| 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous V " **Things which are equal to the same, are equal to one another."** " Very good, Sir. What the second, and what the thirdV " If equals be added to equals, the sums are... | |
| John Martin F. Wright - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " **Things which are equal to the same, are equal to one another."** " Very good, Sir. What the second, and what the third?" " If equals be added to equals the sums are... | |
| Leeds grammar sch - 1828
...: but Patience is equal to Poverty ; therefore Patience and Economy are each equal to Poverty ; but **things which are equal to the same are equal to one another;** therefore Patience and Economy are equal to one another ; wherefore the three, Patience, Economy, and... | |
| Timothy Walker - 1829 - 129 sider
...terminated straight line may be produced to any length in a straight line. i « f 3. Let it be granted **that a circle may be described from any centre, at any distance from that centre.** The moderns, as Legendre, for example, are not thus scrupulous; but constantly suppose lines to be... | |
| John Playfair - 1829 - 186 sider
...other point. 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.** 4. That a straight line which meets one of two parallel straight lines may oe produced till it meet... | |
| George Peacock - 1830 - 685 sider
...represented, or in terms of which they are expressed: without such a definition, the proposition that " **things which are equal to the same are equal to one another,"** could no longer be considered as axiomatic, inasmuch as we should be at a loss for the principle or... | |
| Pierce Morton - 1830 - 272 sider
...the propositions of the following sections, and are therefore here premised : — • AXIOMS.* • 1. **Things, which are equal to the same, are equal to one another.** 2. If equals be added to equals, the wholes arc equal. 3. If equals be taken from equals, the remainders... | |
| William Sewell - 1830 - 371 sider
...experiment. A child never doubts that the fire which burnt him yesterday, will burn him to-day, or that two **things which are equal to the same, are equal to one another,** where he .has once seen the axiom illustrated by a single example—and hence one great advantage in... | |
| Francis Bacon, Basil Montagu - 1831
...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.... | |
| John Playfair - 1832 - 333 sider
...one point to any other point. II. That a terminated straight line may be produced to any length in a **straight line. III. And that a circle may be described...centre, at any distance from that centre. Axioms.** iTHINGS which are equal to the same thing are equal to one another. II. If equals be added to equals,... | |
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