 | 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... | |
 | 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.... | |
 | Charles Guilford Burnham - 1857 - 342 pages
...PmrtL AXIOMS An axiom Is a self-evident proposition. 1. Things wliich are equal to the same thing arc 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... | |
 | Elias Loomis - Conic sections - 1858 - 256 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 arje equal. 3. If equals are taken from equals, the remainders are... | |
 | Euclides - 1858 - 248 pages
...of the angles is a right angle. Ax. 8. Magnitudes which exactly fill the same space are equal. Ax. 2. If equals be added to equals, the sums will be equal. Ax. 1. Magnitudes which are equal to the same, are equal to each other. EXP. Hyp. Concl. 1. 2. Let... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...RHOMBOID is a parallelogram whose angles are all oblique. AXIOMS. 1. Tilings which are equal to the same thing, are equal to each other. 2. If equals...to equals, the sums will be equal. 3. If equals be subtracted from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will... | |
 | Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...demonstration. 77. A Scholium is a remark or obserwition made upon something going before it. 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... | |
 | Adrien Marie Legendre - Geometry - 1871 - 490 pages
...dimensions : length, breadth, and thickness. AXIOMS. 4 1. Thmgs which are equal to the same thing, are equa 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. If equals be added to unequals, the sums will... | |
 | Elias Loomis - Geometry - 1871 - 302 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.... | |
 | Oliver Spencer Munsell - History - 1871 - 360 pages
...and contradiction. For example, take the first, second, and third axioms; I quote from Robinson: " 1. Things which are equal to the s'ame 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... | |
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AXIOMS. 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. 
