 | 1857 - 486 pages
...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...upon it from the opposite angle, and the acute angle. 4. If squares be described on the sides of any triangle, and the angular points be joined, the sum... | |
 | Lucius D. Gould - 1857 - 464 pages
...find the area of a¿ acute ang'ed ti'iangle. .RuZe.—Multiply the length of the longest side by half the perpendicular let fall upon it from the opposite angle, and the product will be the area. Having the baee and pe¿pendiouZar of a ¿ig1¿t angled triangle, to find... | |
 | Euclides - 1858 - 248 pages
...acute angles is less than the squares of the sides containing that acute angle by twice the rectangle contained by either of these sides and the straight...upon it from the opposite angle and the acute angle. CONS.— 12. 1., Pst. 2. DEM. — 7- II. If a at. line be divided into any two parts, the squares of... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...subtending an acute angle 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 angle and the perpendicular lot fall upon it from the opposite angle. If four straight lines... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...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 angle and the perpendicular let fall upon it from the opposite angle. VOLUNTARY PORTION. 1. When... | |
 | Euclides - 1860 - 288 pages
...the acute angles is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight...upon it from the opposite angle, and the acute angle. Given any triangle ABC, and the angle at B one of its acute angles, and upon BC, one pf the sides containing... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...the acute ungles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. Let AB C be any triangle,... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...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...upon it from the opposite angle and the acute angle. In any triangle shew that the sum of the squares of the two sides is equal to twice the square of half... | |
 | Euclides - 1862 - 172 pages
...the squares of the sides containing that angle, by tenet the rectangle contained by either of those sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite anyle, and the acute angle. (References — Prop. i. 16,47; H. 3, 7, 12.) Let ABC be any triarglp,... | |
 | Euclides - 1862 - 140 pages
...an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight...line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. (References— Prop. I. 12, 16, 47; II. 3, 7, 12.)... | |
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Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. 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... 
