preserve">
              <note position="left" xlink:label="note-308-03" xlink:href="note-308-03a" xml:space="preserve">Quo pacto
                <lb/>
              ex ſuperiori
                <lb/>
              tabula deſu-
                <lb/>
              mantur nu-
                <lb/>
              meripro ſin-
                <lb/>
              gulis radicum
                <lb/>
              ſpecieb{us}.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s12890" xml:space="preserve">
              <emph style="sc">Hac</emph>
            extructa tabula, deſumuntur numeri peculiares ex ordinibus trans-
              <lb/>
            uerſalibus hoc ordine. </s>
            <s xml:id="echoid-s12891" xml:space="preserve">Numeri cuiuslibet ordinis tranſuerſalis ordine ſcrib un-
              <lb/>
            tur, ijdemque ordineretrogrado repetuntur, vltimo ſemper ex cepto, & </s>
            <s xml:id="echoid-s12892" xml:space="preserve">penul-
              <lb/>
            timo etiam tuncſolum, quando vltimo æqualis eſt. </s>
            <s xml:id="echoid-s12893" xml:space="preserve">Vt in ſecundo ordine ſu-
              <lb/>
            mitur tantum numerus 2. </s>
            <s xml:id="echoid-s12894" xml:space="preserve">quia cum ſit vltimus, non repetitur. </s>
            <s xml:id="echoid-s12895" xml:space="preserve">In tertio ſumun-
              <lb/>
            tur quo que hi duo tantum 3.</s>
            <s xml:id="echoid-s12896" xml:space="preserve">3. </s>
            <s xml:id="echoid-s12897" xml:space="preserve">quia penultimus non repetitur, cum ab vltimo
              <lb/>
            non differat. </s>
            <s xml:id="echoid-s12898" xml:space="preserve">In quarto autem ſumendi ſunt hi tres. </s>
            <s xml:id="echoid-s12899" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12900" xml:space="preserve">6. </s>
            <s xml:id="echoid-s12901" xml:space="preserve">4. </s>
            <s xml:id="echoid-s12902" xml:space="preserve">In nono hi octo 9.
              <lb/>
            </s>
            <s xml:id="echoid-s12903" xml:space="preserve">36. </s>
            <s xml:id="echoid-s12904" xml:space="preserve">84. </s>
            <s xml:id="echoid-s12905" xml:space="preserve">126. </s>
            <s xml:id="echoid-s12906" xml:space="preserve">126. </s>
            <s xml:id="echoid-s12907" xml:space="preserve">84. </s>
            <s xml:id="echoid-s12908" xml:space="preserve">36. </s>
            <s xml:id="echoid-s12909" xml:space="preserve">9. </s>
            <s xml:id="echoid-s12910" xml:space="preserve">Et in decimo hinouem 10. </s>
            <s xml:id="echoid-s12911" xml:space="preserve">45. </s>
            <s xml:id="echoid-s12912" xml:space="preserve">120. </s>
            <s xml:id="echoid-s12913" xml:space="preserve">210. </s>
            <s xml:id="echoid-s12914" xml:space="preserve">252. </s>
            <s xml:id="echoid-s12915" xml:space="preserve">210. </s>
            <s xml:id="echoid-s12916" xml:space="preserve">120. </s>
            <s xml:id="echoid-s12917" xml:space="preserve">
              <lb/>
            45. </s>
            <s xml:id="echoid-s12918" xml:space="preserve">10. </s>
            <s xml:id="echoid-s12919" xml:space="preserve">&</s>
            <s xml:id="echoid-s12920" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12921" xml:space="preserve">Vbivides, ſemper tot numeros aſſumi, quot ſunt vnitates in primo
              <lb/>
            numero tranſuerſali, minus vno. </s>
            <s xml:id="echoid-s12922" xml:space="preserve">Vtin ordine ſeptimodecimo aſſumendi erunt
              <lb/>
            hiſexdecim 17. </s>
            <s xml:id="echoid-s12923" xml:space="preserve">136. </s>
            <s xml:id="echoid-s12924" xml:space="preserve">680. </s>
            <s xml:id="echoid-s12925" xml:space="preserve">2380. </s>
            <s xml:id="echoid-s12926" xml:space="preserve">6188. </s>
            <s xml:id="echoid-s12927" xml:space="preserve">12376. </s>
            <s xml:id="echoid-s12928" xml:space="preserve">19448. </s>
            <s xml:id="echoid-s12929" xml:space="preserve">24310. </s>
            <s xml:id="echoid-s12930" xml:space="preserve">24310. </s>
            <s xml:id="echoid-s12931" xml:space="preserve">19448. </s>
            <s xml:id="echoid-s12932" xml:space="preserve">12376. </s>
            <s xml:id="echoid-s12933" xml:space="preserve">
              <lb/>
            6188. </s>
            <s xml:id="echoid-s12934" xml:space="preserve">2380. </s>
            <s xml:id="echoid-s12935" xml:space="preserve">680. </s>
            <s xml:id="echoid-s12936" xml:space="preserve">136. </s>
            <s xml:id="echoid-s12937" xml:space="preserve">17. </s>
            <s xml:id="echoid-s12938" xml:space="preserve">& </s>
            <s xml:id="echoid-s12939" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s12940" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12941" xml:space="preserve">
              <emph style="sc">Cvilibet</emph>
            deinde numero præponendæ ſunttot cifræ, quot numeriab eo
              <lb/>
            incluſiue numerantur vſque ad vltimum aſſumptum. </s>
            <s xml:id="echoid-s12942" xml:space="preserve">Vt numero 2. </s>
            <s xml:id="echoid-s12943" xml:space="preserve">ſecundi or-
              <lb/>
            dinis præponenda eſt vna cifra, hoc modo, 20. </s>
            <s xml:id="echoid-s12944" xml:space="preserve">Sed duo tertij ordinis habe-
              <lb/>
            bunt has cifras 300. </s>
            <s xml:id="echoid-s12945" xml:space="preserve">30. </s>
            <s xml:id="echoid-s12946" xml:space="preserve">Sic in nono ordinè, vbiaſſumuntur octo numeri, pri-
              <lb/>
            mus habebit octo cifras, ſecundus ſeptem, tertius ſex, & </s>
            <s xml:id="echoid-s12947" xml:space="preserve">ſic ſemper minuendo
              <lb/>
            vnam. </s>
            <s xml:id="echoid-s12948" xml:space="preserve">Cuius autem radicis extra ctioni inſeruiant prædicti nu neri in quolibet
              <lb/>
            ordine tranſuerſali accepti, pulchrè indicat primus numerus o@dinis </s>
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