Plane Geometry |
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Page iv
... problems are explained in the second Book , and illustrated by examples worked out in full . None but the very simplest exercises are inserted until the student has become familiar with geometrical methods , and is furnished with ...
... problems are explained in the second Book , and illustrated by examples worked out in full . None but the very simplest exercises are inserted until the student has become familiar with geometrical methods , and is furnished with ...
Page viii
... PROBLEMS OF CONSTRUCTION 197 • EXERCISES 207 BOOK V. REGULAR POLYGONS AND CIRCLES . REGULAR POLYGONS AND CIRCLES 211 PROBLEMS OF CONSTRUCTION 226 MAXIMA AND MINIMA 234 EXERCISES . 241 TABLE OF FORMULAS 251 INDEX 253 GEOMETRY ...
... PROBLEMS OF CONSTRUCTION 197 • EXERCISES 207 BOOK V. REGULAR POLYGONS AND CIRCLES . REGULAR POLYGONS AND CIRCLES 211 PROBLEMS OF CONSTRUCTION 226 MAXIMA AND MINIMA 234 EXERCISES . 241 TABLE OF FORMULAS 251 INDEX 253 GEOMETRY ...
Page 4
... problem is a construction to be made so that it shall satisfy certain given conditions . 24. A proposition is an axiom , a theorem , a postulate , or a problem . 25. A corollary is a truth that is easily deduced from known truths . 26 ...
... problem is a construction to be made so that it shall satisfy certain given conditions . 24. A proposition is an axiom , a theorem , a postulate , or a problem . 25. A corollary is a truth that is easily deduced from known truths . 26 ...
Page 98
... limit of ry . Now , the limit of ry = r × limit of y . But the limit of x is a , and the limit of y is b . Therefore , a a = rb ; that is , = r . b PROPOSITION XV . PROBLEM . 286. To find the ratio 98 BOOK II . PLANE GEOMETRY .
... limit of ry . Now , the limit of ry = r × limit of y . But the limit of x is a , and the limit of y is b . Therefore , a a = rb ; that is , = r . b PROPOSITION XV . PROBLEM . 286. To find the ratio 98 BOOK II . PLANE GEOMETRY .
Page 99
George Albert Wentworth. PROPOSITION XV . PROBLEM . 286. To find the ratio of two straight lines . F K ப D EH Let AB and CD be two straight lines . To find the ratio of AB and CD . Apply CD to AB as many times as possible . Suppose ...
George Albert Wentworth. PROPOSITION XV . PROBLEM . 286. To find the ratio of two straight lines . F K ப D EH Let AB and CD be two straight lines . To find the ratio of AB and CD . Apply CD to AB as many times as possible . Suppose ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles are equal apothem arc A'B base 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 length 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 opposite sides parallelogram perimeter plane PROBLEM Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular hexagon regular inscribed regular polygon respectively rhombus right angle right triangle secant segments straight angle supplementary tangent THEOREM third side trapezoid triangle ABC triangles are equal variable vertex Нур
Popular passages
Page 94 - Any two sides of a triangle are together greater than the third side.
Page 42 - 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.
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 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 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 38 - Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof. Place A A'B'C' in the position AB'C, having its greatest side A'C' in coincidence with its equal AC, and its vertex at B', opposite B ; and draw BB'.
Page 55 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 33 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles, and therefore greater than either of them.