Elements of Geometry and Trigonometry |
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Page 13
... position , but not magni- 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and curved . 4. A STRAIGHT LINE is one which does not change its direction at any point . 5 ...
... position , but not magni- 3. A LINE is that which has length , but neither breadth nor thickness . Lines are divided into two classes , straight and curved . 4. A STRAIGHT LINE is one which does not change its direction at any point . 5 ...
Page 21
... position just demonstrated , the sum of any two adjacent angles is equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE ...
... position just demonstrated , the sum of any two adjacent angles is equal to two right angles . PROPOSITION II . THEOREM . If two straight lines intersect each other , the opposite or vertical angles will be equal . Let AB and DE ...
Page 30
... position , that the side BC would be greater than EF ; and if the angle A less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence ...
... position , that the side BC would be greater than EF ; and if the angle A less than D , the side BC would be less than EF . But BC is equal to EF , by hypothesis ; therefore , the angle A can neither be greater nor less than D : hence ...
Page 65
... position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in ...
... position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , will pass through the third , and be perpendicular to the chord . PROPOSITION VII . THEOREM . Through any three points , not in ...
Page 72
... have any one of six positions with respect to each other , depending upon the distance between their centres : 1o . When the distance between their centres is greater than the sum of their radii , they are external 72 GEOMETRY .
... have any one of six positions with respect to each other , depending upon the distance between their centres : 1o . When the distance between their centres is greater than the sum of their radii , they are external 72 GEOMETRY .
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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
AB² ABCD AC² 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...