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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1741 Excerpt: ...5 every one of which Divisors, except that which is equal to the given Quantity is called an Aliquot Part, because if it be taken Aliquot iss that is, certain times, it will precisely constitute thegivenQuantity: As if 6 be a Number proposed, its just Divisors are 1,2,3, andd; but the Aliquot Parts of 6 are only 1,2, and 3; for 6 cannot be a part of 6, but ir may be a Divisor to it self, that is, 6 may be divided by 6, and the Quotient is Unity. Hence it is manifest, that the just Divisors of a Number are more in multimde by one than theNumber of its Aliquot Parts V-The Aliquot Partsof a wholeNumber may be sound out in this manner, viz, . First, if the Number proposed be even, divide it by 2, and reserve the Divisor-Again, if the Quotient be even divide it by 2, and reserve the Divisor; and continue the Division. os of every following Quotient by 2, until the Quotient be an odd number. But if either the number first proposed, or the Quotient resulting from such Division by 2 be odd, divide it by 3, if it will give an Integer Quotient, 2nd continue the Division by 3, in like manner as before by 2, so long as the Quotient is an integer vuihout any Fraction 5 likewise when the Division by 5 ceaseth, divide by 5,7, u, 13,17 19. EV. that is, by every primeNumber, until you find a Quotient lessthan the Divisor and if no such Divisor will give an Integer Quotient before the Quotient is lets than rheDivisor, you may conclude the number first proposed ro be Incomposit, (viz. such as has no Divisor bur it self or Unity) and that last Divisor to be greater than the SqoareRootof the propoled Number. Then by the belp of the prime Divisors to the given Number, all the rest may be found out by the Operation directed in the following Examples. Example 1. Suppose it be...

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