The equation is solved in the Summa of Luca Pacioli as follows; “Add the number to the cose to form...

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The equation is solved in the Summa of Luca Pacioli as follows; “Add the number to the cose to form a number, and then you get one cubo equal to censi plus , after you have reduced to one cubo [divided all the terms by 6]. Then divide the censi in half and multiply this half by itself, and add it onto the number. It will be and the cosa is equal to the root on this plus , which is half of censi” 38Show that Pacioli’s answer is incorrect. What was he thinking of in presenting his rule?
	
Document Preview: The equation XXXXXXXXXXis solved in the Summa of Luca Pacioli as follows; 
 
“Add the number to the cose to form a number, and then you get one cubo equal to

censi plus   , after you have reduced to one cubo [divided all the terms by 6].  Then 
 
divide the censi in half and multiply this half by itself, and add it onto the number.  It 
  
will be   and the cosa is equal to the root on this plus  , which is half of 
     
38
censi” Show that Pacioli’s answer is incorrect.  What was he thinking of in presenting 
his rule? 
His answer would always be incorrect because he would “only managed to replace one cubic equation 
by another” (Katz, 2009, p. 389); never really solving for a complete general solution.

Robert · Accepted Answer

Solution: 
We have,
Using Summa of Luca Pacioli, the problem was solved as: 
Here, initially, cubo is 6, censi is 43, cosa is 79 and number is 30. [according to Pacioli's convention] 
Pacioli's steps: 
 
 Add the number to the cose to form a number
 and then you get one cubo equal to  
 
 
 censi plus
 
 
   
  
 

 
                          
 
 divide the censi in half and multiply this half by itself,

The equation is solved in the Summa of Luca Pacioli as follows; “Add the number to the cose to form a number, and then you get one cubo equal to censi plus , after you have reduced to one cubo...

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