| John Playfair - 1842 - 317 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. **And that a circle may be described from any centre, at any distance from that centre. AXIOMS.** 1. THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals,... | |
| Euclides - 1842
...other point. II. That a terminated straight line may be produced to any length in a straight line. III. **That a circle may be described from any centre, at any distance from that centre.** IV. [Ax. XI.] V. And that if a straight line meets two straight lines, so as to make the two interior... | |
| T H. Howe - 1842
...point within the circle which is thus equally distant from the circumference, is called the Centre. HA **Circle may be described from any centre, at any distance from that centre.** Illustration. The sensible horizon, or circular boundary, which every individual, standing in a clear... | |
| Philip Kelland - 1843 - 147 sider
...I propose to take up the same subject, and inquire, for the sake of precision, whether the truth, " **things which are equal to the same are equal to one another,"** is demonstrable or not. If it be an immediate consequence of our conception of equality, then is it... | |
| James Bates Thomson - 1844 - 237 sider
...point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That any **circle may be described from any centre, at any distance from that centre.** PROBLEM XVI. When the given angle is acute, the segment will be greater than a semicircle ; and when... | |
| Francis Bacon - 1844 - 336 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.... | |
| George Robins Gliddon - 1844 - 66 sider
...Asiatics, the utter destruction of all biblical chronology by thia process would be another. Now, " **things which are equal to •the same are equal to one another."** If they are anterior to Shoopho's pyramid in Egypt, then Weroe must have been occupied in the earliest... | |
| Euclides - 1845
...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. AXIOMS. I. THINGS which are equal to the same** thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals... | |
| Euclid, James Thomson - 1845 - 352 sider
...point : f 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.** J AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals... | |
| Euclid - 1845 - 199 sider
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; But **things which are equal to the same are equal to one another** || ; therefore CA is equal to CB ; wherefore CA, « i Axiom. AB, BC are equal to one another ; and... | |
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