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С НА Р. ІІ. Concerning the Sir Principal Rules of algebraick
arithmetick, of whole Duantities. Sect. 1. addition of whole Duantities. ADDITION of whole Quantities admits of three
Sect. 2. Subtraction of whole Duantities. CUBTRACTION of whole Quantities is performed by one general Rule.
RUL E. Change all the signs of the Subtrabend, (viz. of those Quantities which are to be subtraEted) or fuppose them in your. Mind to be
changed; then add all the Quantities together, as before in Addition, • and their Sum will be the true Remainder or Difference required.
This general Rule is deduced from these evident Truths. .
To subtract an Affirmative Quantity, from an Affirmative, is the same as to add a Negative Quantity to an Affirmative: that is +2a taken from +3a, is the same with — 2 a added to +39. Consequently, to fubtract a Negative Quantity from an Affirmative, will be the same as to add an Affirmative Quantity to an Affirmative: that is - 2a taken from + 3a will be the same with + 2a added to +39.
If these 13 Examples be compared with those in Addition, the Work will appear very evident, these being only the Converse or Proof of those ; according to the Nature of Addition and Subtraction in common Arithmetick.
The Truth of all Operations in Subtraction, where any Doubt arises, may be proved, by adding the Subtrahend to the Remainder, as in Common Arithmetick.
E X A M P L E. From it
01-9bc Take 2 -- 20 361-6da Subtrahend. 1-213 +
+6da9bc Remainder. 2-3141+ 50
Sect. 3. gultiplication of whole Muantities.
ULTIPLICATION of whole Quantities admits
Cafe 1. When the Quantities have like Signs, and no Coëfficients, set or join them together, and prefix the Sign + before. them; and that will be their Product. I IExam.r. Exam.2. Exam.3. Exam. 4. - a lath - a-k
- d . 1 x2 31ab l tabl adtodi tad tbd
Cafe 2. If there be Coefficients; multiply them, and to their P.roduct adjoin the Quantities set together as before.
Chap. 2. Multiplication of Du
Multiplication of Duantities.
Exam.5. Exam.6.1 Exam. 7. | Exam. 8.
-60 3.0 t 2 b atb Thus
1 36 76. 6 · 156 1 x2 31 15 ab 14-42 db ! 18 a +12615 ab + 566.
Cafe 3. When the Quantities have unlike Signs; join them and the Product of their Coëfficients together (as before) but prefix the Sign - before them;
1 Exam.9. Exam. 10. Exam. 11. Exam: 12.
ta -od 40—76 142–76
1 x2 13] -ab 1 - 42 db - 2 af-21bf.-12 af +21bf That is, + into t, or — into —, gives + in the Product.
But + into , or into to, gives - S · That + into + will produce + in the Product, is evident from Multiplication in Common Arithmetick: viz. + s into + 7 will 'give + 35 &c. But that + into —, or — into + should produce the Sign , as in the four last Examples: And that — into — should produce the Sign to as in the second, fourth, and fixth Examples, may perhaps seem somewhat hard to be conceived ; and requires a Demonstration