7. Rafael Bombelli authored l’Algeb

7. Rafael Bombelli authored l’Algebra (1572, and 1579), a set of three books. Bombelli introduces a notation for √ −1, and calls it “piu´ di meno”. The discussion of cubics in l’Algebra follows Cardano, but now the casus irreducibilis is fully discussed. Bombelli considered the equation
x3 = 15x + 4
for which the Cardan formula gives
x =
3 q2 +√−121 + 3 q2−√−121 Bombelli observes that the cubic has x = 4 as a solution, and then proceeds to explain the expression given by the Cardan formula as another expression for x = 4 as follows. He sets 3 q2 +√−121 = a + bi from which he deduces 3 q2−√−121 = a− bi and obtains, after algebraic manipulations, a = 2 and b = 1. Thus x = a + bi + a− bi = 2a = 4

ผลลัพธ์ (แอฟริกา) 1:

7. Rafael Bombelli outeur l'Algebra (1572 en 1579), 'n stel van drie boeke. Bombelli stel 'n notasie vir √ -1, en ​​noem dit "piu 'di meno". Die bespreking van cubics in l'Algebra volg Cardano, maar nou is die casus irreducibilis is ten volle bespreek word. Bombelli beskou as die vergelyking
X3 = 15x + 4
waarvoor die Cardan Formule gee
x =
3 Q2 + √-121 + 3 Q2-√-121 Bombelli waarneem dat die Cubic het x = 4 as 'n oplossing, en dan voortgaan om die uitdrukking te verduidelik. gegee deur die formule Cardan as 'n ander uitdrukking vir x = 4 soos volg. Hy stel 3 q2 + √-121 = a + aanrnerk waaruit hy deduces 3 q2-√-121 = a- bi en verkry, na algebraïese bewerkings, a = 2 en b = 1. Dus x = a + bi + a-. bi = 2a = 4