| Euclid, Thomas Elrington - Geometry - 1872 - 261 pages
...3. That a circle can be described from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . **Things which are equal to the same are equal to one another.** 2. If equals be added to equals, the wholes will be equal. 4. If to unequals, equals be added, the... | |
| Herbert Spencer - Psychology - 1872
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| Student teachers - 1873
...A is the centre of BCD, AC is equal to AIj ; and because B is the centre of ACE, BC is equal to BA, **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... | |
| Religion and science - 1873
...Here again the word is psyche, but containing all the attributes of kardia. The inference is obvious : **things which are equal to the same are equal to one another.** While we may freely admit that, in the terms of a language, this principle will not rigidly apply,... | |
| James Allanson Picton - Pantheism - 1873 - 492 pages
...because the single case is not, and cannot be, adequately presented to it. For the universal truth, that **things which are equal to the same are equal to one another,** cannot be seen in any case until the notion of equality has been acquired. But this notion again never... | |
| Herbert Spencer - Psychology - 1873
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| 1873
...than are producible from the deai Now let us turn to the logical and physical side of the question. **Things which are equal to the same are equal to one another,** and if equals be added to equals the whole are equal. Anatomy teaches us that there is no difference... | |
| Herbert Spencer - Psychology - 1873
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| Charles Mansford - 1874
...AB. [Def. 15.] And because the point B is the centre of the circle ACE, BC is equal to BA. [Def. 15.] **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 thing are equal to one another; [Ax. i.] therefore CA is equal... | |
| 1874 - 72 pages
...living subject than are producible from the dead. Let us turn to the logical side of the question. **Things which are equal to the same are equal to one another.** Anatomy teaches us that there is no difference between the male and female larynx save in size, so... | |
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