 | John Kirkby - Algebra - 1735 - 414 pages
...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... | |
 | Philip Ronayne - Algebra - 1738 - 458 pages
...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... | |
 | Daniel Fenning - Algebra - 1751 - 272 pages
...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... | |
 | William Emerson - Mathematics - 1764 - 582 pages
...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... | |
 | William Emerson - Algebra - 1780 - 574 pages
...equal quantities, the products will be equal. 4. If equal quantities be divided by equal quanties, the quotients will be equal. -' 5. The equal powers...or from equal quantities, unequal ones be added or fubtraded j the fums or remainders will be unequal. 7. If equal quantities be multiplied or divided... | |
 | John Bonnycastle - Algebra - 1782 - 226 pages
...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... | |
 | John Bonnycastle - 1782 - 272 pages
...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... | |
 | William Nicholson - Navigation - 1784 - 462 pages
...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... | |
 | Nicolas Vilant - Algebra - 1798 - 196 pages
...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... | |
 | Thomas Hodson - Education - 1802 - 556 pages
...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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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... 
