| John Playfair - 1837 - 318 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. **And that a circle may be described from any centre, at any distance from that centre. AXIOMS.** 1 . THINGS which are equal to the same thing are equf.l to one another. 2. If equals be added to equals,... | |
| Euclid, James Thomson - 1837 - 390 sider
...the other. 2. That a terminated straight line may be produced to any length in a straight line : 3. **That a circle may be described from any centre, at any distance from that centre.* AXIOMS.** 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals or the... | |
| Edward Tagart - 1837 - 135 sider
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that **things which are equal to the same are equal to one another,** or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged... | |
| William Josiah Irons - 1837
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' **things which are equal to the same are equal to one another,'** he would never get any such proof. If he should find by experience that it had been so, in a million... | |
| Euclides - 1838
...point. II. That a terminated straight line may be produced to any length in a straight line. III. Anil **that a circle may be described from any centre, at any distance from that centre. AXIOMS.** THINGS which are equal to the same thing, are equal to one another. II. If equals be added to equals,... | |
| Richard W. Green - 1839 - 148 sider
...dividing the 1st, x= — >£ Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that **things which are equal to the same, are equal to one another** ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying... | |
| Euclides - 1841 - 351 sider
...other point. II. That a terminated straight line may be produced to any length in a straight line. Ill **And that a circle may be described from any centre, at any distance from that centre. AXIOMS.** L Things which are equal to the same thing, are equal to one another. II. If equals be added to equals,... | |
| Francis Bacon - 1841
...similar to that of music termed the declining of a cadence. Again ; the mathematical postulate, that " **things which are equal to the same are equal to one another,"** is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.... | |
| Francis Bacon - 1841
...similar to that of music termed the declining of a cadence. Again ; the mathematical postulate, that " **things which are equal to the same are equal to one another,"** is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.... | |
| 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " **things which are equal to the same are equal to one another."** The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured... | |
| |