 | Euclides - 1826 - 226 pages
...equal to the square of AH. Which was to be done. PROPOSITION XII. THEOREM. In obtuse angled triangles, the square of the side subtending the obtuse angle is greater than the squares, which are made by the sides containing the obtuse angle by twice the rectangle contained under one... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...twice the rectangle contained by the side upon which, vchen produced, the perpendicular Jails, and the straight line intercepted without the triangle between... | |
 | John Playfair - Geometry - 1829 - 210 pages
...in all respects. In any obtuse-angled triangle, if a perpendicular be drawn from either of the two acute angles to the opposite side produced, the square...side subtending the obtuse angle is greater than the sum of the squares of the sides containing it by twice the rectangle under the base and the distance... | |
 | Euclid - 1835 - 540 pages
...was to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted wit/tout the triangle between the perpendicular and the obtuse angle. Book II. 12. I. U4. 2. c 47.... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...ivan to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...side upon which, when produced, the perpendicular fulls, and the straight line intercepted without the triangle between the perpendicular and the obtuse... | |
 | John Playfair - Geometry - 1836 - 148 pages
...triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, tht square of the side subtending the obtuse angle, is...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle,... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...AH*. PROPOSITION XII. Theorem. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Obs. This proposition is so short,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...AH. PROPOSITION XII. THEOREM. Iii obtuse-angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle,... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...containing the right angle. 10. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the...perpendicular falls and the straight line intercepted, without the triangle, between the perpendicular and the obtuse angle. 11. In acute-angled triangles,... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...was to be done. PROP. XII. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of the acute angles to the opposite side produced, the...perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle. Let ABC be an obtuse angled triangle,... | |
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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... 
