 | John Playfair - 1837 - 332 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 - 410 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 - 156 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 - 160 sider
...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... | |
 | Robert Simson - 1838 - 434 sider
...point. II. That a terminated straight line may be produced to any length in at straight line. III. And that a circle may be described from any centre,...which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equals. m. If equals be taken from enuals, the remainders... | |
 | Euclides - 1838 - 264 sider
...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 - 156 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 - 378 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 - 616 sider
...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.... | |
 | Nicholas Patrick Wiseman - 1841 - 618 sider
...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... | |
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Let it be granted that a straight line may be drawn from any one point to any other point. 
