The compleat arithmetician, or, The whole art of arithmetick, vulgar and decimal in a plain and easie method, suitable to the meanest capacity : in which the multiplication and division of numbers of several denominations, and the rule of alligation are more fully explained than in any treatise of this nature, yet extant / by J.N., Philomath.

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Title
The compleat arithmetician, or, The whole art of arithmetick, vulgar and decimal in a plain and easie method, suitable to the meanest capacity : in which the multiplication and division of numbers of several denominations, and the rule of alligation are more fully explained than in any treatise of this nature, yet extant / by J.N., Philomath.
Author
Newton, John, 1622-1678.
Publication
London :: Printed for John Taylor ... and Christopher Browne ...,
1691.
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Subject terms
Arithmetic -- Early works to 1800.
Link to this Item
http://name.umdl.umich.edu/A52256.0001.001
Cite this Item
"The compleat arithmetician, or, The whole art of arithmetick, vulgar and decimal in a plain and easie method, suitable to the meanest capacity : in which the multiplication and division of numbers of several denominations, and the rule of alligation are more fully explained than in any treatise of this nature, yet extant / by J.N., Philomath." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A52256.0001.001. University of Michigan Library Digital Collections. Accessed May 28, 2025.

Pages

1. Case, where the price of an Integer is shillings only.

4. Where the price of 1, or an Integer is two shillings, the price of as many Integers as you will may be discovered by bare inspection, for two shillings being the tenth of a pound, the double of the first figure (towards the right hand)

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is the number of shillings required, and the rest of the figures are so many pounds. Example, 567 yards at 2 shillings the Yard will cost 56 pounds 14 shillings; for the double of 7 is 14 which I write down by it self as shillings, then taking the rest of the figures towards the left hand for pounds, the answer is 56l. 14s.

5. When the given price of 1 or an Integer is an even number of shillings greater than two, multiply the number of Integers whose price is required, by half the number of shillings given; the double of the first figure towards the right hand in the product being set down for the shil∣lings apart, all the other figures towards the left hand shall be the pounds required.

Example, let the price of 365 Yards be requi∣red, at 14 shillings per 1 Yard: if you multiply 365 by 7 (which is the half of 14 the number of shillings given) the product will be 2562, now the double of 2, the first figure * 1.1 towards the right hand is 4, the other figures are 256 pounds, and so the answer is 256l—4s.

Here note that 4 shillings being the 5th part of a pound, if that be the price of an Integer, it will be all one to multiply by 2 or divide by 5, if the double of the first figure in the product towards the right hand be taken for the shillings according to this rule.

6. When the given price of 1 or an Integer is an odd number of shillings, for the odd shilling

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take the ½. of the price propounded, and add it to the product of the price given by half the num∣ber of shillings remainer, taking the double of the last figure of the products for shillings accor∣ding to the former directions, their sum shall be the answer required. Example, let the price of 367 Yards be required at 9 shillings the Yard. The twentieth part of 367 * 1.2 is 18 pound 7 shillings, and the product of 367 by 4 (half the number of the shillings remaining) is 1468 that is 146 pound 16 shillings, which being ad∣ded to 18l. 7 shillings, the answer is 165 pound, 3 shillings.

Note, When 5 shillings is the given price of an Integer the shortest way will be to divide the num∣ber whose price is required by 4, because 4 is the first part of a pound; thus if the worth or price of 367 Yards at 5 shillings the Yard were re∣quired, the answer would be 91¾ that is 91l. 15s.

Notes

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