 | Silas Ellsworth Coleman - Arithmetic - 1897 - 178 pages
...simple truths, or axioms: Ax. 1. If equal numbers are added to equal numbers, the sums are equal. Ax. 2. If equal numbers are subtracted from equal numbers, the remainders are equal. Ax. 3. If equal numbers are multiplied by equal numbers, the products are equal. Ax. 4. If equal numbers... | |
 | George Albert Wentworth - Algebra - 1898 - 516 pages
...truths, called axioms : Ax. 1. If equal numbers are added to equal numbers, the sums are equal. Ax. 2. If equal numbers are subtracted from equal numbers, the remainders are equal. Ax. 3. If equal numbers are multiplied by equal numbers, the products are equal. Ax. 4. If equal numbers... | |
 | James Morford Taylor - Algebra - 1900 - 504 pages
...they are equal to each other. 4. If equal numbers are added to equal numbers, the sums are equal. 5. If equal numbers are subtracted from equal numbers, the remainders are equal. 6. If equal numbers are multiplied by equal numbers, the products are equal. 1. If equal numbers are... | |
 | George Albert Wentworth - Algebra - 1906 - 440 pages
...true without proof. Ax. 1. If equal numbers are added to equal numbers, the sums are equal. Ax. 2. If equal numbers are subtracted from equal numbers, the remainders are equal. Ax. 3. If equal numbers are multiplied by equal numbers, the products are equal. Ax. 4. If equal numbers... | |
 | James William Nicholson - Algebra - 1909 - 332 pages
...point, respectively: I. If equal numbers are added to equal numbers, the sums are equal numbers. II. If equal numbers are subtracted from equal numbers, the remainders are equal numbers. III. If equal numbers are multiplied by equal numbers, the products are equal numbers. IV. If equal... | |
 | John Charles Stone, James Franklin Millis - Algebra - 1911 - 698 pages
...principles, called axioms : I. If equal numbers are added to equal numbers, the sums are equal. II. If equal numbers are subtracted from equal numbers, the remainders are equal. III. If equal numbers are multiplied by equal numbers, the products are equal. IV. If equal numbers... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1912 - 508 pages
...number. That is : For any pair of numbers a and b there is one and only one number c such that a + c = b. The process of finding the number с when a and...By definition of subtraction, the equality b — a = с implies that с is a number such that с + a = b. Adding a to each member of the equality b —... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Algebra - 1912 - 238 pages
...one and only one number с such that a + с = b. The process of finding the number с when a and Ь are given is called subtraction. This operation is...By definition of subtraction, the equality b — a = с implies that с is a number such that с + a = b. Adding a to each member of the equality Ь —... | |
 | Ernst Rudolph Breslich - Mathematics - 1925 - 302 pages
...be known : a. // equal numbers are added to equal numbers, the sums are equal. (Addition axiom.) b. If equal numbers are subtracted from equal numbers, the remainders are equal. (Subtraction axiom.) c. The percentage formula: P rb d. The interest formula: l = 77in rpt 100 e. The... | |
 | United States. Navy. Bureau of Naval Personnel - Mathematical computers - 1964 - 280 pages
...same number may therefore be added to both sides of an equation without destroying the equality. 2. If equal numbers are subtracted from equal numbers the remainders are equal. The same number may therefore be subtracted from both sides of an equation without destroying the equality.... | |
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Axioms (1) If equal numbers are added to equal numbers, the sums are equal. 
