 Things that 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 multiplied by equals, the products are equal.  Plane and Solid Geometry: Suggestive Method - Page 9by George Clinton Shutts - 1904 - 97 pagesFull view - About this book
 | George Washington Hull - Geometry - 1807 - 408 pages
...are respectively the conclusion and hypothesis of the second. 8. Axioms. 1. Things which are equal tu the same thing, or equal things, are equal to each other. 2. If the same operation be performed on equals, the results will be equal. 3. The whole is greater than... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...proposition, or in the course of a demonstration. 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. 4. If equals are added... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...proposition, or in the course of a demonstration. Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes arje equal. 3. If equals are taken from equals, the remainders are equal. 4. If equals are added... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...proposition, or in the course of a demonstration. 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. 4. If equals are added... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...following are some of the most important axioms and postulates. Axioms. 1°. Things equal to the same thing are equal to each other. 2°. If equals are added...equal. 3°. If equals are subtracted from equals, the remainders are equal. . 4°. If equals are multiplied by equals, the products are equal. 5°. If equals... | |
 | James Bates Thomson - Algebra - 1878 - 322 pages
...= what ? AXIOMS. 59. An Axiom is a self-evident truth. 1. Things which are equal to the same thing, are equal to each other. 2. If equals are added to...equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are multiplied by equals, the products are equal. 5. If equals are... | |
 | Franklin Ibach - Geometry - 1882 - 208 pages
...Scholium is a comment on one or more propositions. 39. AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to...equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal. 5. If equals are subtracted... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...dimensions of length, breadth, and thickness. AXIOMS. 1. Things which are equal to the same thing, are equal to each other. 2. If equals are added to...equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal. 5. If equals are subtracted... | |
 | George Anthony Hill - Geometry - 1888 - 200 pages
...each equal to a third, are equal to each other; or, for any magnitude, its equal may be substituted. 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 multiplied by equals, the products are... | |
 | George Anthony Hill - Geometry - 1888 - 202 pages
...each equal to a third, are equal to each other; or, for any magnitude, its equal may be substituted. 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 multiplied by equals, the products are... | |
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