Mathematics, mechanics, heatAmerican School of Correspondence, 1903 - Engineering |
From inside the book
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Page 6
... vertical or opposite , when the sides of one are the prolongations of the sides of the other , as angle A O C and angle B O D. THEOREM I. 30. If one straight line meets another straight line , the adjacent angles thus formed , are equal ...
... vertical or opposite , when the sides of one are the prolongations of the sides of the other , as angle A O C and angle B O D. THEOREM I. 30. If one straight line meets another straight line , the adjacent angles thus formed , are equal ...
Page 8
... vertical angles are equal . Let the straight lines A B and C D intersect at E. To prove that angle A E C = angle B E D. By § 28 , angle A E Cis the supplement of angle A E D. Angle B E D is also the supplement of angle A ED ; and ...
... vertical angles are equal . Let the straight lines A B and C D intersect at E. To prove that angle A E C = angle B E D. By § 28 , angle A E Cis the supplement of angle A E D. Angle B E D is also the supplement of angle A ED ; and ...
Page 19
... vertical angle , and its vertex is called the vertex of the triangle . The altitude of a triangle is the perpendicular drawn from the vertex to the base . 68. Since a straight line is the shortest distance between two points , it ...
... vertical angle , and its vertex is called the vertex of the triangle . The altitude of a triangle is the perpendicular drawn from the vertex to the base . 68. Since a straight line is the shortest distance between two points , it ...
Page 24
... vertical angle , and the triangle . 84 . Corollary II . An equilateral triangle is equiangular . THEOREM XXII . 85. Conversely , if two angles of a triangle are equal , the sides opposite them are equal , and the triangle is isosceles ...
... vertical angle , and the triangle . 84 . Corollary II . An equilateral triangle is equiangular . THEOREM XXII . 85. Conversely , if two angles of a triangle are equal , the sides opposite them are equal , and the triangle is isosceles ...
Page 32
... ( vertical angles ) . Therefore the triangles are equal ( Theorem XVII ) and A D = BC , ( homologous . ) Similarly the triangles A E B and C ED are equal , and A B CD , ( homologous . ) Hence the opposite sides of the quadrilateral are ...
... ( vertical angles ) . Therefore the triangles are equal ( Theorem XVII ) and A D = BC , ( homologous . ) Similarly the triangles A E B and C ED are equal , and A B CD , ( homologous . ) Hence the opposite sides of the quadrilateral are ...
Common terms and phrases
acting altitude amount beam body called center of gravity chart circle coefficient compass Corollary course cubic dead reckoning decimal degrees diameter direction distance divided earth elastic elastic limit energy equal equation EXAMPLES FOR PRACTICE factor of safety feet per second foot foot-pounds force formula friction gear given greater Greenwich mean heat Hence hour angle hypothenuse kinetic latitude length liquid load logarithm longitude magnetism mantissa mercury meridian miles minute molecules motion move multiplied Nautical orifice parallel parallelogram pendulum perpendicular plane polygon position poundal pounds per square pressure proportional pulley quadrant radius resultant revolutions revolutions per minute right angles right triangles sextant shaft ship ship's side specific gravity square inch straight line stress substance surface temperature Theorem tion triangles A B C unit velocity vertical vessel weight wheel wrought iron
Popular passages
Page 70 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Page 39 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 32 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.
Page 6 - Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
Page 7 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 54 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 21 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 31 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.
Page 60 - The area of a triangle is equal to one-half the product of its base and altitude.
Page 46 - An angle formed by a tangent and a chord is measured by onehalf the intercepted arc.