| Robert Potts - 1855 - 554 sider
...that the evidence of the conclusion is manifest.—Dr Whewett. 199. 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.—Bacon.... | |
| Robert Potts - 1855
...that the evidence of the conclusion is manifest.—Dr Whewell. 199. The mathematical postulate, that " **things which are equal to the same are equal to one another,** 1 ' is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.—Bacon.... | |
| 1855
...art equal to ta<A other. (Euclid 11, 5.) This is nothing more than an application of the axiom, that **things which are equal to the same are equal to one another.** And с : d : : m : n 2. If a :.* : : m : я And m : n : : с : d Cor. If a : 6 : : m : я l m : п>... | |
| Edward Tagart - 1855 - 504 sider
...of nature and fact. In mathematical reasoning, no axiom is more constantly employed than this — ' **things which are equal to the same are equal to one another.'** Are the ideas of equality and inequality in the mind of a child before things have been observed, measured,... | |
| Francis Bacon, Basil Montagu - 1857
...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. Lastly:... | |
| James Yates - 1858 - 79 sider
...differences must exist in all attempts to compare the lengths of different objects. Euclid's axiom, " **Things, which are equal to the same, are equal to one another," is** strictly true only of mathematical lines and other imaginary quantities. In practice it is sufficient,... | |
| 1858
...Christ was the " son of David ;" hence were Solomon and Christ the one or parallel characters, for **things which are equal to the same are equal to one another.** If the " last days " were to be the days of Christ, and if those were to be as the " days of Noah,"... | |
| 1858
...David;" Christ was the "son of David;" hence were Solomon and Christ the one or parallel characters, for **things which are equal to the same are equal to one another.** If the " last days " were to be the days of Christ, and if those were to be as the " days of Noah,"... | |
| Rev. James Mcosh - 1860
...as the " Common Notions," so far as they relate to quantity, prefixed by Euclid to his Elements. " **Things which are equal to the same are equal to one another."** " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders... | |
| Eucleides - 1860
...are equal to one another in area. CONSTRUCTION. — Draw BE and CH. DEMONSTRATION. Syllogism 1. Da **(Things which are equal to the same) ARE equal to one another.** [Ax. 1.] ii The straight lines BC and EH ARE equal to the same FG. [Hypoth. and I. 34] i Therefore... | |
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