Elements of Geometry and Trigonometry |
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Page 34
... drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line : 2o . Any two oblique ... draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction , the side BC ...
... drawn to differ- ent points of it : 1o . The perpendicular will be shorter than any oblique line : 2o . Any two oblique ... draw FC , FD . 1o . In the triangles ABC , FBC , we have the side AB equal to BF , by construction , the side BC ...
Page 35
... drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ... draw the lines DA and DB . Then will DA and DB be equal ( P. XV . ) : hence , D is A D F E # B equally distant from ...
... drawn ; for , if there could be more , there would be at least two equal oblique lines on the same side of the ... draw the lines DA and DB . Then will DA and DB be equal ( P. XV . ) : hence , D is A D F E # B equally distant from ...
Page 36
... draw IA and IB . One of these lines , as IA , will cut EF in some point D ; draw DB . Then , from what has just been shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and ...
... draw IA and IB . One of these lines , as IA , will cut EF in some point D ; draw DB . Then , from what has just been shown , DA and DB will be equal ; but IB is less than the sum of ID and DB ( P. VII . ) ; and because the sum of ID and ...
Page 42
... draw FH and EG perpendicular to CD ; they will also be perpendicular to AB ( P. XX . , C. 1 ) , and will measure the distance between AB and CD , at the points F and E. Draw also FG . The lines FH and EG are parallel ( P. XVIII ...
... draw FH and EG perpendicular to CD ; they will also be perpendicular to AB ( P. XX . , C. 1 ) , and will measure the distance between AB and CD , at the points F and E. Draw also FG . The lines FH and EG are parallel ( P. XVIII ...
Page 45
... draw diagonals AC , AD . The polygon will be divided into as many triangles , less two , as it has sides , having the point A for a common vertex , and for bases , the sides of the polygon , except the two which form the angle A. It is ...
... draw diagonals AC , AD . The polygon will be divided into as many triangles , less two , as it has sides , having the point A for a common vertex , and for bases , the sides of the polygon , except the two which form the angle A. It is ...
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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...