[62] For that which measures a measure is itself a measure; so that if a measure of a could have a measure in common with b, a itself would have a common measure with b.
[63] A prime number is one which is prime to all numbers except its own multiples, or has no divisors except 1 and itself.
[64] Expand (a-1)ᵇ by the binomial theorem; shew that when b is a prime number every coefficient which is not unity is divisible by b; and the proposition follows.
[65] The principle of this mode of demonstration of Horner’s method was stated in Young’s Algebra (1823), being the earliest elementary work in which that method was given.
[66] Various exceptions may arise when an equation has two nearly equal roots. But I do not here introduce algebraical difficulties; and a student might give himself a hundred examples, taken at hazard, without much chance of lighting upon one which gives any difficulty.
[67] This form might be also applied to the integer portions; but it is hardly needed in such instances as usually occur. See the article Involution and Evolution in the Supplement to the Penny Cyclopædia.
[68] After the second step, the trial will rarely fail to give the true figure.
[69] The solution of x³ + 0x² + 0x-2 = 0.
[70] Taken from a paper on the subject, by Mr. Peter Gray, in the Mechanics’ Magazine.
[71] Taken from a paper on the subject, by Mr. Peter Gray, in the Mechanics’ Magazine.