## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 16

Page 14

... angle BAC , or simply , the angle A. 11. When one straight line meets another the two angles which they form are called

... angle BAC , or simply , the angle A. 11. When one straight line meets another the two angles which they form are called

**adjacent angles**. Thus , the A- angles ABD and DBC are adjacent . 12. A RIGHT ANGLE is formed by one straight line ... Page 20

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**adjacent angles**will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA and DCB be equal to two right angles . At C , let CE be drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D ... Page 21

... angles about the point of intersection , which have received different names , with respect to each other . are 1o .

... angles about the point of intersection , which have received different names , with respect to each other . are 1o .

**ADJACENT ANGLES**those which lie on the same side of one line , and on opposite sides of the other ; thus , ACE and ... Page 22

... angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its

... angle ACD , we have , ACE DCB . Hence , the proposition is proved . Cor . 1. If one of the angles about C all of the others will be right angles also . each of its

**adjacent angles**will be a right angle ; and from the proposition just ... Page 38

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**angles**on the same side . are 3o . ALTERNATE**ANGLES**, those that lie on opposite sides . of the secant and within ...**adjacent**. Thus , EGB and GHD are opposite exterior and interior**angles**. PROPOSITION XIX . THEOREM . If two ...### Other editions - View all

Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence

### Popular passages

Page 28 - If two triangles have two sides of the one equal to two sides of the...

Page 100 - The area of a triangle is equal to half the product of its base by its altitude.

Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 59 - A chord is a straight line joining the extremities of an arc.

Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.

Page 123 - Similar triangles are to each other as the squares of their homologous sides.

Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...