 In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the...  Elementary Course of Geometry ... - Page 33by Charles William Hackley - 1847 - 103 pagesFull view - About this book
 | 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... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...AD — BD in the 2d figure. And AC + BC . AC — BC = AB.AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...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
...AB . AD - BD in the 2d figure. And AC+BC . AC — BC =AB . AD + BD in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...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 Butler - Mathematics - 1814 - 528 pages
...from the former,) -- Therefore AB>* —~Ub\* + ~*Tl1= ...... 2 bx * * That is, the square of ^B/the side subtending the obtuse angle,, is greater than the sum of the squares of CB and AC, the sides containing the obtuse angle, by (2 bx) twice the rectangle BC, CD. QED 175. Prop.... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...in the 1st figure. THEOREM 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,... | |
 | Euclides - 1816 - 588 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the, rectangle contained by the side upon... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side subtenHing 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 (he Perpendicular from the Obtuse Angle. Let ABC be a triangle, obtuse... | |
 | John Playfair - 1819 - 354 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the square of the side 'subtending the obtuse angle is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...— BD in the 2d figure. And AC + BC . AC — BC = AB . AB -f- BB in the 1st figure. THEOREM XXXVI. IN any Obtuse-angled Triangle, the Square of the Side...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... | |
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