HIERONYMUS CARDANO

Catchword: 17 Number

3 Number & position, & unknown quantity. In 16th-century algebra, "position" (positio) usually refers to the unknown $x$, while "unknown quantity" (ignota quantitas) may refer to a second variable or a higher power like $x^2$ treated as a separate entity.
4 Number & square of the position, & unknown quantity; or number & square of the unknown quantity & position; or number with the square of the position of the unknown quantity; or number & the product of the position times the unknown quantity, with another of them, or with the square of one of them.

Primitive Chapters original: "Capitula primitiua"	Derivative Chapters original: "Capitula deriuatiua"
1 Number equal to the square & things. In modern notation: $N = x^2 + x$.	1 Number equal to the square-square & square. $N = x^4 + x^2$. 2 Number equal to the cube-square & cube. $N = x^6 + x^3$.
2 Number & thing equal to the square.	3 Number & square equal to the square-square. 4 Number & cube equal to the cube-square.
3 Number & square equal to things.	5 Number & square-square equal to the square. 6 Number & cube-square equal to the cube.
4 Number equal to the cube & things.	7 Number equal to the square & cube-square. Cardano follows a pattern where the derivative power is a multiple of the primitive power. 8 Number equal to the cube & the cube of the cube.
5 Number & thing equal to cubes.	9 Number & square equal to the cube-square. 10 Number & cube equal to the cube-cube.
6 Number & cube equal to things: the first equation. Cardano distinguishes between "first" and "second" equations when a form has two distinct positive solutions.	11 Number & cube-square equal to the square: first equation. 12 Number & cube-cube equal to the cube: first equation.
7 Number & cube equal to things: the second equation.	13 Number & cube-square equal to the square: second equation. 14 Number & cube-cube equal to the cube: second equation.
8 Number equal to the square & cube.	15 Number equal to the square-square & cube of the square. cube of the square: $x^6$. 16 Number equal to the cube-square & cube of the cube.
9 Number & square equal to the cube.	17 Number & square-square equal to the cube of the square. 18 Number & cube-square equal to the cube-cube.
10 Number & cube equal to the square: first equation.	19 Number & cube-square equal to the square-square: first equation. 20 Number & cube-cube equal to the cube-square: first equation.
11 Number & cube equal to the square: second equation.	21 Number & cube-square equal to the square-square: second equation. 22 Number & cube-cube equal to the cube-square: second equation.
12 Number equal to things, square, & cube.	23 Number equal to the square & square-square & cube-square. 24 Number equal to the cube & cube-square & cube-cube.
13 Number & thing equal to square & cube.	25 Number & square equal to square-square & cube-square. 26 Number & cube equal to cube-square & cube-cube.
14 Number & thing & square equal to the cube.	27 Number & square & square-square equal to the cube-square. 28 Number & cube & cube-square equal to the cube-cube.
15 Number & square equal to things & cube: first equation.	29 Number & square-square equal to the square & cube-square: first equation. 30 Number & cube-square equal to the cube & cube-cube: first equation.
16 Number & square equal to things & cube: second equation.	31 Number & square-square equal to the square & cube-square: second equation. 32 Number & cube-square equal to the cube & cube-cube: second equation.