Schultze and Sevenoak's Plane and Solid Geometry |
From inside the book
Results 1-5 of 67
Page 87
... meet in 0 ; and 0 is equidistant from A , B , and C. Q. E. D. Ex . 396. Construct a point O equidistant from three vertices of a quadrilateral . Ex . 337. Construct a circle which passes through the QUADRILATERALS 87 882.
... meet in 0 ; and 0 is equidistant from A , B , and C. Q. E. D. Ex . 396. Construct a point O equidistant from three vertices of a quadrilateral . Ex . 337. Construct a circle which passes through the QUADRILATERALS 87 882.
Page 88
Arthur Schultze, Frank Louis Sevenoak. Ex . 337. Construct a circle which passes through the three vertices of a given triangle . Ex . 398. If EK , FI , and DH are perpen- dicular bisectors of the sides of triangle ABC , what kind of ...
Arthur Schultze, Frank Louis Sevenoak. Ex . 337. Construct a circle which passes through the three vertices of a given triangle . Ex . 398. If EK , FI , and DH are perpen- dicular bisectors of the sides of triangle ABC , what kind of ...
Page 94
... passes through 0 . CD passes through 0 . ( 168 ) ( 168 ) Q. E. D. .. AE , BF , and CD are concurrent . Ex . 413. If two medians of a triangle are equal , the triangle is isosceles . Ex . 414. Two observers , at A and at 94 PLANE GEOMETRY.
... passes through 0 . CD passes through 0 . ( 168 ) ( 168 ) Q. E. D. .. AE , BF , and CD are concurrent . Ex . 413. If two medians of a triangle are equal , the triangle is isosceles . Ex . 414. Two observers , at A and at 94 PLANE GEOMETRY.
Page 108
... passes through the center of the circle . Ex . 509. In the diagram opposite , if the radii OD , OE , and OF are respectively perpendicular to the sides of the equilateral triangle ABC , then AD = DB = BE = EC = CF = FA . Ex . 510. If ...
... passes through the center of the circle . Ex . 509. In the diagram opposite , if the radii OD , OE , and OF are respectively perpendicular to the sides of the equilateral triangle ABC , then AD = DB = BE = EC = CF = FA . Ex . 510. If ...
Page 109
... passes through the center of the circle . Ex . 514. Two points , each equidistant from the ends of a chord , de- termine a line passing through the center of the circle . PROPOSITION IV . PROBLEM 192. To circumscribe a circle about a ...
... passes through the center of the circle . Ex . 514. Two points , each equidistant from the ends of a chord , de- termine a line passing through the center of the circle . PROPOSITION IV . PROBLEM 192. To circumscribe a circle about a ...
Other editions - View all
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.