 | Pierce Morton - Geometry - 1830 - 584 pages
...sections, and are therefore here premised : — • AXIOMS.* • 1. Things, which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders are equal. 4. The doubles of equals are... | |
 | John Playfair - Euclid's Elements - 1835 - 336 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 wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Mathematics - 1835 - 684 pages
...following sections, and are therefore here premised : — AXIOMS.* 1. Things, which are equal to the same, 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. The doubles of equals are... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...product of A and B. Axioms. • 1. Things which are equal to the same thing, are equal to each other. -2. If equals be added to equals, the wholes will...If equals be added to unequals, the wholes will be miequal. 5. If equals be taken from unequals, the remainders will be unequal. 6. Things which are double... | |
 | Mathematics - 1836 - 488 pages
...which being produced ever so far both ways, do not meet. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes ere equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...described from any centre, and with any radius. AXIOMS. 1. Things which are equal to the same thing ate 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,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...centre, at any distance from that centre. AXIOMS. 1 . THINGS which are equal to the same thing are equf.l 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,... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...self evident truth. .. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the wholes will be...be taken from equals the remainders will be equal. ClOEST.— 11. What is a theorem 1 12. What is a problem 1 13. What is a proposition 1 May it be a... | |
 | Euclides - 1840 - 192 pages
...any centre, with any interval 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 wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...propounded by Euclid in the first book, are the following : — 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 taken from equals, the remainders are equal. 4. If equals be added to unequals,... | |
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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 taken from equals, the remainders are equal. 
