 Accordingly, no geometrical proposition, as, for instance, that any two sides of a triangle are greater than the third side, can ever be derived from the general conceptions of line and triangle, but only from perception.  The Principles of psychology - Page 404by Herbert Spencer - 1873Full view - About this book
 | 1798 - 618 pages
...general system of mathematical truth. If, for example, it be alleged, that it is needless to demonstrate that any two sides of a triangle are greater than the third, it may be replied that this is no doubt a truth, which, without proof, most men will be inclined to... | |
 | 734 pages
...as of the geometrical theorem that one circle cannot cut another circle in more than two points, or that any two sides of a triangle are greater than the third side. Indeed we think Mr. Gambier inconsistent when he affirms, of the former propositions that no doubt... | |
 | Dugald Stewart - 1814 - 528 pages
...enunciation. I do not allude to those theorems the truth of which is obvious almost to sense, such as, that any two sides of a triangle are greater than the third side, or that one circle cannot cut another circle in more than two points ; but to some propositions with... | |
 | John Bonnycastle - 1816 - 490 pages
...the earth, M the moon in the horizon, and M' the same in the zenith, and draw MA, MC ; then because any two sides of a triangle are greater than the third side, MA and AC are greater than MC or M'C ; and therefore, if from each AC be subtracted, there will remain... | |
 | John Playfair - 1819 - 354 pages
...general system of mathematical truth. If, for example, it be alleged, that it is needless to demonstrate that any two sides of a triangle are greater than the third ; it may be replied, that this is no doubt a truth, which, without proof, most men will be inclined... | |
 | Dugald Stewart - 1829 - 482 pages
...enunciation. I do not allude to those theorems the truth of which is obvious almost to sense, such as, that any two sides of a triangle are greater than the third side, or that one circle cannot cut another circle in more than two points ; but to some propositions with... | |
 | Dugald Stewart - 1829 - 474 pages
...enunciation. I do not allude to those theorems the truth of which is obvious almost to sense, such as, that any two sides of a triangle are greater than the third side, or that one circle cannot cut another circle in more than two points ; but to some propositions with... | |
 | Perry Fairfax Nursey - 1837 - 504 pages
...given time, will have arrived at the point D. Now I presume that Kinclaven does not require to be told, that any two sides of a triangle, are greater than the third side; and therefore, I suppose he will admit that the line AD, which the body under the action of the two... | |
 | Condy Raguet - 1840 - 472 pages
...a scholar, who, at the threshold, should refuse to admit that two parallel lines can never meet, or that any two sides of a triangle are greater than the third. The powerful reasoning of Adam Smith, the clear demonstrations of Say, and the forcible and able expositions... | |
 | Richard Whately - 1840 - 508 pages
...consequently in the Terms, which are the exact representatives of those Definitions. • B. iv. c. 2. § 1. KG That any two sides of a Triangle are greater than the third — in other words that it is impossible to construct a triangle, one of whose sides shall be equal... | |
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