Elements of Geometry |
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A B C AABC AACB ABCD acute adjacent angles alt.-int altitude arc A B base bisect centre circumference circumscribed coincide COROLLARY describe an arc diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular polygon equilateral equilateral polygon exterior angles figure Geometry given circle given line given point given straight line greater homologous sides hypotenuse Iden isosceles triangle Let A B limit line A B measured by arc middle point number of sides parallelogram perimeter perpendicular PHILLIPS EXETER ACADEMY plane PROBLEM prove Q. E. D. PROPOSITION quadrilateral quantities radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct rhombus right angles right triangle SCHOLIUM segment shortest side sides of equal similar polygons subtend tangent THEOREM third side triangle ABC variable vertex vertices
Popular passages
Page 144 - 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 38 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 134 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 200 - In any proportion, the product of the means is equal to the product of the extremes.
Page 173 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 159 - In any triangle the product of two sides is equal to the product of the diameter...
Page 132 - 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 70 - I) is a parallelogram, E and F the middle points of AD and BC respectively ; show that BE and DF will trisect the diagonal A C.
Page 48 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Page 81 - A straight line perpendicular to a radius at its extremity is a tangent to the circle. Let MB be perpendicular to the radius OA at A.