 | 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... | |
 | James B. Dodd - Algebra - 1859 - 368 pages
...Axiom is a truth which is self-evident, — neither admitting nor requiring any demonstration; such as, 1. Things which are equal to the same thing, are equal...equals, the remainders will be equal. 4. If equals be multiplied by equals, the products will be equal. 5. If equals be divided by equals, the quotients... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...are called homologous sides or angles. AXIOMS. 34. An AXIOM is a self-evident trath ; such as, — 1. Things which are equal to the same thing, are equal...remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. -• 5. If equals be taken from unequals, the remainders will be... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...are called homologous sides or angles. AXIOMS. 34. An AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal...remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | Benjamin Greenleaf - Geometry - 1863 - 504 pages
...are called homologous sides or angles. AXIOMS. 34. An AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal...remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
 | 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... | |
 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...are called homologous sides or angles. AXIOMS. 34. An AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal...remainders will be equal. 4. If equals be added to unequals, the sums will be unequal. 5. If equals be taken from unequals, the remainders will be unequal.... | |
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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... 
