| Francis Bacon - 1841 - 616 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.... | |
| 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... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...(11. Definition) to AB ; and because the point B is the centre of the circle ACE, BC is equal to AB : But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another, (1. Axiom) ; therefore CA is equal... | |
| Euclides - 1842 - 316 pages
...shall at length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS 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... | |
| 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... | |
| 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.... | |
| 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... | |
| Euclid - Geometry - 1845 - 218 pages
...circle BCD, AC is equal \ to AB ; and because the point B is the centre t is nefim of the circle ACE, BC is equal to BA : But it has been proved that CA is...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... | |
| Euclides - 1845 - 546 pages
...AC is equal to AB; (def. 15.) and because the point B is the centre of the angle ACE, therefore BC is equal to BA ; but it has been proved that CA is...equal to AB; but things which are equal to the same thing arc equal to one another ; (ax. 1.) therefore CA is equal to CB ; wherefore CA, AB, BC are equal... | |
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