 | Lucius D. Gould - Carpentry - 1853 - 234 pages
...find the area of an acute angled triangle. Rule. — 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 base and perpendicular of a right angled triangle, to find the... | |
 | 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... | |
 | Robert Potts - 1855 - 1050 pages
...quadrilateral ADFEis equal to either of ic triangles CFE or BDF. taining 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. 6. The angles in the same segment of a circle are equal to one another. AB and AC are given in position,... | |
 | Euclides - 1855 - 270 pages
...intercepted between the acute angle and the perpendicular drawn to it from the opposite angle, Let ABС be any triangle, and the angle at B one of its acute angles ; and to B С, one of the sides containing it, draw the perpendicular AD from the opposite angle at A (I.... | |
 | John Playfair - Geometry - 1855 - 334 pages
...containing that angle, by twice the rectangle contained by cither of these sides, and the straight hne intercepted between the perpendicular, let fall upon it from the opposite angle, and the acutt angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 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. 7. If a point be taken... | |
 | Euclides - 1856 - 168 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...angle and the acute angle. Let ABC be any triangle (Figs. 43, 42) and the angle at B one of its acute angles ; AD the perpendicular on BC (produced if... | |
 | John Playfair - Euclid's Elements - 1856 - 346 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...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 - 200 pages
...the squares on the sides containing that angle, by twice the rectangle contained by either of those sides and the straight line intercepted between the...upon it from the opposite angle, and the acute angle. In any acute.angled triangle, lines are drawn through the angles perpendicular to the sides respectively... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...angles is less than the sum of the squares on the sides including this angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular drawn to this side, produced if necessary, from the opposite angular... | |
| |
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... 
