 | 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
...straight line. 3. And that a circle may be described from any centre, at any distance from that centre. Axioms. 1. Things which are equal to the same thing...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
...straight line : 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing...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... | |
 | Charles Scott Venable - 1881 - 380 pages
...a supposition made either in the enunciation of a proposition, or in the course of a demonstration. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. The whole is greater than its part. 3. The whole is equal to the sum of all its parts. 4. From one... | |
 | Marianne Nops - 1882 - 278 pages
...axioms may of course be extended to any multiple or fraction. Axioms 2-5 form a second connected group. 2. ' If equals be added to equals the wholes are equal.'...equals be taken from equals the remainders are equal.' If A=C and B=D, A±B=C±D. 4. ' If equals and unequals be added together, the wholes are unequal.'... | |
| |
Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal... 
