| Aristotle, Thomas Taylor - First philosophy - 1801 - 482 pages
...and at the fame time denied, of the fame : alfo, that which is employed by geometry, viz. that thofe **things which are equal to the fame thing are equal to each other;** that which the natural philofopher ufes, that nothing can be generated from that which is not; and... | |
| Timothy Walker - Geometry - 1829 - 156 pages
...just proved that AHG=HG D. Consequently FHB=HGD ; each being equal to AHG ; for it is an axiom that **things which are equal to the fame thing are equal to each other.** 35 . THEOREM. When two parallels are crossed by a straight line, the sum of the two interior angles... | |
| Charles Davies - Surveying - 1839 - 376 pages
...connexion, their use, their restriction, or their extension. Axioms. I. Things which are equal to the same **thing, are equal to each other. 2 If equals be added to equals, the wholes will** he equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to... | |
| Scottish school-book assoc - 1845 - 444 pages
...may be described from any centre, and with any radius. AXIOMS. 1. Things that are equal to the same **thing are equal to each other. 2. If equals be added to equals, the** sums are equals. 3. If equals be taken from equals, the remainders are equals. 4. If equals be added... | |
| Almon Ticknor - Measurement - 1849 - 156 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 be added to equals, the** whole will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals... | |
| Charles Guilford Burnham - 1850 - 350 pages
...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 be added to unequals,... | |
| 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... | |
| James B. Dodd - Algebra - 1859 - 368 pages
...— neither admitting nor requiring any demonstration; 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 532 pages
...angles. AXIOMS. 34. An 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... | |
| Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles. AXIOMS. 34. An AXIOM is a self-evident trath ; 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... | |
| |