| George Bentham - Logic - 1827 - 304 pages
...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 - 364 pages
...: 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 - Geometry - 1829 - 210 pages
...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 - Geometry - 1829 - 138 pages
...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... | |
| English literature - 1829 - 430 pages
...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 - Geometry - 1830 - 584 pages
...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 - Classical education - 1830 - 390 pages
...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 - Algebra - 1830 - 732 pages
...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 - Law - 1831 - 478 pages
...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 - Euclid's Elements - 1832 - 358 pages
...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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