 | William Somerville Orr - Science - 1854 - 534 pages
...than the squares of the sides (С В, В A) containing that angle, by twice the rectangle (C BB D) contained by either of these sides, and the straight line intercepted between the perpendicular (AD) and the acute angle (B) : that is, A C2 = С В2 + В A3— twice С BB D. First, let AD fall... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...the rectangle contained by the parts. 6. In every triangle, the square of the side subtending either of the acute angles, is less than the squares of the...sides, and the straight line intercepted between the acute angle, and the perpendicular let fall upon it from the opposite angle. 7. If a point be taken... | |
 | John Playfair - Euclid's Elements - 1856 - 346 pages
...therefore, AB2=BC2-f AC2+2BC.CD ; that is, AB2 is greater than BC2+AC2 by 2BC.CD. PROP. XIII. THEOR. In every triangle the square of the side subtending...let fall upon it from the opposite angle, and the acuteangle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...subtending either of the acute angles is less than the sum of the squares on the sides including this angle, by twice the rectangle contained by either...sides, and the straight line intercepted between the acute angle and the perpendicular drawn to this side, produced if necessary, from the opposite angular... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...perpendicular and the obtuse angle. In every triangle the square of the side subtending an acute angle is less than the squares of the sides containing that...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
...is, divides them into two equal parts. 3. In every triangle the square of the side subtending either of the acute angles is less than the squares of the...sides and the straight line intercepted between the acute angle and the perpendicular let full upon it from the opposite angle. Prove this only when all... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...triangle, the square on the side subtending either of the acute ungles, is less than the squares on the sides containing that angle, by twice the rectangle...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,... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...square on a side opposite an acute angle is less than the sum of the squares on the other two sides, by twice the rectangle contained by either of these sides, and the distance from the vertex of the acute angle to the foot of the perpendicular let fall on this side,... | |
 | Euclides - 1862 - 140 pages
...THEOREM. In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle...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.)... | |
 | 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,... | |
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In every triangle, the square on the side subtending either of 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 line intercepted between the acute... 
