Question

Advantages and disadvantages of nopier bone

Answer 1

Answer:

An 18th century set of Napier's Bones

Napier's bones is a manually-operated calculating device created by John Napier of Merchiston, Scotland for calculation of products and quotients of numbers. The method was based on Arab mathematics and the lattice multiplication used by Matrakci Nasuh in the Umdet-ul Hisab and Fibonacci's work in his Liber Abaci. The technique was also called Rabdology. Napier published his version in 1617 in Rabdology, printed in Edinburgh, Scotland, dedicated to his patron Alexander Seton.

Explanation:

Answer 2

During the multiplication of a number, which has identical digits, we have to use identical rods. That's why Napier suggested rods to take the form of a parallelepiped, on the four surfaces of which to be inscribed four digital columns of rods in such manner, that the four faces of each rod to contain multiples of one of the nine digits, and is similar to one of the slips just described, the first rod containing the multiples of 0, 1, 9, 8, the second of 0, 2. 9, 7, the third of 0, 3, 9, 6, the fourth of 0, 4, 9, 5, the fifth of 1, 2, 8 , 7 (see the nearby figure), the sixth of 1, 3, 8, 6, the seventh of 1, 4, 8, 5, the eighth of 2, 3, 7, 6, the ninth of 2, 4, 7, 5, and the tenth of 3, 4, 6, 5. Each rod, therefore, contains on two of its faces factors of digits which are complementary to those on the other two faces, and the factors of a digit and its complement are reversed in position.

When the second factor is multidigital, then intermediate products must be written manually, shifting one position leftwards, then intermediate products must be added (see the drawing below). After arranging rods for the multiplicand side by side, we have to multiply the multiplicand (46785399) by the units of the multiplier (96431). This the result is 46785399x1=46785399. Then we have to multiply the multiplicand by the tens the multiplier 46785399x3=140356197, shifting the result one position left and to continue, while all digits of the multiplier will be used. Then we have to add manually the partial factors. It was a matter of time, someone to think about, that if we have an adding machine, the multiplication can be done without any thinking, and this happened only some years later—Wilhelm Schickard, who used Napier's Rods in his Rechenuhr (Calculating Clock).