| Edward Albert Bowser - Geometry - 1890 - 418 pages
...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 equal. 4. If equals be... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...can be drawn between two points. 38. AXIOMS. 1. Things which are equal to the same or equal things **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 differences will be equal. 4. If equals... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...truth to another the following general axioms are also employed, viz. : (l.) Things equal to the same **thing are equal to each other. (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... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...truth to another the following general axioms are also employed, viz. : (1.) Things equal to the same **thing are equal to each other. (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... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things **are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added... | |
| Arthur Schultze - 1901 - 260 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things **are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...conclusion and the hypothesis of the other. AXIOMS 1. Things that are equal to the same or equal things **are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be added... | |
| Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...stated as follows: GENERAL AXIOMS 1. Things which are equal to the same thing, or to equal things, **are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Doubles of equals... | |
| William Frank White - Mathematical recreations - 1908 - 274 pages
...equations with a list of axioms such as the following: 1. Things equal to the same thing or equal things **are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. If equals be multiplied... | |
| Francis William Rolt-Wheeler - Science - 1909 - 356 pages
...and also assumes its infinitude. The five common notions are : 1. Things which are equal to the same **thing are equal to each other. 2. If equals be added to equals, the** sums are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide... | |
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