| Augustus De Morgan - 1837
...If a = b + c, then a + v = 6 + cM. 2. If equal numbers be taken from equal numbers, the remainders **are equal numbers. That is, if a = b and c = d, then a — c** = b—d. If a =p — g and 6 = p— 2?, then a — 6 = (p — 9)_(?_2}) = p — 9— /i + 2y = 9. If... | |
| Augustus De Morgan - Algebra - 1837 - 248 pages
.../—-. If Then - = <4 or T = 2 T = 6 = 6 4. If equal numbers be divided by equal numbers, the quotients **are equal numbers. That is, if a = b and c = d, then** - = -j. If C u m = n, then — ==-. Ifa=t> — c and p + g = z, then — — = 4 — c Tr _ , TT 14... | |
| Robert Potts - Arithmetic - 1876
...4. Numbers or aggregates of numbers which are equal to tho samo number are equal to one another. 5. **If equal numbers be added to equal numbers, the sums are equal.** 6. If equal numbers be added to unequal numbers : or if unequal numbers be added to equal numbers,... | |
| ROBERT POTTS - 1876
...4. Numbers or aggregates of numbers which are equal to the same number are equal to one another. 5. **If equal numbers be added to equal numbers, the sums are equal.** 6. If equal numbers be added to unequal numbers : or if unequal numbers be added to equal numbers,... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 494 pages
...number expressions are said to be equal if they represent the same number. Axiom I. If equal numbers are **added to equal numbers, the sums are equal numbers. That is, if a** = 6 and с = d, then a + с = 6 + d. Axiom I implies that two numbers have one and only one sum. This... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1908 - 194 pages
...Axiom I the sums are the same and hence equal. Therefore from Axiom I follows the axiom usually given : **If equal numbers be added to equal numbers, the sums are equal numbers.** Since Axiom I asserts that the sum of two numbers is unique, it is often called the uniqueness axiom... | |
| Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1909 - 261 pages
...commutative. That is, a + b = b+a. III. Addition is associative. That is, (а + b) + с = a + (b + c). IV. **If equal numbers be added to equal numbers, the sums are equal numbers. That is, if a = b, and** с = d, then * The operations are fundamental in that no attempt is made to define them. The "laws"... | |
| Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1912 - 481 pages
...number expressions are said to be equal if they represent the same number. Axiom I. If equal numbers are **added to equal numbers, the sums are equal numbers. That is, if a = b and** с = d, then a + с = b + d. Axiom I implies that two numbers have one and only one sum. This fact... | |
| H. L. Rietz. Ph. D. - 1919
...assumptions since no attempt is made to prove them. III. Addition is associative. That is, (а IV. **If equal numbers be added to equal numbers, the sums are equal numbers. That is, if** а = b, and c = d, then a + с — b + d. V. The product of any two numbers is a uniquely determined... | |
| Henry Lewis Rietz, Arthur Robert Crathorne - Algebra - 1919 - 268 pages
...addition. That is, a(b + c)= ab + ac. IX. If equal numbers be multiplied by equal numbers, the products **are equal numbers. That is, if a = b, and c = d, then** ac = bd. The following laws X and XI lead us to definitions of subtraction and division, and enable... | |
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