Tartaglia, Niccolo, Quesiti et inventioni diverse, 1554

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              <p type="main">
                <s id="s.001003">
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                della uoſira radice, cioe el treppio de ſeſſantatre, che ſaria. </s>
                <s id="s.001004">189. et. </s>
                <s id="s.001005">189. file à fanti. </s>
                <s id="s.001006">21.
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                per fila ue ne peruenira.
                  <emph.end type="italics"/>
                C.H. D
                  <emph type="italics"/>
                oue ſapro io doue ſe debbia mettere quelle due, &
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                due file de archibuſeri, per cognoſcere el luoco doue ſe debbia ſmembrare in tre par­
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                te per metter li in battaglia quadra di gente.
                  <emph.end type="italics"/>
                N. L
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                a uoſtra radice (cioe ſeſſantatre)
                  <lb/>
                ui da el tutto, cioe, che tal diuiſione ſe fa alle. </s>
                <s id="s.001007">63. &. </s>
                <s id="s.001008">63. file talmente, che la prima par­
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                te ſara de ſeſſantatre file, & coſi etiam la ſeconda, & la terza.
                  <emph.end type="italics"/>
                C.H. V
                  <emph type="italics"/>
                e ho inteſo be
                  <lb/>
                nißimo in quanto a questa parte, e pero ſeguitate.
                  <emph.end type="italics"/>
                N. M
                  <emph type="italics"/>
                aſe nel partire la uoſtra ra­
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                dice per tre ui auanzaſſe uno (come accaderia ſe li propoſti fanti fuſſeno. </s>
                <s id="s.001009">5776. che la
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                radice di quelli ſaria ſettantaſei, la qual radice diuidendola per tre, ne ueneria. </s>
                <s id="s.001010">25. &
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                auanzeria uno: hor dico, che tutte le file, che reuſciran de queſti tai fanti ſar anno pur
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                el treppio della radice, cioe el treppio de ſettantaſei, che ſaria. </s>
                <s id="s.001011">228. & perche tutta
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                queſta fila de file ua diuiſa ſempre in tre parti (come diſopra fu detto, etiam fatto) a
                  <lb/>
                ſettanta ſei file per parte (cioe tanto quanto e la noſtraradice) hor dico, che la prima,
                  <lb/>
                & la ultima de queſte tre parte, ſi debbano far caminar a uinticinque fanti per fila,
                  <lb/>
                cioe quanto che é il terzo della noſtra radice, & perche el ne auanzo uno (come di ſo­
                  <lb/>
                pra appare) dico che quel tal. </s>
                <s id="s.001012">1. ſi debbe mettere ſempre nella ſeconda parte, cioe in
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                quella di mezzo, cioe facendo caminar quelli della detta ſeconda parte à. </s>
                <s id="s.001013">26. fanti per
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                fila, talmente, che la prima, & la ultima parte della gran fila delle file, ſaranno à. </s>
                <s id="s.001014">25.
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                fanti per fila, & la ſeeonda parte ſara de fanti. </s>
                <s id="s.001015">26. per fila, & il medeſimo ſi debbe fa
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                re in ogni altra radice, che partita per. </s>
                <s id="s.001016">3. ue auanzi ſolamente. </s>
                <s id="s.001017">1. ma quando l'auan­
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                zaſſe. </s>
                <s id="s.001018">2. ſeguita tutto al contrario, cioe, che la prima, & la ultima parte uuol eſſer de
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                uno fante de piu, di quello ſara el terzo della nostra radice, come, eſſempi gratia ſe li
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                detti fanti fuſſeno. </s>
                <s id="s.001019">2809. la ſua radice ſara. </s>
                <s id="s.001020">53. la qual partita per tre, ne uien. </s>
                <s id="s.001021">17. &
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                auanza. </s>
                <s id="s.001022">2. e per
                  <expan abbr="tãto">tanto</expan>
                dico, che tai fanti ſe ne formara file.
                  <emph.end type="italics"/>
                159. (
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                cioe el treppio de.
                  <emph.end type="italics"/>
                53.)
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                  <emph type="italics"/>
                le quale file. </s>
                <s id="s.001023">159. diuidendole pur i tre parti, ne uenira. </s>
                <s id="s.001024">53. per parte, cioe el numero del
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                la radice, & la prima, & terza parte uol eſſer de uno fante de piu del terzo della no­
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                ſtra radice, cioe uoleno eſſer de fanti. </s>
                <s id="s.001025">18. per fila, & la ſeconda parte, cioe la parte de
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                mezzo, uol eſſer puramente el terzo della nostra radice, cioe de fanti. </s>
                <s id="s.001026">17. per fila tal­
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                mente, che de tutte le. </s>
                <s id="s.001027">159. file, le prime. </s>
                <s id="s.001028">53. file, & coſi le ultime. </s>
                <s id="s.001029">53. file uoranno eſſer
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                de fanti. </s>
                <s id="s.001030">18. per fila, & le. </s>
                <s id="s.001031">53. file di mezzo uoranno eſſer ſolamente de fanti. </s>
                <s id="s.001032">17. per
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                fila. </s>
                <s id="s.001033">Et in quella che nel partire la radice per. </s>
                <s id="s.001034">3. auanza ſolamente uno ua al contrario
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                di queſta, cioe, che la prima, & terza parte della detta gran fila delle file, uoleno ſem­
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                pre tanti fanti per fila, quanto ſara la terza parte integra della nostra radice, & la
                  <lb/>
                parte di mezzo, cioe la ſeconda uora uno fante de piu del ditto terzo della nostra radi
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                ce. </s>
                <s id="s.001035">Et perche mai puo auanzar piu che uno, ouer dui, à partire la detta noſtra radice
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                per. </s>
                <s id="s.001036">3. le dette nostre regole ue ſatisfar anno in ogni quantita de fanti ſi quadrata, ouer
                  <lb/>
                non quadrata, perche, come di ſopra fu detto, nelle quantita, ouer numerinon quadra­
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                ti, ſempre ſe piglia la radice propinqua di quel tal numero, & di quella ſe ne ſerue, co
                  <lb/>
                me di ſopra è ſtato detto, & de quello reſiduo, ouer ſuperfluo de fanti, che ſoperchiaſ­
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                ſeno el quadrato di tal radice el ſargente li aſſetta ſecondo el ſuo parere, eſſempi gra­
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                tia, ſe li detti fanti fuſſeno quattromilla, el qual numero non è quadrato, nondimeno di
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                co, che di quello ſe debbia cauar la ſua radice propinqua, la quale ſara
                  <emph.end type="italics"/>
                63. (
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                uero è, che
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                </s>
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