Plane Geometry |
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Page 77
... circumscribed about a polygon , if all the vertices of the polygon are in the circumference ( Fig . 3 ) . 232. A circle is inscribed in a polygon , if the sides of the polygon are tangent to the circle ; and a polygon is circum- scribed ...
... circumscribed about a polygon , if all the vertices of the polygon are in the circumference ( Fig . 3 ) . 232. A circle is inscribed in a polygon , if the sides of the polygon are tangent to the circle ; and a polygon is circum- scribed ...
Page 108
... circumscribed quadri- lateral is equal to the sum of the other two sides . Ex . 104. If the sum of two opposite angles of a quadri- lateral is equal to two right angles , a circle may be circum- scribed about the quadrilateral . B M Let ...
... circumscribed quadri- lateral is equal to the sum of the other two sides . Ex . 104. If the sum of two opposite angles of a quadri- lateral is equal to two right angles , a circle may be circum- scribed about the quadrilateral . B M Let ...
Page 109
... circumscribed quadrilateral are supplementary . Ex . 112. The radius of a circle inscribed in an equilateral triangle is equal to one third the altitude of the triangle . △ OEF is equiangular and equilateral ; FEA = △ FAE . .. AF EF ...
... circumscribed quadrilateral are supplementary . Ex . 112. The radius of a circle inscribed in an equilateral triangle is equal to one third the altitude of the triangle . △ OEF is equiangular and equilateral ; FEA = △ FAE . .. AF EF ...
Page 110
... H B E K Ex . 127. The median of a trapezoid circumscribed about a circle is equal to one fourth the perimeter of the trapezoid ( Ex . 103 ) . Ex . 128. Two fixed circles touch each other externally 110 BOOK II . PLANE GEOMETRY .
... H B E K Ex . 127. The median of a trapezoid circumscribed about a circle is equal to one fourth the perimeter of the trapezoid ( Ex . 103 ) . Ex . 128. Two fixed circles touch each other externally 110 BOOK II . PLANE GEOMETRY .
Page 123
... circumscribe a circle about a given triangle , B Let ABC be the given triangle . Bisect AB and BC . At E and D , the points of bisection , erects . § 302 $ 301 Since BC is not the prolongation of AB , these Is will inter- sect at some ...
... circumscribe a circle about a given triangle , B Let ABC be the given triangle . Bisect AB and BC . At E and D , the points of bisection , erects . § 302 $ 301 Since BC is not the prolongation of AB , these Is will inter- sect at some ...
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Common terms and phrases
AB² ABCD AC² acute angle adjacent angles altitude angles are equal apothem arc A'B base bisector bisects called centre chord circumference circumscribed circle coincide decagon diagonals diameter divide Draw equal circles equiangular equiangular polygon equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed regular intercepted intersecting isosceles trapezoid isosceles triangle legs limit line drawn median middle point number of sides parallelogram perimeter perpendicular plane PROBLEM Proof prove Q. E. D. PROPOSITION quadrilateral radii radius ratio rectangle regular hexagon regular inscribed regular polygon rhombus right angle right triangle secant segments straight angle supplementary tangent THEOREM third side trapezoid triangle ABC triangle is equal variable vertex
Popular passages
Page 33 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Page 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 191 - 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Page 169 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.
Page 32 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Page 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 162 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.