TARTACLIA REVEALS HIS SECRET. 251 



Find two numbers z and y, so that z y c in the first 

 case or z -}-?/ c in the second and third cases, and 

 zy :n (-J-6) 3 : then x ^/ 3 z y/ 3 y in the first case, and 

 x = y% -f- y^j/ in the other two. The original verses 

 are given in a note below. Tartalea was not by any 

 means singular in his practice of converting such a rule 

 into a versified enigma. In this respect he followed the 

 example set by the first of the Italian printed algebrists, 

 Luca di Borgo, who had for each of the three forms of 

 which an equation of the second degree is susceptible, a 

 particular rule, instead of one general rule that sufficed for 

 all. The three rules he expressed in three Latin quatrains, 

 of which one will be found cited below as a specimen of 

 the manner 1 . It was not, therefore, any individual con- 



Tu osseruarai quest 'altri contratti 

 Del numer farai due tal part' a uolo 

 Che luna in 1'altra si produca sclrietto 

 El terzo cubo delle cose in stolo 

 Delle qual poi, per commun precetto 

 Torrai li lati cubi insierae gionti 

 Et cotal summa sara il tuo concetto 

 El terzo poi de questi nostri conti 

 Se solue col secondo se ben guardi 

 Che per natura son quasi congionti 

 Questi trouai, et non con passi tardi 

 Nel mille cinquecent'e quatro e trenta 

 Con fondamenti ben said' e gagliardi 

 Nella citta dal mar' intorno centa." 



Quesiti et Invention^ p. 123. 



I have not ventured to interfere with the allowance originally made by 

 Tartalea to his poem, of one full stop and two commas. 

 1 Primi canonis versus. 



" Si res et census numero coequantur a rebus 



