The Essentials of GeometryD.C. Heath & Company, 1899 - 395 σελίδες |
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Σελίδα 50
... . ) Note . The point E is called the centre of the parallelogram . PROP . XLI . THEOREM . 112. ( Converse of Prop . XL . ) If the diagonals of a quadrilateral bisect each other , the figure is a parallelogram ( Fig . of Prop . XL . ) Given.
... . ) Note . The point E is called the centre of the parallelogram . PROP . XLI . THEOREM . 112. ( Converse of Prop . XL . ) If the diagonals of a quadrilateral bisect each other , the figure is a parallelogram ( Fig . of Prop . XL . ) Given.
Σελίδα 72
... centre ; as ABCD . An arc is any portion of the circum- ference ; as AB . A radius is a straight line drawn from the centre to the circumference ; as OA . A J D C A diameter is a straight line drawn through the centre , having its ...
... centre ; as ABCD . An arc is any portion of the circum- ference ; as AB . A radius is a straight line drawn from the centre to the circumference ; as OA . A J D C A diameter is a straight line drawn through the centre , having its ...
Σελίδα 73
... centre , and whose sides are radii ; as AOC . An inscribed angle is an angle whose ver- tex is on the circumference , and whose sides are chords ; as ABC . An angle is said to be inscribed in a segment when its vertex is on the arc of ...
... centre , and whose sides are radii ; as AOC . An inscribed angle is an angle whose ver- tex is on the circumference , and whose sides are chords ; as ABC . An angle is said to be inscribed in a segment when its vertex is on the arc of ...
Σελίδα 75
... centre . Hence , segments ABC and ADC coincide throughout , and are equal . Therefore , AC bisects the O , and its circumference . PROP . II . THEOREM . 153. A straight line cannot intersect a circumference at more than two points . MA ...
... centre . Hence , segments ABC and ADC coincide throughout , and are equal . Therefore , AC bisects the O , and its circumference . PROP . II . THEOREM . 153. A straight line cannot intersect a circumference at more than two points . MA ...
Σελίδα 76
... centre . .. arc AB = arc A'B ' . PROP . IV . THEOREM . 155. ( Converse of Prop . III . ) In equal circles , or in the same circle , equal arcs are intercepted by equal central angles . A B A M M ' Given ACB and A'C'B ' central of equal ...
... centre . .. arc AB = arc A'B ' . PROP . IV . THEOREM . 155. ( Converse of Prop . III . ) In equal circles , or in the same circle , equal arcs are intercepted by equal central angles . A B A M M ' Given ACB and A'C'B ' central of equal ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude apothem approach the limit area ABC axis base and altitude BC² bisector bisects centre chord circle circumference circumscribed coincide cone of revolution Converse of Prop diagonals diameter diedral angle distance Draw line equally distant equilateral equivalent exterior angle faces Find the area frustum Given line given point Hence homologous homologous sides hypotenuse intersecting isosceles triangle lateral area lateral edges line drawn line joining middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedral polyedron prism pyramid quadrilateral radii radius rectangle regular inscribed regular polygon rhombus right angles right triangle segment side BC similar slant height spherical polygon spherical triangle square tangent tetraedron THEOREM trapezoid triangle ABC triangular prism triedral vertex vertices volume Whence
Δημοφιλή αποσπάσματα
Σελίδα 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Σελίδα 49 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Σελίδα 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Σελίδα 73 - A chord is a straight line joining the extremities of an arc ; as AB.
Σελίδα 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 205 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Σελίδα 170 - 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.
Σελίδα 224 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Σελίδα 325 - A right circular cone may be generated by the revolution of a right triangle about one of its legs as an axis.