The square on a side of a triangle is greater than, equal to, or less than the sum of the squares on the other two sides, according as the angle contained by those sides is obtuse, right, or acute. The difference in the... General Announcement - McGill University - Page 29by McGill University - 1910Full view - About this book
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...be less than, equal to, or greater than the square on BC, according as the square on BC is greater than, equal to, or less than the sum of the squares on BA and AC ; hence the line DC is less than equal to, or greater than the line BC, according as the... | |
| Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...CD. These results may be collected as follows : The square on a side of a triangle is greater tlum, equal to, or less than the sum of the squares on the other sides, according as the angle opposite to the first is obtuse, a right angle, or acute. EXERCISES... | |
| Euclid - Euclid's Elements - 1904 - 488 pages
...is acute, we have by n. 13, AB2 = BC2 + CA2 - 2 BC . CD. These results may be collected as follows : The square on a side of a triangle is greater than,...equal to, or less than the sum of the squares on the other sides, according as the angle opposite to the first is obtuse, a right angle, or acute. EXERCISES... | |
| University of Allahabad - 1907 - 528 pages
...c + ....)= ka + kb + kc + (a + b)* = a2 + 2ab + ba (ab)z = aa - 2ab + ba a' - b2 = (a + b) (a - b) The square on a side of a triangle is greater than,...is obtuse, right, or acute. The difference in the case of inequality is twice the rectangle contained by one of the two sides and the projection on it... | |
| University of Allahabad - 1908 - 568 pages
...to the following Algebraical indentities : — k (a (a+b)2 = (a— b)a = aa —b2 = (a + b)(a— b). The square on a side of a triangle is greater than,...is obtuse, right, or acute. The difference in the case of inequality is twice the rectangle contained by one of the two sides and the projection on it... | |
| Henry Sinclair Hall - 1908 - 286 pages
...hence, in this case, SBC , CD = 0. Thus the three results may be collected in a single enunciation : The square on a side of a triangle is greater than,...equal to, or less than the sum of the squares on the other sides, according as the angle contained by those sides is obtuse, a right angle, or acute ; the... | |
| University of Allahabad - 1909 - 638 pages
.......) = ka + kb + kc+ (a + b)2 = a2 +2ab + b3. (a— b)2 =a2— 2ab + ba. a2— b2 = (a + b)(a— b). The square on a side of a triangle is greater than,...the angle contained by those sides is obtuse, right, ur ncnte. The difference in the case of inequality is twice the rectangle contained by one of the two... | |
| University of Melbourne - 1909 - 984 pages
...— k(a + b + c+...) = o*-A» = (« + 4) (ab). The square on a side of ;\ triangle is greater thiin. equal to, or less than the sum of the squares on the...is obtuse, right, or acute. The difference in the casen of inequality is twice the rectangle contained by one of the two sides and the projection on... | |
| University of Allahabad - 1910 - 682 pages
...k (a + b + c + ) = ka + kb + kc + (a+b)2 -aa +2ab + ba . (ab;a -aa -2ab + ba . aa-b" =(a + b) (ab). The square on a side of a triangle is greater than,...sum of the squares on the other two sides, according aa the angle contained by those sides is obtuse, right, or acute. The difference in the case of inequality... | |
| Sir Gooroodass Banerjee - Education - 1910 - 380 pages
...Proposition XLj VII of Book I, and all these three may be enunciated together thus : — The square on any side of a triangle is greater than, equal to, or less...squares on the other two sides, according as the angle between them is greater than, equal to, or less than a right angle, the excess or defept being equal... | |
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