Elements of Geometry and Trigonometry |
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Page 99
... units in its base by the number of linear units in its altitude . Scholium 2. The product of two lines is sometimes called the rectangle of the lines , because the product is equal to the area of a rectangle constructed with the lines ...
... units in its base by the number of linear units in its altitude . Scholium 2. The product of two lines is sometimes called the rectangle of the lines , because the product is equal to the area of a rectangle constructed with the lines ...
Page 152
... unit . Taking the figures as far as they agree , and denoting the number of units in the required area by , we have , approximately , π 3.141592 ; that is , the area of a circle whose radius is 1 , is 3.141592 . Scholium . For practical ...
... unit . Taking the figures as far as they agree , and denoting the number of units in the required area by , we have , approximately , π 3.141592 ; that is , the area of a circle whose radius is 1 , is 3.141592 . Scholium . For practical ...
Page 154
... unit . By increasing the number of sides , a still closer approximation may be had . PROPOSITION XIV . THEOREM . The area of a circle is equal to half the product of its circumference and radius . O Let be the centre of a circle , OC ...
... unit . By increasing the number of sides , a still closer approximation may be had . PROPOSITION XIV . THEOREM . The area of a circle is equal to half the product of its circumference and radius . O Let be the centre of a circle , OC ...
Page 181
... unit . The unit generally employed is a cube constructed on the linear unit as an edge . PROPOSITION I. THEOREM . The convex surface of a right prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K ...
... unit . The unit generally employed is a cube constructed on the linear unit as an edge . PROPOSITION I. THEOREM . The convex surface of a right prism is equal to the perim- eter of either base multiplied by the altitude . Let ABCDE - K ...
Page 197
... unit , the parallelopipedon AZ will be a cube constructed on that unit , as an edge ; and consequently , it will be the unit of volume . Under this supposition , the last proposition becomes , whence , 1 : vol . AG vol . AG :: : 1 : AB ...
... unit , the parallelopipedon AZ will be a cube constructed on that unit , as an edge ; and consequently , it will be the unit of volume . Under this supposition , the last proposition becomes , whence , 1 : vol . AG vol . AG :: : 1 : AB ...
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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...