| Euclides - 1838 - 264 pages
...to be done. PROP. XII. THEOR. In an obtuseangledtriangle, if a perpendicular be drawnfrom 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. Let ABC be an obtuse angled triangle,... | |
| Euclid - Geometry - 1838 - 478 pages
...square of AH : CKD PROP. Xn. THEOR. In obtuse angled triangles, if a perpendicular be drawn from any of **the acute angles to the opposite side produced, the...twice the rectangle contained by the side upon which,** wnen produced, the perpendicular falls, and the straight line intercepted without the triangle between... | |
| Euclides - 1840 - 82 pages
...In an obtuse-angled triangle, the square of the side subtending the obtuse angle exceeds the sum of **the squares of the sides containing the obtuse angle, by twice the rectangle contained by** either of those sides and the produced part of it intercepted between the perpendicular let fall on... | |
| Euclides - 1841 - 378 pages
...to be done. PROP. XII. THEOR. In obtuse-angled Mangles, if a perpendicular be dratcn 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. obtuse angle ACB, and from the... | |
| Euclides - 1842 - 320 pages
...square of AH. QEF PROP. XII. THEOR. IN obtuse-angled triangles, if a perpendicular be drawn from any of **the acute angles to the opposite side produced, the...squares of the sides containing the obtuse angle, by** twiee the rectangle contained by the side upon which, when produced, the perpendicular falls, and the... | |
| Perry Fairfax Nursey - Industrial arts - 1843
...EK also subtends the obtuse angle EPK of ihe triangle EPK, and by (12 Prop. 2 Book Eu.) it is.— " **The square of the side subtending the obtuse angle...obtuse angle, by twice the rectangle contained by** one of the sides about the obtuse angle, and the line intercepted without by a perpendicular to it... | |
| Euclid - Geometry - 1845 - 218 pages
...done. PROPOSITION 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,... | |
| Euclides - 1845 - 544 pages
...the squares of the sides containing the right angle ; but in an obtuse-angled triangle (Euc. n. 12), **the square of the side subtending the obtuse angle is greater than the** square of the side containing the obtuse angle ; and in an acute-angled triangle (Euc. n. 13), the... | |
| Euclides - 1846 - 292 pages
...AH. « . E. v. 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,... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...PROP. XLVII. THEOR. 12. 2 Eu . 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. A Y str. line BD is divided into... | |
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