Elements of Geometry, Part 1American Book Company, 1896 - Geometry |
Other editions - View all
Common terms and phrases
ABCD adjacent angles altitude angles of parallel apothem assigned quantity bisecting bisector centre of symmetry chord circle whose radius circumference circumscribed circle coincide construct a square decagon diagonals diameter distance divided Draw equally distant equiangular polygon equilateral triangle Exercise.-The exterior angle Find the area given circle given line given point given straight line GIVEN TO PROVE given triangle Hence homologous sides hypotenuse included angle inscribed polygon inscribed regular intersection isosceles triangle length locus mean proportional measured by arc middle points number of sides one-nth opposite sides parallel to BC parallelogram perimeter perpendicular Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rectangle regular hexagon regular inscribed regular polygon respectively equal rhombus right angles right triangle segment square equivalent straight line joining symmetry tangent THEOREM third side triangle ABC triangles are equal unequal vertex vertices
Popular passages
Page 46 - ... 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 67 - 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 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Page 148 - 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.
Page 56 - Two oblique lines cutting off equal distances from the foot of the perpendicular are equal.
Page 46 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.
Page 127 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 181 - The areas of two similar triangles are to each other as the squares of any two homologous sides.