| Science - 1875 - 884 pages
...the same time be and not be ; 2. That if equals be added to equals, the wholes are equal ; 3. That **things which are equal to the same are equal to one another.** It so happens that each of these propositions which he has assumed to be true is, if true, much more... | |
| Euclid - Geometry - 1872 - 284 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 - 670 pages
...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... | |
| Samuel Wilberforce - Apologetics - 1872 - 502 pages
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that **things which are equal to the same are equal to one another** to actual things, we should first have to ascertain the fact that the two things were exactly equal,... | |
| James Allanson Picton - Pantheism - 1873 - 520 pages
...believes the axioms of Euclid, but simply because of the impossibility of thinking the contrary. That " **things which are equal to the same are equal to one another " is a** truth clear at once to any mind capable of understanding its terms, without the slightest necessity... | |
| Herbert Spencer - 1873 - 678 pages
...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 - 626 pages
...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... | |
| James Allanson Picton - Pantheism - 1873 - 548 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... | |
| Henry Major - Student teachers - 1873 - 588 pages
...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, AB, BC, are equal to one another; and the triangle ABC... | |
| Victoria Institute (Great Britain) - Religion and science - 1873 - 518 pages
...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,... | |
| |