Elements of Geometry and Trigonometry |
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Page 68
... altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the trape- zoid DB . D DE F B DEC A F B 8. The area and surface of a figure ...
... altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the trape- zoid DB . D DE F B DEC A F B 8. The area and surface of a figure ...
Page 69
... altitudes , are equivalent . CF EDF CE Let AB be the common base of D the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line ...
... altitudes , are equivalent . CF EDF CE Let AB be the common base of D the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line ...
Page 70
... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the ...
... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the ...
Page 71
... altitude AD : they are to each other as their bases AB , AE . F E B Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 and 4. If AB be divided into 7 equal parts , AE will contain ...
... altitude AD : they are to each other as their bases AB , AE . F E B Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 and 4. If AB be divided into 7 equal parts , AE will contain ...
Page 72
... altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases multiplied by their altitudes . Let ABCD , AEGF , be two rectangles ; then will the ...
... altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases multiplied by their altitudes . Let ABCD , AEGF , be two rectangles ; then will the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.