Elements of Geometry and Trigonometry |
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Page 77
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is ...
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is ...
Page 79
... quadrant ( P. XVII . , S. ) . B A 0 in- A Cor . 3. Any angle BAC , scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in ...
... quadrant ( P. XVII . , S. ) . B A 0 in- A Cor . 3. Any angle BAC , scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in ...
Page 239
... quadrant ( B. III . , P. XVII . , S. ) : hence , the two poles of a great circle are at equal distances from the circumference . Cor . 2. The two poles of a small circle are at unequal distances from the circumference , the sum of the ...
... quadrant ( B. III . , P. XVII . , S. ) : hence , the two poles of a great circle are at equal distances from the circumference . Cor . 2. The two poles of a small circle are at unequal distances from the circumference , the sum of the ...
Page 242
... quadrant ; the point being the pole of the arc DE , the distance C CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
... quadrant ; the point being the pole of the arc DE , the distance C CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
Page 251
... quadrants , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The angles opposite the equal sides are right angles ( P. III . , C. 3 ) : hence , the sides AB and AC are quadrants . B If the angle ...
... quadrants , and their point of intersec- tion will be the pole of the other side ( P. III . , C. 4 ) . The angles opposite the equal sides are right angles ( P. III . , C. 3 ) : hence , the sides AB and AC are quadrants . B If the angle ...
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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...