Elements of Geometry and Trigonometry |
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Page 251
... feet and CB 672 feet , and also the contained angle ACB - 55 ° 40 ' : requi- red the distance AB . = Ans . 592.967 feet . 6. Being on a horizontal plane , and wanting to ascertain the height of a tower , standing on the top of an ...
... feet and CB 672 feet , and also the contained angle ACB - 55 ° 40 ' : requi- red the distance AB . = Ans . 592.967 feet . 6. Being on a horizontal plane , and wanting to ascertain the height of a tower , standing on the top of an ...
Page 274
... feet , we should understand that one square foot is taken for the unit of measure , and that this unit is contained ... feet , it will be most convenient to express the area in square feet ; if the linear dimensions are yards , it will ...
... feet , we should understand that one square foot is taken for the unit of measure , and that this unit is contained ... feet , it will be most convenient to express the area in square feet ; if the linear dimensions are yards , it will ...
Page 275
... feet . Ans . 66 . 3. To find the number of square yards in a triangle , whose base is 49 and altitude 25 feet . Ans . 68.7361 . CASE II . When two sides and their included angle are given . RULE . Add together the logarithms of the two ...
... feet . Ans . 66 . 3. To find the number of square yards in a triangle , whose base is 49 and altitude 25 feet . Ans . 68.7361 . CASE II . When two sides and their included angle are given . RULE . Add together the logarithms of the two ...
Page 276
... feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 . CASE III . When the three sides are known . RULE . - 1 . Add the three sides together , and take half their sum . 2. From this half - sum subtract each side ...
... feet and 21.25 feet , and their included angle 45 ° ? Ans . 20.8694 . CASE III . When the three sides are known . RULE . - 1 . Add the three sides together , and take half their sum . 2. From this half - sum subtract each side ...
Page 277
... feet are contained in a plank , whose length is 12 feet 6 inches , the breadth at the greater end 15 inches , and at the less end 11 inches ? Ans . 131 sq . ft . 3. How many square yards are there in a trapezoid , whose parallel sides ...
... feet are contained in a plank , whose length is 12 feet 6 inches , the breadth at the greater end 15 inches , and at the less end 11 inches ? Ans . 131 sq . ft . 3. How many square yards are there in a trapezoid , whose parallel sides ...
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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 convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn 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 parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall 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 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 11 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
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 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
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 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 159 - S-ahc be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.