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Books Books 1 - 10 of 24 on If equal numbers be added to equal numbers, the sums are equal numbers. That is,....  
" If equal numbers be added to equal numbers, the sums are equal numbers. That is, if a = b and c = d, then a + c = b + d, If a = b c and x = p g, then a + x = (b c) + (p q) = b +p c q. "
Elements of algebra priliminary to the differential calculus ... - Page 2
by Augustus De Morgan - 1837 - 256 pages
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Elements of algebra, preliminary to the differential calculus

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 = bd. If a =p g and 6 = p 2?, then a 6 = (p 9)_(?_2}) = p 9 /i + 2y = 9. If...
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The Elements of Algebra Preliminary to the Differential Calculus: And Fit ...

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...
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Elementary Arithmetic: With Brief Notices of Its History, Volumes 1-12

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,...
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ELEMENTARY ARITHMETIC, WITH BRIEF NOTICES OF ITS HISTORY

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,...
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High School Algebra: Complete Course

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...
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High School Algebra: Advanced Course

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...
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College Algebra

Henry Lewis Rietz - 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"...
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First Principles of Algebra: Complete Course

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...
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College Algebra

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...
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College Algebra, Volume 2

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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