 | 1844 - 456 páginas
...circle. 4. The sides about the equal angles of equiangular triangles are proportional. 5. Having giving two sides of a triangle, and the angle opposite to one of them, construct the triangle. If the given angle be greater than a right angle, what condition is requisite... | |
 | Royal Military Academy, Woolwich - 1853 - 400 páginas
...affection ; as is evident from Prop, x., Cor. 2. PROPOSITION XII. Two angles of a triangle and the side opposite to one of them being given, it is required...which a triangle constructed with these data admits. Let B be the given angle to which the given side BC is adjacent, and A the other given angle : it is... | |
 | Robert Potts - 1855 - 1050 páginas
...circle and the perpendicular let fall upon the remaining side from its opposite angle. 8. Having given two sides of a triangle and the angle opposite to one of them, give formulae for solving the triangle ; and thence shew when there are two triangles, and when only... | |
 | Edward Butler (A.M.) - 1862 - 154 páginas
...These observations will be illustrated by the geometrical construction of the problem : — " Given the two sides of a triangle and the angle opposite to one of them, to describe the triangle." The logarithmic expressions derived from the formulae are : 1 sinB=16-|-l-sin... | |
 | William Chauvenet - 1871 - 380 páginas
...equal to or greater than the sum of the other two (I. 66). F C" E PROPOSITION XXXV.— PROBLEM. 84. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. We shall consider two cases. / ' 1st. When the given angle A is acute, "... | |
 | Dublin city, univ - 1871 - 366 páginas
...s. $d. i to. Solve the quadratic 22- IO £ + 3 8-* ~ x- 2 ~2' TEIOOKOMETRY. MR. -WILLIAMSON. 1. Give two sides of a triangle, and the angle opposite to one of them ; show how the remaining parts are determined. State clearly in what case the solution is ambiguous.... | |
 | William Chauvenet - 1872 - 382 páginas
...sides is equal to or greater than the sum of the other two (I. 66). PROPOSITION XXXV.—PROBLEM. 84. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. We shall consider two cases. / ' 1st. When the given angle A is acute, "... | |
 | 1876 - 646 páginas
...circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. 3. Two sides of a triangle and the angle opposite to one of them being given to construct the triangle. 4. The area of a circle is equal to half the product of its circumference... | |
 | Elias Loomis - 1877 - 458 páginas
...solution will always be possible wheij each side is less than the sum of the other two. PROBI.EM XI. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. Draw an indefinite straight line BC. At the point B make the angle ABC equal... | |
 | F. B. Stevens - 1884 - 202 páginas
...circle by the perpendicular let fall upon the third side from the vertex of the opposite angle. 3. Two sides of a triangle and the angle opposite to one of them being given, to construct the triangle. 4. The area of a circle is equal to half the product of its circumference... | |
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The problem is impossible when one of the given sides is equal to or greater than the sum of the other two (I. 66). F C" E PROPOSITION XXXV.— PROBLEM. 
