Elements of Geometry and Trigonometry |
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Page 63
... serves for making a circum- A D ference pass through three given points A , B , C ; and also for describing a circumference , in which , a given triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
... serves for making a circum- A D ference pass through three given points A , B , C ; and also for describing a circumference , in which , a given triangle ABC shall be inscribed . PROBLEM XIV . Through a given point , to draw BOOK III . 63.
Page 64
... inscribed in a semicircle is a right angle ( Prop . XVIII . Cor . 2. ) ; therefore AB is a perpendicular at the ... inscribe a circle in a given triangle . Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and ...
... inscribed in a semicircle is a right angle ( Prop . XVIII . Cor . 2. ) ; therefore AB is a perpendicular at the ... inscribe a circle in a given triangle . Let ABC be the given triangle . Bisect the angles A and B , by the lines AO and ...
Page 65
... inscribed in the triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle ...
... inscribed in the triangle ABC ; for the side AB , being perpendicular to the radius at its extremity , is a tangent ; and the same thing is true of the sides BC , AC . Scholium . The three lines which bisect the angles of a tri- angle ...
Page 94
... inscribed in the same segment ( Book III . Prop . XVIII . Cor . 1. ) ; for the same reason the angle C - B ; the triangles are there- fore similar , and the homologous sides give the proportion AO : DO : CO : OB . B Cor . Therefore AO ...
... inscribed in the same segment ( Book III . Prop . XVIII . Cor . 1. ) ; for the same reason the angle C - B ; the triangles are there- fore similar , and the homologous sides give the proportion AO : DO : CO : OB . B Cor . Therefore AO ...
Page 96
... inscribed circle . For , the triangles AOB , BOC , AOC , which have a common vertex at O , have for their com- mon altitude the radius of the inscribed circle ; hence the sum of these triangles will be equal to the sum of the bases AB ...
... inscribed circle . For , the triangles AOB , BOC , AOC , which have a common vertex at O , have for their com- mon altitude the radius of the inscribed circle ; hence the sum of these triangles will be equal to the sum of the bases AB ...
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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 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 Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment side BC 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 18 - If two triangles have two sides of the one equal to two sides of the...
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 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 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 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 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.
Page 287 - How many square feet are there in the convex surface of the frustum of a square pyramid, whose slant height is 10 feet, each side of the lower base 3 feet 4 inches, and each side of the upper base 2 feet 2 inches ? Ans.
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.