| 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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