 | Ignace Gaston Pardies - Geometry - 1734 - 192 pages
...PROP. II. In an Acute-angled Triangle, the Square of the Side (h) fubtending an Acute Angle, " is lefs than the Sum of the Squares of the other two Sides, by double the Rettangle under the whole Safe, (b + a) and the Segment of the Bafe (a) which is next to... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. ( Let ABC be a triangle, obtuse... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subren .ing the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rrctungle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle,... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtending the Obtuse Angle, is Greater than the Sum of the Squares of the other two Sides, by Twice the Rectangle of the Base and the Distance of the Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse... | |
 | George Lees - 1826 - 266 pages
...' j . ,1 ' ' Book III. PROP. V. THEOREM. The square of one of the sides of a triangle is greater or less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and its segment, intercepted between the perpendicular and the angle opposite to that side,... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...explained more fully in another place. THEOREM. 191. In any triangle, the square of the side opposite either of the acute angles, is less than the sum of the squares of the sides containing it, by twice the rectangle contained by either of ilie latter sides and the distance... | |
 | Euclides - 1834 - 518 pages
...rectangle BC, CD. Therefore, in obtuse-angled triangles, &c. Q. £. D. PROPOSITION XIII. See N. THEOR. — In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides,... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...p!ace. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle ts less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the opposite-... | |
 | Adrien Marie Legendre - Geometry - 1838 - 376 pages
...GEOMETRY. PROPOSITION XII. THEOREM. In every triangle, the square of a side opposite an acute angle is less than the sum of the squares of the other two sides, by twice the rectangle contained by the base and the distance from the acute angle to the foot of the perpendicular let fall from the opposite... | |
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In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute... 
