Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 69
Page 60
... TANGENT is a straight line which touches the circumference in one point . This point is called , the point of contact , or , the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
... TANGENT is a straight line which touches the circumference in one point . This point is called , the point of contact , or , the point of tangency . 12. Two circles are tangent to each other , when they touch each other in one point ...
Page 68
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A then will it ...
... tangent to the circle at that point ; conversely , if a straight line is tangent to a circle at any point , it will be perpendicular to the radius drawn to that point . 1o . Let BD be perpendicular to the radius CA , at A then will it ...
Page 69
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then will the intercepted arcs MN and PQ be equal . For , draw the radius CH perpendicular to the chord H MP ; it will also be be per- A B M P ( B. I. ...
... tangent ; or , both may be tangents . 1o . Let the secants AB and DE be parallel : then will the intercepted arcs MN and PQ be equal . For , draw the radius CH perpendicular to the chord H MP ; it will also be be per- A B M P ( B. I. ...
Page 70
Adrien Marie Legendre Charles Davies. 3o . Let the tangents DE and IL be parallel , and let H and K be their points of contact : then will the in- tercepted arcs HMK and HPK be equal . For , draw the secant AB parallel to ᎠᎬ ; then ...
Adrien Marie Legendre Charles Davies. 3o . Let the tangents DE and IL be parallel , and let H and K be their points of contact : then will the in- tercepted arcs HMK and HPK be equal . For , draw the secant AB parallel to ᎠᎬ ; then ...
Page 71
... tangent externally . Let C and D be the centres of two circles , and let the distance between the centres be equal to the sum of the radii : then will the circles be tangent externally . For , they will have a point A , on the line CD ...
... tangent externally . Let C and D be the centres of two circles , and let the distance between the centres be equal to the sum of the radii : then will the circles be tangent externally . For , they will have a point A , on the line CD ...
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
ABē ABCD ACē 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...