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ABCD altitude angle contained apothegm arc ABC base bisect the angle Book chord circumference circumscribed coincide concave polygon cone construct convex polygon convex surface diagonal diameter diedral divided draw drawn equal arcs equal Theo equal to half equally distant equilateral triangle equivalent exterior angles figure frustum given angle given line given point half the arc half the product Hence hypotenuse inscribed angle intersect isosceles Let ABC locus measured by half multiplied number of equal number of sides oblique lines parallel parallelogram parallelopiped pendicular pentagon perimeter perpendicular plane prism PROBLEM Prove pyramid quadrilateral Ques radii radius rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle secants segment similar slant height sphere square subtends tangent THEOREM trapezoid triangle ABC triedral vertex XXVI XXXIII
Page 64 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Page 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Page 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 60 - It follows, then, that the area of a circle is equal to half the product of its circumference and its radius.
Page 67 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Page 87 - 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.
Page 40 - The area of any parallelogram is equal to the area of a rectangle having the same base and altitude.
Page 86 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.