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" If equal quantities be subtracted 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, the quotients will be equal.... "
The Navigator's Assistant: Containing the Theory and Practice of Navigation ... - Side xv
av William Nicholson - 1784 - 222 sider
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Arithmetical Institutions: Containing a Compleat System of Arithmetic ...

John Kirkby - 1735 - 414 sider
...in the Divifion of 12 by 2. Here 12 is the Dividend, 2 the Divifor, and 6 the Retient. AXIOM XX. 77. If equal Quantities be divided by equal Quantities, the Quotients will be equal. 4-t HYPOTHESIS VIII. 78. The Sign of Divißon is -7- ie By. Ex. g r. 6 -•- 3 denotes that б is to...
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A Treatise of Algebra in Two Books: The First Treating of the Arithmetical ...

Philip Ronayne - 1738 - 458 sider
...be equal. 3. If equal Quantities be Multiplyed by equal Quantities, the Produfls will be equal. 4. If equal Quantities be Divided by equal Quantities, the Quotients will be equal. 5. Thofe Quantities that are equal to one and the fame thing, are equal to one another. 6. Every Whole...
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The Young Algebraist's Companion: Or, A New & Easy Guide to Algebra ...

Daniel Fenning - 1751 - 272 sider
...by any Quantity or Number, as 12, then will 12 xz: 96. This is plain from the next Axiom. AXIOM 4. If equal Quantities be divided by equal Quantities, the Quotients will be equal. Suppofe i2x — 96, then dividing by 12, *• will be equal to 8, as per Axiom 3. AXIOM 5. Thofe Numbers...
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1782 - 226 sider
...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, the quotients will be equal. 5. The equal powers or roots of equal quantities are equal. 6. Two quantities refpeftively equal to...
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The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - 1798 - 196 sider
...AXIOM IX. If equal quantities be multiplied by equal quantities, the produfls will be equal, AXIOM X. If equal quantities be divided by equal quantities, the quotients will be equal. - ' t AXIOM XI. If equal quantities be equally involved or evolved» the powers or roots. vvilUb'e...
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The Accomplished Tutor: Or, Complete System of Liberal Education ...

Thomas Hodson - 1802 - 556 sider
...be equal. a. If equal quantities be multiplied by equal quantities, the produces will be equal. And if equal quantities be divided by eq~ual quantities, the quotients will be- equal. 3. If equal quantities be raifed to equal powers, the produfts willfte equal. 4. Qiiamtities equal...
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The Young Algebraist's Companion ...: New Ed. To which is Added a Supplement ...

Daniel Fenning - 1802 - 274 sider
...quantity or number, as 12, then will 12 x = 96. This is plain from the ne\t Axiom. F AXIOM a AXIOM 4. I If equal quantities be divided by equal quantities, the quotients will be equal. Suppofe 12 .r = 96, then divid, ing by 12, x will be equal to 8, as per Axiom 3. AXIOM 5. Thofe numbers...
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A Complete Treatise on Arithmetic, Rational and Practical: Wherein the ...

Paul Deighan - 1804 - 504 sider
...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, the quotients will be equal. ' 5. The equal powers or roots of equal quantities, are equal. 6. If to or from equal quantities, unequal...
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A Practical System of Algebra: Designed for the Use of Schools and Private ...

Peter Nicholson - 1831 - 326 sider
...12 + 8=20 ; if we multiply the right hand side by 3, we have 5/3=15, which is 5 less than 20. ('*) If equal quantities be divided by equal quantities, the quotients will be equal. Ex. 0) 4+2=6. Dividing by 2 ; 2+1 = 3. Ex. W If 4,r=8 ; Dividing by 4; a1 =2. Proof, 4.r=4X2=8. (13)...
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A New Introduction to the Science of Algebra ...

Silas Totten - 1836 - 320 sider
...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, the quotients will be equal. In an equation, the unknown quantity may be connected with known quantities, by addition, by subtraction,...
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