Elements of Geometry and Trigonometry |
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Page 65
... 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 the same straight line , one circumference may be made to pass , and ...
... 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 the same straight line , one circumference may be made to pass , and ...
Page 66
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences passing through the ...
... pass through these points , and but one ; which was to be proved . Cor . Two circumferences cannot intersect in more than two points ; for , if they could intersect in three points , there would be two circumferences passing through the ...
Page 72
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
... pass through a common point of that line , are tangent to each other at that point . And if a straight line be drawn tangent to one of the circles at their common point , it will be tangent to them all at that point . Scholium . From ...
Page 77
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : centre : then will it be measured by half of the arc DE . E A For , draw the radius CD . The external BOOK III . 77.
... without the angle . 1o . Let EAD be an inscribed an- gle , one of whose sides AE passes through the centre : centre : then will it be measured by half of the arc DE . E A For , draw the radius CD . The external BOOK III . 77.
Page 89
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
... pass a circumference through any three points not in a straight line . If the points are vertices of a triangle , the circle will be circumscribed about it . PROBLEM XIV . Through a given point , to draw a tangent to a given circle ...
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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...