 | 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,... | |
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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. 
