Elements of Geometry and Trigonometry |
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Page 15
... draw the line CF , making with AC the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle ...
... draw the line CF , making with AC the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1. ) ; and since ACE is a straight line , the angle FCE will likewise be a right angle ...
Page 18
... drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the ... draw CG . The C triangle GAC is equal to DEF , since , by 18 GEOMETRY .
... drawn to the extremities of either side , their sum will be less than the sum of the two other sides of the triangle . Let any point , as O , be taken within the ... draw CG . The C triangle GAC is equal to DEF , since , by 18 GEOMETRY .
Page 21
... draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B4 and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the ...
... draw CD . Now , in the two triangles BDC , BAC , we have BD = AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B4 and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the ...
Page 22
... drawn to that line . Let A be the point , and DE the given line . A BE Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D- draw FC . Then , the two triangles ...
... drawn to that line . Let A be the point , and DE the given line . A BE Let us suppose that we can draw two perpendiculars , AB , AC . Produce either of them , as AB , till BF is equal to AB , and D- draw FC . Then , the two triangles ...
Page 23
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of the ...
... draw FC , FD . First . The triangle BCF , is equal to the triangle BCA , for they have the right angle CBF CBA , the ... drawn ; for , if there could be more , we should have at least two equal oblique lines on the same side of 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 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.