## An intire system of arithmetic Volume 6 ; or, Arithmetic in all its parts. Containing I. Vulgar; II. Decimal; III. Duodecimal; IV. Sexagesimal; V. ... IX. Algebraical. With the arithmetic of negat

### Edward Hatton

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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. 1731 edition. Excerpt: ...(7684615.384 Example 9. To divide a Decimal by a mixt Number,--as.5 by 7.5 i and to have 2 89 places Decimal in the Quo-" I10 tient: which are sufficient in 1 cafe of Decimals of a Gallon, and the Quotient not 're-quired to be multiplied by 20.any thing; as follows.--70" ' '.50' ' 8 Rests These are illthe Varieties that can happen in Division of Decimals: And the Exemplification of the two Rules first above, appear at one View thus. Of Decimals by way of Vulgar Fraclions.. To work any Question so as to give the Answer exquisitely (without omitting any thing) by Decimals as well as by Vulgar Fraclions. Note, This is my own-Thought, as.the reft of what, is new its Decimals is. It has been one great Objection against Decimals,, that.where the Decimals in Quotients happen not to be compleat,. but infinite, the Answer cannot be exhibited so accurately/as td be truly said to be the whole Truth: But this is easily solved, by considering; the Nature of the Remainers in the dividing and making a Fraction of that and the Divisor.--# So that the P_roof of.this depends both upon Vulgar and Decimal Fractions worked promiscuously, or of Decimal, worked by.way of Vulgar Fractions,.. ' '-'k To instance in Example 3. foregoing, the true Quote (as in the Margin below is proved) is =.3846003: For the 37 is what remained in dividing the last part of the Dividend; and besides the 2 places next the right hand thereof, there being. 8 more Decimal places towards the left hand, therefore so many Cyphers are in the Numerator of that part expressed by way of Vulgar Fractions, which must always be observed. ' ' '-:f:'" The Truth of this appears by reducing this mixt Number to one Fraction: for the Product of.3846003 multiplied by the Denominator.321, produceth....

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