Elementary Geometry, Plane and Solid: For Use in High Schools and AcademiesMacmillan, 1901 - 440 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα xi
... Spherical Angles , Triangles , and Polygons Polar Triangles 380 387 Section IV . Areas of Spherical Triangles Section V. Volume of the Sphere . Miscellaneous Exercises 394 405 409 410 Classified Summary . APPENDIX PLANE TRIGONOMETRY 416 ...
... Spherical Angles , Triangles , and Polygons Polar Triangles 380 387 Section IV . Areas of Spherical Triangles Section V. Volume of the Sphere . Miscellaneous Exercises 394 405 409 410 Classified Summary . APPENDIX PLANE TRIGONOMETRY 416 ...
Σελίδα 369
... . ( 2 ) The volume of a circular cone is equal to one - third the product of its altitude and the area of its base . V = } πr2h . § 579 . CHAPTER IX THE SPHERE SECTION I PLANE SECTIONS AND TANGENT 2 B SUMMARY ] 369 CYLINDERS AND CONES.
... . ( 2 ) The volume of a circular cone is equal to one - third the product of its altitude and the area of its base . V = } πr2h . § 579 . CHAPTER IX THE SPHERE SECTION I PLANE SECTIONS AND TANGENT 2 B SUMMARY ] 369 CYLINDERS AND CONES.
Σελίδα 370
... not coincide are called concentric spheres . Spheres having the same centre and one point in common must coincide throughout . PROPOSITION I 583. The section of a sphere made by 370 CHAPTER IX THE SPHERE Plane Sections and Tangent Planes.
... not coincide are called concentric spheres . Spheres having the same centre and one point in common must coincide throughout . PROPOSITION I 583. The section of a sphere made by 370 CHAPTER IX THE SPHERE Plane Sections and Tangent Planes.
Σελίδα 371
... sphere and A , B , C three points on the section made by any plane L. It is required to prove that ABC is a circle ... sphere . Therefore all points common to the plane and sphere are equidistant from P. Therefore the section of the ...
... sphere and A , B , C three points on the section made by any plane L. It is required to prove that ABC is a circle ... sphere . Therefore all points common to the plane and sphere are equidistant from P. Therefore the section of the ...
Σελίδα 372
... sphere , and subtends a right angle at the centre of the sphere . 586. COROLLARY II . The centre of any circle of a sphere is the foot of the perpendicular drawn from the centre of the sphere to the plane of the circle . 587. COROLLARY ...
... sphere , and subtends a right angle at the centre of the sphere . 586. COROLLARY II . The centre of any circle of a sphere is the foot of the perpendicular drawn from the centre of the sphere to the plane of the circle . 587. COROLLARY ...
Άλλες εκδόσεις - Προβολή όλων
Elementary Geometry, Plane and Solid; for Use in High Schools and Academies Thomas F 1859-1945 Holgate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
Elementary Geometry Plane and Solid: For Use in High Schools and Academies Thomas F. Holgate Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² adjacent angles altitude angle formed angles are equal apothem base bisector bisects centre chord coincide convex convex polygon COROLLARY DEFINITION diagonals diameter dicular dihedral angle draw equal angles equal in area equiangular equidistant equilateral triangle EXERCISES face angles figure given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal interior angles isosceles triangle length Let ABC line perpendicular magnitudes measure mid-point number of sides opposite sides pair parallel planes parallelepiped parallelogram perimeter perpen plane angles point of contact point of intersection polyhedral angle polyhedron prism Proof Prop Proposition VIII pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right angles right triangle segments side BC similar sphere square subtended supplementary angle surface tangent tetrahedron theorem triangle ABC triangle is equal trihedral vertex volume
Δημοφιλή αποσπάσματα
Σελίδα 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 230 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Σελίδα 55 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Σελίδα 76 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Σελίδα 43 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.
Σελίδα 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.
Σελίδα 27 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Σελίδα 200 - The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Σελίδα 229 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.