Schultze and Sevenoak's Plane and Solid Geometry |
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Page 24
... ( Prop . II ) are homologous sides , C and c ' homolo- gous angles , the medians drawn from △ and A ' respectively homologous medians , etc. Ex . 86. Hyp . Za = 30 ° , ≤ b = 30 ° , 4 c = 60 ° , ≤ d = 60 ° . To prove AABCA ADC . Ex . 87 ...
... ( Prop . II ) are homologous sides , C and c ' homolo- gous angles , the medians drawn from △ and A ' respectively homologous medians , etc. Ex . 86. Hyp . Za = 30 ° , ≤ b = 30 ° , 4 c = 60 ° , ≤ d = 60 ° . To prove AABCA ADC . Ex . 87 ...
Page 31
... Prop . IV ( compare § 121 ) . A B A B ' B Ex . 144 Ex . 145 Ex . 146 D ' D Ex . 147 Ex . 144. If ABC and ADC are two isosceles triangles on the same base , AC , then △ BAD = △ BCD . Ex . 145. If in quadrilateral ABCD , AB = LA = LC ...
... Prop . IV ( compare § 121 ) . A B A B ' B Ex . 144 Ex . 145 Ex . 146 D ' D Ex . 147 Ex . 144. If ABC and ADC are two isosceles triangles on the same base , AC , then △ BAD = △ BCD . Ex . 145. If in quadrilateral ABCD , AB = LA = LC ...
Page 52
... Prop . XIII . ] A E B I F 2 Given parallel lines AB and CD , and the alt . int . 1 and 2 . To prove 21 = 22 . Proof STATEMENTS REASONS Either 122 , or 21 22 . Suppose that 122 , then AB is not || to CD . Two lines are not Il if a ...
... Prop . XIII . ] A E B I F 2 Given parallel lines AB and CD , and the alt . int . 1 and 2 . To prove 21 = 22 . Proof STATEMENTS REASONS Either 122 , or 21 22 . Suppose that 122 , then AB is not || to CD . Two lines are not Il if a ...
Page 53
... Prop . XIV . ] E 2 B 3 Given parallel lines AB and CD and the cor . & 1 and 2 . To prove 21 = 22 . Proof STATEMENTS 21 = 23 . Vertical 42 = 23 . .. 21 = 22 . Q. E. D. REASONS are equal . Alt . int . of || lines are equal . Things equal ...
... Prop . XIV . ] E 2 B 3 Given parallel lines AB and CD and the cor . & 1 and 2 . To prove 21 = 22 . Proof STATEMENTS 21 = 23 . Vertical 42 = 23 . .. 21 = 22 . Q. E. D. REASONS are equal . Alt . int . of || lines are equal . Things equal ...
Page 55
... Prop . XV . ] B 土 2/3 Given AB || CD , and the int . 1 and 2 , lying on the same side of a transversal . To prove 1 is the sup . of 2 . Proof STATEMENTS 23 is the sup . of 2 . 21 = 23 . .. 1 is the sup . of 2 . REASONS If two adj ...
... Prop . XV . ] B 土 2/3 Given AB || CD , and the int . 1 and 2 , lying on the same side of a transversal . To prove 1 is the sup . of 2 . Proof STATEMENTS 23 is the sup . of 2 . 21 = 23 . .. 1 is the sup . of 2 . REASONS If two adj ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - Two triangles having 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 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - 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.
Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.