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" Algebraic operations are based upon definitions, and the following axioms : 1. If equal quantities be added to equal quantities, the sums will be equal. 2. If equal quantities be subtracted from equal quantities, the remainders will be equal. 3. If equal... "
A Complete Treatise on Arithmetic, Rational and Practical: Wherein the ... - Seite 65
von Paul Deighan - 1804 - 177 Seiten
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Arithmetical Institutions: Containing a Compleat System of Arithmetic ...

John Kirkby - 1735 - 380 Seiten
...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 - 421 Seiten
...Quantities remaining will 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 - 238 Seiten
...Side 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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Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., Band 4

William Emerson - 1764
...equal quantities, the produits will be equal. 4. If equal quantities be divided by equal quanties, the quotients will be equal. 5. The equal powers or...multiplied or divided by unequal quantities ; the producís or quotients will be unequal. 8. Quantities feverally equal to a third, are equal to one...
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1782 - 201 Seiten
...for thofe that are unknown. AXIOMS. 1. If equal quantities be added to equal quantities the wholes will be equal. 2. If equal quantities be taken from...powers or roots of equal quantities are equal. 6. Two quantities refpeftively equal to a third. are equal to each other. 'f. The whole is equal to all...
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An Introduction to Algebra: With Notes and Observations: ... By John ...

John Bonnycastle - 1782 - 201 Seiten
...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...powers or roots of equal quantities are equal. 6. Two quantities refpeftively equal to a third, are equal to each other. 7. The whole is equal to all...
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The Navigator's Assistant: Containing the Theory and Practice of Navigation ...

William Nicholson - 1784 - 223 Seiten
...equal. III. If equal quantities be multiplied by equal quantities, the produces will be equal. IV. If equal quantities be divided by equal quantities, the quotients will be equal, V. Things V. Things equal to one and the fame thing, are equal to each other. THEOREM I. In any feries...
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The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - 1798 - 170 Seiten
...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
...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 - 219 Seiten
...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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