| George Bentham - 1827 - 298 sider
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. **Things which are equal to the same, are equal to one another.** 2. When of two things, one only is equal to a third, and the other is not equal to that third, these... | |
| 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... | |
| John Playfair - 1829 - 186 sider
...POSTULATES. 1. LET it be !granted that a straight line may be drawn from any one point to any 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... | |
| Timothy Walker - 1829 - 129 sider
...granted that a straight line may be drawn from any one point to any other point. 2. Let it be granted **that a 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... | |
| 1829
...convenient to substitute for it. How do you reconcile the admission of Euclid's postulate, " that a **straight line may be produced to any length in a straight line,** 1 ' with the neces-, I. «*_ xy — x + y, II. 3x* — 2xy + y 3 — 4>x — 4y + 3 = 0. III. x>=xy... | |
| Pierce Morton - 1830 - 272 sider
...is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, **a terminated straight line may be produced to any length in a straight line** ; 3dly, from the greater of two straight lines, a part may be cut off equal to the less ; and 4thly,... | |
| 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... | |
| 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... | |
| 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
...POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. II. **That a terminated straight line may be produced to...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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