 | Nicholas Patrick Wiseman - 1841 - 618 pages
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " things which are equal to the same are equal to one another." The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured... | |
 | Euclides - 1842 - 316 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 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.... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...POSTULATES. 1. LET it be granted that a straight line may be drawA 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. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1.... | |
 | T H. Howe - 1842 - 458 pages
...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... | |
 | Sir Edward Johnson - Language and languages - 1842 - 622 pages
...word which is equivalent to any one of them, must, therefore, also be equivalent to the others, since things which are equal to the same, are equal to one another. I have said that when we wish to convert a noun into a verb, we do so by prefixing the word to. Thus,... | |
 | Philip Kelland - Algebra - 1843 - 168 pages
...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 - Geometry - 1844 - 268 pages
...enumerate three postulates. 1. 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 any circle may be described from any centre, at any distance from that centre. PROBLEM XVI.... | |
 | George Robins Gliddon - Egypt - 1844 - 92 pages
...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... | |
 | Francis Bacon - Induction (Logic) - 1844 - 348 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.... | |
 | Euclid - Geometry - 1845 - 218 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...which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders... | |
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Let it be granted that a straight line may be drawn from any one point to any other point. 
