 | Charles Davies - Geometry - 1850 - 238 pages
...perpendicular to the base. Thus, AB is the base and CD is the altitude of the trapezoid. Of Axioms. 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 equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
 | Charles Guilford Burnham - 1850 - 350 pages
...more common use in this work, see Art. 54, or Part I. AXIOMS An axiom is a self-evident proposition. 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 equal. 8. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
 | Janet Taylor - Nautical astronomy - 1851 - 674 pages
...simple operation. A proposition is a general term signifying cither a problem or a theorem. AXIOMS. 1. Things which are equal to the same thing, are equal to each other. 2. When equals are added to equals, the wholes are equal. 3. When equals are taken from equals, the remainders... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...and the altitude is a line drawn from the opposite side or angle, perpendicular to the base. AX1OMS. 1. Things which are equal to the same thing are equal...each other. . 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals,...remainders will be equal. 4. If equals be added to unequals, the wholes will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be equal. 3. If equals be taken from equals,...remainders will be equal. 4. If equals be added to unequals, the wholes will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | Charles Guilford Burnham - Arithmetic - 1857 - 328 pages
...or quantities on one side of the sign of equality. AXIOMS An axiom is a -self-evident proposition. 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 equal 3. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
 | Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...tests of equality between two quantities : 1. Things which are equal to the tame or to 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 remainders will be equal. 4. Like parts of equal things are equal. 5. Like... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the wholes will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | Elias Loomis - Conic sections - 1857 - 242 pages
...supposition made either in the enunciation of a 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.... | |
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AXIOM is a self-evident truth ; such as, — 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... 
