 | John Morley (visct.) - 1873 - 370 oldal
...world, and rules it with majestic power and supreme justice, in the. same way in which he believed that any two sides of a triangle are greater than the third side. That there is a mysterious being penetrating all creation with force, was not a proposition to be demonstrated,... | |
 | Herbert Spencer - 1873 - 678 oldal
...the more special mathematical propositions have the same character. One of these is the proposition that any two sides of a triangle are greater than the third side. We have the same trait in those most abstract cognitions which Logic formulates. If there exist more... | |
 | Herbert Spencer - 1873 - 670 oldal
...the more special mathematical propositions have the same character. One of these is tho proposition that any two sides of a triangle are greater than the third side. We have the same trait in those most abstract cognitions which Logic formulates. If there exist more... | |
 | Edward Atkins - 1874 - 428 oldal
...FC, the more remote ; and FC greater than FG. CONSTRUCTION. — Join BE, CE, GE. PROOF. — Because any two sides of a triangle are greater than the third side, BE, EF are greater than BF (I. 20). But AE is equal to BE ; therefore AE, EF, that is, AF is greater... | |
 | Robert Potts - 1876 - 446 oldal
...of the lines AG, GB is a minimum. For take any other point H in CD, and join EH, HB, AH. Then since any two sides of a triangle are greater than the third side, therefore EH, HB are greater than EB in the triangle EHB. But EG is equal to AG, and EHlo AH; therefore... | |
 | Edward Atkins - 1876 - 130 oldal
...more remote ; and FC greater than FG. ror CONSTRUCTION. — Join BE, CE, GE. BE+EF PROOF. — Because any two sides of a triangle are greater than- the third side, BE, EF are greater than BF (I. 20). But AE is equal to BE ; therefore AE, EF, that is, AF is greater... | |
 | Joseph Wollman - 1879 - 120 oldal
...reason for the limitation in the data ? This is the 22nd proposition in the First Book ; the 2oth proves that any two sides of a triangle are greater than the third side, and it can be easily seen by drawing the figure that a triangle cannot be constructed if any two of... | |
 | S S. Pugh - 1879 - 246 oldal
...across a patch of fallow. The track ran round the field. Now all boys who have studied Euclid know that any two sides of a triangle are greater than the third side ; and though Val was not much of a geometrician, he knew that it was much nearer to cross the field... | |
 | 1879 - 748 oldal
...assumptions, but he proves propositions tbat artf at least as self-evident as some that he takes for granted. That *• any two sides of a triangle are greater than the third," is as pelfevident as that "all right, angles are equal to one another," and much more so than hi3 asumption... | |
 | Isaac Todhunter - 1880 - 426 oldal
...than DH. Take M, the centre of the circle ABC, [III. 1. and join ME, MF, MC, MH, ML, MK. Then, because any two sides of a triangle are greater than the third side, [I. 20. therefore EM, MD are greater than ED. But EMis equal to AM; [I.Dcf.\5. therefore AM, MD are... | |
| |
One of these is the proposition that any two sides of a triangle are greater than the third side. 
