An Elementary Geometry |
From inside the book
Results 1-5 of 11
Page 17
... QRST . 60. A Rhombus is an equilateral rhomboid ; as UVWX . L K M N P 0 R S Q T U V X W 61. A Diagonal is a line joining the vertices of two angles not adjacent ; as DB . THEOREM XVII . 62. The opposite sides and angles of BOOK I. 17.
... QRST . 60. A Rhombus is an equilateral rhomboid ; as UVWX . L K M N P 0 R S Q T U V X W 61. A Diagonal is a line joining the vertices of two angles not adjacent ; as DB . THEOREM XVII . 62. The opposite sides and angles of BOOK I. 17.
Page 18
... diagonal BD . As BC and AD are parallel , the alternate angles CBD and BDA are equal ( 17 ) ; and as AB and DC are parallel , the alternate angles A B D and BDC are equal ; therefore the two triangles ABD and BDC , having the two angles ...
... diagonal BD . As BC and AD are parallel , the alternate angles CBD and BDA are equal ( 17 ) ; and as AB and DC are parallel , the alternate angles A B D and BDC are equal ; therefore the two triangles ABD and BDC , having the two angles ...
Page 20
... diagonals A C , AD , AE , are drawn , the polygon will be divided into as many triangles as it has sides minus two ; and the sum of the angles of each triangle is equal to two right angles ( 33 ) ; therefore the sum of the angles of all ...
... diagonals A C , AD , AE , are drawn , the polygon will be divided into as many triangles as it has sides minus two ; and the sum of the angles of each triangle is equal to two right angles ( 33 ) ; therefore the sum of the angles of all ...
Page 23
... diagonals of a parallelogram bisect each other . 86. ( Converse of 85. ) If the diagonals of a quadrilateral bisect each other , the figure is a parallelogram . 87. The diagonals of a rhombus bisect each other at right angles . 88 ...
... diagonals of a parallelogram bisect each other . 86. ( Converse of 85. ) If the diagonals of a quadrilateral bisect each other , the figure is a parallelogram . 87. The diagonals of a rhombus bisect each other at right angles . 88 ...
Page 24
... diagonals of a rectangle are equal . 99. The diagonals of a rhombus bisect the angles of the rhombus . 91. Straight lines bisecting the adjacent angles of a parallelogram are perpendicular to each other . 92. From the vertices of a ...
... diagonals of a rectangle are equal . 99. The diagonals of a rhombus bisect the angles of the rhombus . 91. Straight lines bisecting the adjacent angles of a parallelogram are perpendicular to each other . 92. From the vertices of a ...
Other editions - View all
Common terms and phrases
ABC and DEF ABCD adjacent altitude angle ABC apothem base and altitude bisect centre chord circ circumference coincide cone construct the triangle convex surface Corollary cube cylinder diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square given triangle half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining mean proportional measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel propositions quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VIII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.