 Things 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 subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.  Elements of Plane Geometry - Page 14by Franklin Ibach - 1882 - 196 pagesFull view - About this book
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...corollary is a consequence, obvious, or easily deduced from a proposition or a definition. 30. GENERAL AXIOMS. 1. Things which are equal to the same thing...equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...and not perpendicular to it. ASSUMPTIONS 54. 1. Things equal to the same thing, or to equal things, are equal to each other. 2. If equals are added to...equals are added to unequals, the sums are unequal in the same order. 5. If equals are subtracted from unequals, the remainders are unequal in the same... | |
 | David Eugene Smith - Geometry - 1911 - 360 pages
...proof is of no value, however, save as a curiosity. 2. And if to equals equals are added, the wholes are equal. 3. If equals are subtracted from equals, the remainders are equal. Axioms 2 and 3 are older than Euclid's time, and are the only ones given by him relating to the solution... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...will lit wholly iu the surface. ASSUMPTIONS 54. 1. Things equal to the same thing, or to equal things, are equal to each other. 2. If equals are added to...equals are added to unequals, the sums are unequal in the same order. 5. If equals are subtracted from unequals, the remainders are unequal in the same... | |
 | William Betz, Harrison Emmett Webb, Percey Franklyn Smith - Geometry, Plane - 1912 - 360 pages
...magnitudes, are equal to each other. In other words, A magnitude may be substituted for its equal. 2. If equals are added to equals, the sums are equal....equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
 | William Betz, Harrison Emmett Webb - Geometry, Modern - 1912 - 368 pages
...magnitudes, are equal to each other. In other words, A magnitude may be substituted for its equal. 2. If equals are added to equals, the sums are equal....equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 490 pages
...from another theorem. AXIOMS AND POSTULATES 1. Things equal to the same thing, or to equal things, are equal to each other. 2. If equals are added to...equals are added to unequals, the sums are unequal in the same sense. 5. If equals are subtracted from unequals, the remainders are unequal in the same... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...from another theorem. AXIOMS AND POSTULATES 1. Things equal to the same thing, or to equal things, are equal to each other. 2. If equals are added to...equals are added to unequals, the sums are unequal in the same sense. 5. If equals are subtracted from unequals, the remainders are unequal in the same... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 248 pages
...Axiom 2, etc. 155. AXIOMS. 1. Magnitudes which are equal to the same magnitude, or to equal magnitudes, are equal to each other. 2. If equals are added to...equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
 | William Betz - Geometry - 1916 - 536 pages
...magnitudes, are equal to each other. In other words, A magnitude may be substituted for its equal. 2. If equals are added to equals, the sums are equal....equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are divided by equals, the quotients are... | |
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