Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 1-5 of 19
Page v
... BOOK V. Regular Polygons - Measurement of the Circle , Exercises , 142 163 BOOK VI . Planes , and Polyedral Angles , 165 187 Exercises , BOOK VII . 189 Polyedrons , .. Exercises , 221 9 BOOK VIII . PAGE Cylinder , Cone , and Sphere.
... BOOK V. Regular Polygons - Measurement of the Circle , Exercises , 142 163 BOOK VI . Planes , and Polyedral Angles , 165 187 Exercises , BOOK VII . 189 Polyedrons , .. Exercises , 221 9 BOOK VIII . PAGE Cylinder , Cone , and Sphere.
Page vi
... Cylinder , Cone , and Sphere , Exercises , 223 248 BOOK IX . Spherical Geometry ,. Exercises , 250 277 PLANE TRIGONOMETRY . Definition of Logarithms , Rules for Characteristics , General Principles , .... INTRODUCTION . Table of ...
... Cylinder , Cone , and Sphere , Exercises , 223 248 BOOK IX . Spherical Geometry ,. Exercises , 250 277 PLANE TRIGONOMETRY . Definition of Logarithms , Rules for Characteristics , General Principles , .... INTRODUCTION . Table of ...
Page 222
... two regular polyedrons of the same kind are similar . 18. Show that the drons are to each homologous edges surfaces of any two similar polye- other as the squares of any two BOOK VIII . THE CYLINDER , THE CONE , AND 222 GEOMETRY .
... two regular polyedrons of the same kind are similar . 18. Show that the drons are to each homologous edges surfaces of any two similar polye- other as the squares of any two BOOK VIII . THE CYLINDER , THE CONE , AND 222 GEOMETRY .
Page 223
... CYLINDER , THE CONE , AND THE SPHERE . DEFINITIONS . P A H 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side AB , as an ...
... CYLINDER , THE CONE , AND THE SPHERE . DEFINITIONS . P A H 1. A CYLINDER is a volume which may be generated by a rectangle revolving about one of its sides as an axis . Thus , if the rectangle ABCD be turned about the side AB , as an ...
Page 224
... cylinder , when its bases are inscribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circum- scribing ...
... cylinder , when its bases are inscribed in the bases of the cylinder . In this case , the cylinder is said to be circumscribed about the prism . The lateral edges of the inscribed prism are elements of the surface of the circum- scribing ...
Other editions - View all
Common terms and phrases
ABCD AC² adjacent angles altitude apothem Applying logarithms bisects centre chord circle circumference circumscribed cone consequently convex surface cosec cosine Cotang cylinder denote diagonals diameter difference distance divided draw drawn edges equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle inscribed intersection isosceles less Let ABC log sin lower base lune mantissa number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron principle demonstrated prism PROBLEM.-In PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment semi-circumference similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square straight line subtracting supplement Tang tangent THEOREM THEOREM.-Show tri-rectangular triangle ABC triangular prism triedral angle upper base vertex vertices volume whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 90 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 18 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 253 - For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...
Page 61 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 94 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 126 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 125 - THEOREM. Similar triangles are to each other as the squares of their homologous sides.