Treatise on Geometry and Trigonometry: For Colleges, Schools and Private Students. Written for the Mathematical Course of Joseph Ray, M.D.Sargent, Wilson & Hinkle, 1868 - 420 σελίδες |
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Σελίδα vii
... OF VOLUME , SIMILAR POLYEDRONS , REGULAR POLYEDRONS , · 213 222 226 232 239 241 CONES , CYLINDERS , CHAPTER XI . SOLIDS OF REVOLUTION . 247 249 SPHERES , SPHERICAL AREAS , SPHERICAL VOLUMES , MENSURATION , CONTENTS . vii.
... OF VOLUME , SIMILAR POLYEDRONS , REGULAR POLYEDRONS , · 213 222 226 232 239 241 CONES , CYLINDERS , CHAPTER XI . SOLIDS OF REVOLUTION . 247 249 SPHERES , SPHERICAL AREAS , SPHERICAL VOLUMES , MENSURATION , CONTENTS . vii.
Σελίδα viii
... SPHERES , SPHERICAL AREAS , SPHERICAL VOLUMES , MENSURATION , PART FOURTH . — TRIGONOMETRY . CHAPTER XII . PAGE . • 250 261 270 276 PLANE TRIGONOMETRY . MEASURE OF ANGLES , 277 FUNCTIONS OF ANGLES , 279 CONSTRUCTION AND USE OF TABLES ...
... SPHERES , SPHERICAL AREAS , SPHERICAL VOLUMES , MENSURATION , PART FOURTH . — TRIGONOMETRY . CHAPTER XII . PAGE . • 250 261 270 276 PLANE TRIGONOMETRY . MEASURE OF ANGLES , 277 FUNCTIONS OF ANGLES , 279 CONSTRUCTION AND USE OF TABLES ...
Σελίδα 246
... sphere , which is described by the revolution of a semicircle about the diameter , will be considered separately . 719. As the curved surfaces of the cone and of the cylinder are generated by the motion of a straight line , it follows ...
... sphere , which is described by the revolution of a semicircle about the diameter , will be considered separately . 719. As the curved surfaces of the cone and of the cylinder are generated by the motion of a straight line , it follows ...
Σελίδα 250
... SPHERES . 737. A SPHERE is a solid de- scribed by the revolution of a semicircle about its diameter as an axis . The center , radius , and diame- ter of the sphere are the same as those of the generating circle . The spherical surface ...
... SPHERES . 737. A SPHERE is a solid de- scribed by the revolution of a semicircle about its diameter as an axis . The center , radius , and diame- ter of the sphere are the same as those of the generating circle . The spherical surface ...
Σελίδα 251
... sphere is equally distant from the center . This property of the sphere is frequently given as its definition . 739. Corollary . - All radii of the same sphere are equal . The same is true of the diameters . 740. Corollary . - Spheres ...
... sphere is equally distant from the center . This property of the sphere is frequently given as its definition . 739. Corollary . - All radii of the same sphere are equal . The same is true of the diameters . 740. Corollary . - Spheres ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles altitude angles equal apothem axis base bisect chord circle circumference circumscribed coincide cone Corollary Corollary.-The cosine Cotang curved surface cylinder demonstrated diagonals diameter dicular diedral angles diedral whose edge distance divided draw equal angles equally distant equivalent EXERCISES faces figure formula four right angles frustum functions Geometry given angle given line given point given straight line given triangle gles greater Hence homologous lines hypotenuse included angle inscribed intersection Join less let fall logarithm mantissa number of sides opposite sides parallel lines parallelogram parallelopiped perimeter perpen perpendicular polyedral prism Problem.-Given proportional pyramid quadrilateral radii radius ratio regular polygon respectively equal right angled triangle secant similar similarly arranged sine slant hight sphere spherical excess spherical polygon spherical triangle square student subtracting symmetrical Tang tangent tetraedrons theorem Theorem.-The triedral vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 183 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Σελίδα 238 - The volume of any parallelopiped is equal to the product of its base by its altitude.
Σελίδα 72 - Problem. — To draw a line through a given point parallel to a given line.
Σελίδα 141 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 91 - Conversely, if two angles of a triangle are equal, the sides opposite them are also equal, and the triangle is isosceles.
Σελίδα 173 - The areas of two circles are to each other as the squares of their radii ; or, as the squares of their diameters. 502. Corollary. — When the radius is unity, the area is expressed by -. 503. Theorem — The area of a sector is measured by half the product of its arc by its radius.
Σελίδα 240 - Corollary — The volume of any pyramid is equal to one-third of the product of its base by its altitude. For any pyramid...
Σελίδα 260 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Σελίδα 137 - The squa/re described on the difference of two straight lines is equivalent to the sum of the squares described on the two lines, diminished by twice the rectangle contained by the lines.
Σελίδα 274 - The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.