Essentials of Solid GeometryGinn & Company, 1924 - 238 σελίδες |
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Σελίδα
... SPHERE PAGE 1 19 41 51 95 103 ྴཋ བྲ སྤྲ 77 91 I. FUNDAMENTAL THEOREMS . 119 II . SPHERICAL POLYGONS 131 III . MENSURATION 143 IV . GENERAL REVIEW 159 vii SUPPLEMENT I. INCOMMENSURABLE CASE OF § 108 PAGE 169 II.
... SPHERE PAGE 1 19 41 51 95 103 ྴཋ བྲ སྤྲ 77 91 I. FUNDAMENTAL THEOREMS . 119 II . SPHERICAL POLYGONS 131 III . MENSURATION 143 IV . GENERAL REVIEW 159 vii SUPPLEMENT I. INCOMMENSURABLE CASE OF § 108 PAGE 169 II.
Σελίδα
... SPHERICAL TRIANGLES 183 IV . PRACTICAL MENSURATION 191 V. RECREATIONS 223 VI . HISTORY OF GEOMETRY 227 VII . IMPORTANT FORMULAS 233 INDEX 235 plus minus + SYMBOLS AND ABBREVIATIONS The following are the viii CONTENTS.
... SPHERICAL TRIANGLES 183 IV . PRACTICAL MENSURATION 191 V. RECREATIONS 223 VI . HISTORY OF GEOMETRY 227 VII . IMPORTANT FORMULAS 233 INDEX 235 plus minus + SYMBOLS AND ABBREVIATIONS The following are the viii CONTENTS.
Σελίδα 1
... spheres . In considering the theory of the subject we shall not need to construct the solid figures by means of the straight- edge and compasses , and hence we shall not discuss any problems of construction . 2. References to Plane ...
... spheres . In considering the theory of the subject we shall not need to construct the solid figures by means of the straight- edge and compasses , and hence we shall not discuss any problems of construction . 2. References to Plane ...
Σελίδα 118
... . and 113 in . respectively , revolve about their third sides . Find the ratio of the total areas of the solids generated and find their volumes . BOOK VIII OF GEOMETRY THE SPHERE I. FUNDAMENTAL THEOREMS 163. 118 BOOK VII CONES.
... . and 113 in . respectively , revolve about their third sides . Find the ratio of the total areas of the solids generated and find their volumes . BOOK VIII OF GEOMETRY THE SPHERE I. FUNDAMENTAL THEOREMS 163. 118 BOOK VII CONES.
Σελίδα 119
... sphere . The terms center , radius , chord , and diameter are used as in the case of the circle . This is the modern ... sphere as the solid inclosed by a spherical surface or spheric surface . In modern mathematics the volume of a ...
... sphere . The terms center , radius , chord , and diameter are used as in the case of the circle . This is the modern ... sphere as the solid inclosed by a spherical surface or spheric surface . In modern mathematics the volume of a ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABC and A'B'C altitude altitude h angles are equal axis bisects called chord circle circumscribed cone of revolution congruent conic surface Consider Ex Corollary corresponding cube cubic diagonal diameter dihedral angles distance Draw equivalent Exercises face angles Find the area Find the volume formed formula frustum given line given point Hence inches inscribed intersection isosceles lateral area lateral edges lateral faces line segment locus of points lower base measuring number of degrees oblique opposite parallel planes parallelogram perimeter perpendicular plane geometry plane passing pole polyhedral angles Proof Proposition Prove radii rectangular parallelepiped regular polygon regular polyhedrons regular pyramid right angles right circular cylinder Similarly slant height sphere of radius spherical degrees spherical excess spherical polygon spherical triangle straight line tangent tetrahedron Theorem third side total surface triangular prism trihedral upper base vertex vertices zone
Δημοφιλή αποσπάσματα
Σελίδα 7 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.
Σελίδα 40 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.
Σελίδα 176 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Σελίδα 10 - 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 15 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 77 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.
Σελίδα 3 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Σελίδα 24 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 16 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 15 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.