 Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.  Elements of Plane Geometry - Page 14by Franklin Ibach - 1882 - 196 pagesFull view - About this book
 | David Martin Sensenig - Algebra - 1889 - 388 pages
...Axioms. 45. An Axiom is a self-evident truth. 46. The following are the principal axioms of algebra : 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be subtracted from equals the remainders will... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...line. 3. That a circle may be described with any centre, at any distance from that centre. AXIOMS. 46. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals the sums will be equal. 3. If equals be taken from equals the remainders will be... | |
 | George Albert Wentworth - Geometry - 1893 - 270 pages
...produced to any distance, or can be terminated at any point. 82. AXIOMS. 1. Tilings which are equal to the same thing are equal to each other. 2. If equals are...added to equals the sums are equal. 3. If equals are taken from equals the remainders are equal. 4. If equals are added to unequals the sums are unequal,... | |
 | John Macnie - Geometry - 1895 - 390 pages
...state them for convenience of reference. AXIOMS. 1. Magnitudes equal to the same or equal magnitudes are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...That a circumference may be described about any point as a centre with a radius of given length. 82. AXIOMS. 1. Things which are equal to the same thing...added to equals the sums are equal. 3. If equals are taken from equals the remainders are equal. 4. If equals are added to unequals the sums are unequal,... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...propositions which have been proved can be employed to establish the truth of the proposition. AXIOMS 49. 1. Things which are equal to the same thing are equal...added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.... | |
 | William James Milne - Geometry - 1899 - 396 pages
...be employed to establish the truth of the proposition. AXIOMS 49. 1. Tiiings which are equal to the same thing are equal to each other. 2. If equals are...added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...INDEX 463 GENERAL AXIOMS. 1. Magnitudes which are equal to the same magnitude, or equal magnitudes, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...that 34. GENERAL AXIOMS. 1. Magnitudes which are equal to the same magnitude, 01 equal magnitudes, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal... | |
 | George Albert Wentworth - Geometry - 1899 - 498 pages
...that 34. GENERAL AXIOMS. 1. Magnitudes which are equal to the same magnitude, or equal magnitudes, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal... | |
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