Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 60
Page iii
... manner impairing the gener ality of the truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a ...
... manner impairing the gener ality of the truths evolved . The term solid , used not only by LEGENDRE , but by many other authors , to denote a limited portion of space , seems calculated to introduce the foreign idea of matter into a ...
Page vi
... Manner of Using the Table , Multiplication by Logarithms , Division by Logarithms , · Arithmetical Complement , • 1 Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
... Manner of Using the Table , Multiplication by Logarithms , Division by Logarithms , · Arithmetical Complement , • 1 Raising to Powers by Logarithms , Extraction of Roots by Logarithms , PLANE TRIGONOMETRY . Plane Trigonometry Defined ...
Page 22
... manner , we find , ACD + ACE = ACD + DCB ; and , taking away the common 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 ...
... manner , we find , ACD + ACE = ACD + DCB ; and , taking away the common 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 ...
Page 25
... manner that the angle A shall coincide with the anlge D , A D the side AB taking B CE F the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the vertex B will coincide with the vertex E ; and because ...
... manner that the angle A shall coincide with the anlge D , A D the side AB taking B CE F the direction DE , and the side AC the direction DF . Then , because AB is equal to DE , the vertex B will coincide with the vertex E ; and because ...
Page 40
... manner , it may be proved that the sum of HGA and GHC , is equal to two right angles . Cor . 1. If HGB is a right angle , GHD will be a right angle also hence , if a line is perpendicular to one of two parallels , it is perpendicular to ...
... manner , it may be proved that the sum of HGA and GHC , is equal to two right angles . Cor . 1. If HGB is a right angle , GHD will be a right angle also hence , if a line is perpendicular to one of two parallels , it is perpendicular to ...
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
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...