Elements of Geometry and Trigonometry |
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Page 41
... manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line meet two parallels , the opposite exterior and interior angles will be equal . The angles DHG and IIGA are equal , from what has just been shown . The ...
... manner , it may be shown that BGH and GHC are equal . Cor . 3. If a straight line meet two parallels , the opposite exterior and interior angles will be equal . The angles DHG and IIGA are equal , from what has just been shown . The ...
Page 44
... manner , opposite interior angle C since AE and CB are parallel , and AB cuts them , the alternate angles ABC and BAE are equal : hence , the sum of the three angles of the triangle BAC , is equal to the sum of the angles CAB , BAE ...
... manner , opposite interior angle C since AE and CB are parallel , and AB cuts them , the alternate angles ABC and BAE are equal : hence , the sum of the three angles of the triangle BAC , is equal to the sum of the angles CAB , BAE ...
Page 76
... manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB : arc AD ; which was to be proved . Cor . 1. The intercepted arcs are ...
... manner , it may be shown that the fourth term cannot be less than AD : hence , it must be equal to AD ; therefore , we have , angle ACB : angle ACD :: arc AB : arc AD ; which was to be proved . Cor . 1. The intercepted arcs are ...
Page 91
... manner , it may be shown that OD is equal to OF From 0 as a centre , with a radius OD , describe a circle , and it will be the circle required . For , each side is perpendicular to a a radius at its extremity , and is therefore tangent ...
... manner , it may be shown that OD is equal to OF From 0 as a centre , with a radius OD , describe a circle , and it will be the circle required . For , each side is perpendicular to a a radius at its extremity , and is therefore tangent ...
Page 97
... manner , it may be shown that it cannot be less than AE ; consequently , it must be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . : Cor . If rectangles have equal bases , they are to each other as their altitudes ...
... manner , it may be shown that it cannot be less than AE ; consequently , it must be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . : Cor . If rectangles have equal bases , they are to each other as their altitudes ...
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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...