 | James Allanson Picton - 1870 - 250 pages
...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form... | |
 | Great Britain - 1870 - 688 pages
...properties as emotion we shall not only have established points of resemblance between the two (for things which are equal to the same are equal to one another), but we shall have actually reached the common ground, or kind of border-land, upon which internal emotion... | |
 | James Allanson Picton - Theology - 1870 - 248 pages
...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form... | |
 | 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, Charles Peter Mason - Geometry - 1872 - 216 pages
...will not meet, however far they may be produced). To prove this we must know, — 1 . That magnitudes which are equal to the same are equal to one another. (Ax. I.) 2. That if two straight lines intersect one another, the vertically opposite ^/s are equal. (Prop.... | |
 | 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... | |
 | Christian evidence society, 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,... | |
 | 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... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...triangle. Because 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...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... | |
 | James Allanson Picton - Matter - 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... | |
| |
AB; but things which are equal to the same are equal to one another... 
