 Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal. 4. If equals be added to unequals the wholes are unequal. 5. If equals...  Elements of Plane Geometry According to Euclid - Page 1by Andrew Bell - 1837 - 240 pagesFull view - About this book
 | Moffatt and Paige - 1879 - 428 pages
...centre, at any distance from that centre. AXIOMS. (1) Things that are equal to the same thing, are equal to one another. (2) If equals be added to equals,...from unequals, the remainders are unequal. (6) Things that are double of the same thing are equal to one another. (7) Things that are halves of the same... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...centre, with a radius equal to any given line. Axioms. 1. Things which are equal to the same thing are 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. If equals be added to unequals, the wholes are... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...of a circle from any centre with any radius. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals,...be taken from unequals, the remainders are unequal. Things which are double of the same are equal to one another. Things which are halves of the same are... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...any centre, at any distance from that centre. AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals...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
...be proved. The following are the axioms of Euclid : 1. Things which are equal to the same thing are equal to one another. 2. 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... | |
 | George Albert Wentworth - Geometry, Modern - 1881 - 266 pages
...remainders are equal. 4. When equals are added to unequals the sums are unequal. 5. When equals are taken from unequals the remainders are unequal. 6. Things which are double the same thing, or equal things, are equal to each other. 7. Things which are halves of the same thing,... | |
 | 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.'... | |
 | Euclides - 1883 - 176 pages
...Propositions I. 2 and I. 3 may be omitted. Axioms. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals...unequals the remainders are unequal. 6. Things which are doubles of the same thing are equal to one another. 7. Things which are halves of the same thing are... | |
 | Moffatt and Paige - 1883 - 576 pages
...centre, at any distance from that centre. AXIOMS. (1) Things that are equal to the same thing, are equal to one another. (2) If equals be added to equals,...(5) If equals be taken from unequals, the remainders arc unequal. (6) Things that are double of the same thing are equal to one another. (7) Things that... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...any centre, at any distance from that centre AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals...from equals the remainders are equal. 4. If equals bo added to unequals the wholes are unequal. 5. If equals be taken from unequals the remainders are... | |
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