| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...described from any centre, at any distance from that centre. AXIOMS. 1. Tiiings which are equal to the **same thing are equal to one another. 2. If equals...wholes are equal, 3. If equals be taken from equals the** remamders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals be taken... | |
| Alexander Bain - Logic - 1870 - 478 pages
...unquestionable axioms, conforming to both the criteria. The five succeeding are — AXIOMS OF EDCLID. 209 **(3) If equals be taken from equals, the remainders are equal. (4) If equals be added to** tmequals, the wholes are unequal. (5) If from unequals, equals be taken, the remainders are unequal.... | |
| Euclid - Geometry - 1872 - 284 pages
...from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same **are equal to one another. 2. If equals be added to equals, the wholes** will be equal. 4. If to unequals, equals be added, the wholes are unequal. 5. If from unequals, equals... | |
| William Alexander Myers - Circle-squaring - 1873 - 238 pages
...polygon with any given number of sides expressed by 2 n -f- 1, provided, 2 n -|- 1 is a prime number. **AXIOMS. 1. Things which are equal to the same thing...another. 2. If equals be added to equals the wholes** will be equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to... | |
| Edward Atkins - 1874 - 428 pages
...point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And **that a circle may be described from any centre, at...If equals be added to equals the wholes are equal.** I 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the... | |
| William Alexander Myers - Circle-squaring - 1874 - 207 pages
...a polygon with any given number of sides expressed by 2n + 1, provided, 2n -(- 1 is a prime number. **AXIOMS. 1. Things which are equal to the same thing...another. 2. If equals be added to equals the wholes** will be equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to... | |
| Edward Atkins - 1877 - 72 pages
...described from any centre, at any distance from that centre. Axioms. 1. Tilings which are equal to the **same thing are equal to one another. 2. If equals be added to equals the wholes are equal.** EXPLANATION OF TERMS AND ABBREVIATIONS. 9 3. If equals be taken from equals the remainders are equal.... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...straight line ; 3. That a circle may be described from any centre, with a radius equal to any given line. **Axioms. 1. Things which are equal to the same thing...added to equals, the wholes are equal. 3. If equals be** subtracted from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...point : 2. That a terminated straight line may be produced to any length in a straight line : 3. And **that a circle may be described from any centre, at...the remainders are equal. 4. If equals be added to** uncquala the wholes are unequal. 5. If equals be taken from unequals the remainders are unequal. 6.... | |
| T S. Taylor - 1880 - 152 pages
...evidently true that it need not (or indeed cannot) be proved. The following are the axioms of Euclid : **1. Things which are equal to the same thing are equal...If equals be added to equals, the wholes are equal.** 20. (Not given by Euclid, tut assumed by him). If the same thing be added to equals the wholes are... | |
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