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" The following axioms underlie the principles of all algebraic operations : 1. If the same quantity or equal quantities be added to equal quantities, the sums will be equal. 2. If the same quantity or equal quantities be subtracted from equal quantities,... "
New Elementary Algebra: Designed for Common and High Schools and Academies - Page 30
by Shelton Palmer Sanford - 1879 - 332 pages
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Arithmetical Institutions: Containing a Compleat System of Arithmetic ...

John Kirkby - Algebra - 1735 - 414 pages
...Sum or Aggregate, by collecting together two or more given Homogeneous Quantities. AXIOM XVI. 60. If equal Quantities be added to equal Quantities their Sums will be equal. HYPOTHESIS III. 61. The Sign of Addition is + ie Plus or More. Ex. gr. 6-\-г denotes the Sum of 6...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...value of the unknown quantity. Theģe processes arc grounded upon the following AXIOMS. (60.) 1. If equal quantities be added to equal quantities, their sums will be equal. 2. If equal quantities be subtracted from equal quantities, their remainders will be equal. 3. If equal quantities...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 352 pages
...they are placed together, for the convenience of reference. JO 83. Axiom I. If the same <,uai>tity or equal quantities be added to equal quantities,...equal. 2. If the same quantity or equal quantities he subtracted from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied...
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A Practical System of Algebra: Designed for the Use of Schools and Private ...

Peter Nicholson - Algebra - 1831 - 326 pages
...power. The fundamental principles, for the solution of equations, depend on the following AXIOMS: W If equal quantities be added to equal quantities, their sums will be equal ; for example, if we add 4 to each side of the equation 2 + 3=5, we shall have, 2 + 3 +4=5+4; te by...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1841 - 356 pages
...demonstrations and the solutions of problems, thev are placed together, for the convenience of reference. 63. Axiom 1. If the same quantity or equal quantities be added to equal quantities, their turns will be equal. 2. If the same quantity or equal quantities be subtracted from equal quantities,...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 320 pages
...are of this kind. ••1. If the same quantity or equal quantities be added to equa. quantities, the sums will be equal. 2. If the same quantity or equal quantities be subtracted from equil quantities, the remainders will be equal. 3. If equal quantities be multiplied by the same quantity...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1842 - 356 pages
...quantity or equal quantities be subtracted from equal quantities, the remainders will be equal. 63. Axiom 1. If the same quantity or equal quantities...added to equal quantities, their sums will be equal. 3. If equal quantities be multiplied into the same, or equal quantities, the products will be equal....
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1842 - 350 pages
...Then y will become known, if it be discovered tc be equal to the sum of a and 6: that is if y=a+b. 2. If the same quantity or equal quantities be subtracted...from equal quantities, the remainders will be equal. 63. Axiom 1. If the same quantity or equal quantities be added to equal quantities, their sums will...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1842 - 326 pages
...presented to the mind. These propositions are called axioms ; the following are of this kind. AXIOMS. 1. If the same quantity or equal quantities be added to equal quantities, the sums will be equal. 2. If the same quantity or equal quantities be subtracted from equal quantities,...
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An Elementary Treatise on Algebra: Theoretical and Practical ...

Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...to Algebra, and are the principles on which tlie truth of all algebraical operations finally rest: Axiom 1. If the same quantity or equal quantities...from equal quantities, the remainders will be equal. 4. If equal quantities be multiplied into the same, or equal quantities, the products will be equal....
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