 | Euclid, John Playfair - 1795 - 462 หน้า
...mathematical truth. If, for example, it be alleged, that it is needlefs to demonftrate that any two fides of a triangle are greater than the third ; it may...that this is no doubt a truth, which, without proof, mod men will be inclined to admit ; but, are we for that reafon to account it of no confequence to... | |
 | 734 หน้า
...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... | |
 | Dugald Stewart - 1814 - 528 หน้า
...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... | |
 | John Playfair - 1819 - 350 หน้า
...true if this proposition were supposed to be false ? Is it not useful to know, that unless it be true, that any two sides of a triangle are greater than the third, neither could it be true, that the greater aide of every triangle is opposite to the greater angle,... | |
 | Euclid, John Playfair - 1826 - 326 หน้า
...eonneeting that 'proposition with others, and aseertaining its plaee in the general system of mathematieal truth. If, for example, it be alleged, that it is...; it may be replied, that this is no doubt a truth whieh, without proof, most men will be inelined to admit ; but are we for that reason to aeeount it... | |
 | Dugald Stewart - 1829 - 482 หน้า
...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... | |
 | Dugald Stewart - 1829 - 474 หน้า
...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... | |
 | John Playfair - 1832 - 358 หน้า
...mathematical sciences depend: it is this, which, by preventing any one truth from being single and insulated, connects the different parts so firmly, that they...it of no consequence to know what the propositions are, which must cease to be true if this proposition were supposed to be false? Is it not useful to... | |
 | John Playfair - 1833 - 346 หน้า
...it be alleged, that it is needless to demonstrate that any two sides of a triangle are greater thaa the third ; it may be replied, that this is no doubt...it of no consequence to know what the propositions are, which must cease to be true if this proposition were supposed to be false ? Is it not useful to... | |
 | Perry Fairfax Nursey - 1837 - 504 หน้า
...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... | |
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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. 
