Plane Geometry |
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Page 211
... inscribed in a circle is a regular polygon . A B Let ABC etc. be an equilateral polygon inscribed in a circle . To prove that the polygon ABC etc. is a regular polygon . Proof . The arcs AB , BC , CD , etc. , are equal . Hence , arcs ...
... inscribed in a circle is a regular polygon . A B Let ABC etc. be an equilateral polygon inscribed in a circle . To prove that the polygon ABC etc. is a regular polygon . Proof . The arcs AB , BC , CD , etc. , are equal . Hence , arcs ...
Page 212
... inscribed in , any regular polygon . E Let ABCDE be a regular polygon . 1. To prove that a circle may be circumscribed about ABCDE . Proof . Let be the centre of the circle which may be passed through A , B , and C. § 258 Then and By ...
... inscribed in , any regular polygon . E Let ABCDE be a regular polygon . 1. To prove that a circle may be circumscribed about ABCDE . Proof . Let be the centre of the circle which may be passed through A , B , and C. § 258 Then and By ...
Page 213
... circumscribed about the polygon . § 231 2. To prove that a circle may be inscribed in ABCDE . Proof . Since the sides of the regular polygon are equal chords of the circumscribed circle , they are equally distant from the centre . $ 249 ...
... circumscribed about the polygon . § 231 2. To prove that a circle may be inscribed in ABCDE . Proof . Since the sides of the regular polygon are equal chords of the circumscribed circle , they are equally distant from the centre . $ 249 ...
Page 214
... regular inscribed poly- gon ; and the tangents drawn at the points of division form a regular circumscribed polygon . E I D H C K G B Suppose the circumference divided into equal arcs AB , BC , etc. Let AB , BC , etc. , be the chords ...
... regular inscribed poly- gon ; and the tangents drawn at the points of division form a regular circumscribed polygon . E I D H C K G B Suppose the circumference divided into equal arcs AB , BC , etc. Let AB , BC , etc. , be the chords ...
Page 215
... regular inscribed polygon form a circumscribed regular polygon , whose sides are parallel to the sides of the inscribed polygon and whose vertices lie on the radii ( prolonged ) of the in- scribed polygon . For two corresponding sides ...
... regular inscribed polygon form a circumscribed regular polygon , whose sides are parallel to the sides of the inscribed polygon and whose vertices lie on the radii ( prolonged ) of the in- scribed polygon . For two corresponding sides ...
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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.