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" Algebraic operations are based upon definitions and the following 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,... "
A Theoretical and Practical Treatise on Algebra: ... Designed for Schools ... - Page 11
by Horatio Nelson Robinson - 1858 - 360 pages
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Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., Volume 4

William Emerson - Mathematics - 1764 - 582 pages
...equal quantities be added to equal quantities, the fums will be equal. 2. If equal quantities be taken from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the produits will be equal. 4. If equal quantities be divided by equal quanties,...
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An Introduction to Algebra: With Notes and Observations: ... By John ...

John Bonnycastle - 1782 - 272 pages
...quantities be added to equal quantities the wholes will be equal. я. If equal quantities be taken from equal quantities, the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the produfts will be equal. 4. If equal quantities be divided by equal quantities,...
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A Complete Treatise on Arithmetic, Rational and Practical: Wherein the ...

Paul Deighan - Arithmetic - 1804 - 504 pages
...equ.il quantities be added to equal quantities, the fums will be equal. 2. If equal quantities be taken from equal quantities the remainders will be equal. 3. If equal quantities be multiplied by equal quantities, the products will be equal. 4. If equal quantities be divided by equal quantities,...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1814 - 304 pages
...reference. 63. Axiom 1. If the same quantity or equal quantities be added to equal quantities, their sums will be equal. 2. If the same quantity or equal quantities...be multiplied into the same, or equal quantities, tkeproduets will be equal. 4. If equal quantities be divided by the same or equal quantities, the quotienti...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - Arts - 1819 - 432 pages
...equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be taken from equal quantities, the remainders will be equal 3. If equal quantities be multiplied by the same, or equal quantities, the products will be equal. 4. If equal quantities be divided by...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 332 pages
...equations : — 1. If equal quantities be added to equal quantities, the suras will be equal. 2. If equal quantities be subtracted from equal quantities,...will be equal. 3. If equal quantities be multiplied by equal quantities, the products will be equal. 4. lf,equal quantities be divided by equal quantities,...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 314 pages
...FIRST DEGREE. i 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...will be equal. 3. If equal quantities be multiplied by the same quantity or by equal quantities, the products will be equal. 4. If equal quantities be...
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An Elementary Treatise on Algebra: For the Use of Students in High Schools ...

Thomas Sherwin - Algebra - 1841 - 320 pages
...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
...equal. 63. Axiom 1. If the same quantity or equal quantities be added to equal quantities, their sums will be equal. 3. If equal quantities be multiplied...same, or equal quantities, the products will be equal. 5. If the same quantity be both added to and subtractea from another, the value of the latter will...
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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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