 | 1827 - 608 sider
...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 - 632 sider
...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 - 364 sider
...: 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 - 138 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 - 210 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 - 732 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 - 584 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 - 390 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 - 478 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.... | |
 | John Playfair - 1832 - 358 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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Let it be granted that a straight line may be drawn from any one point to any other point. 
