| John Playfair - 1819 - 317 sider
...point. V H. . That a terminated straight line may be produced to any length in a straight line. HI. **And that a circle may be described from any centre,...centre. AXIOMS. I. THINGS which are equal to the same** thing are equal to one anotheii II. If equals be added to equals, the wholes are equal. HI. If equals... | |
| George Townsend - 1819 - 147 sider
...circumstance indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as **things which are equal to the same, are equal to one another,** the Patriarchs are the Caesars, and the Caesars the sons of Jacob, because they are both synonymous... | |
| Euclid, Robert Simson - 1821 - 516 sider
...any one point to any other point. That a terminated straight line may be produced to any length in a **straight line. III. And that a circle may be described...which are equal to the same are equal to one another.** If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders... | |
| Henry Aldrich - 1821
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, **Things which are equal to the same are equal to one another** ; and, Things of which one is equal and the other not equal to the same, are not equal to one another.... | |
| Euclid - 1822 - 179 sider
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o Axioms. 1. **Things which are equal to the same are equal to one another.** 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
| Peter Nicholson - 1825 - 372 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. AXIOMS.** 1. Thingi which ate equal to the same are equal to one another. 2. If equals be added to equals the... | |
| Euclides - 1826
...continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. **Things which are equal to the same are equal to one another.** 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
| Euclid - 1826 - 180 sider
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And **things which are equal to the same are equal to one another.** Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,... | |
| John Martin Frederick 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... | |
| 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... | |
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