The Elements of GeometryMacmillan, 1886 - 366 Seiten |
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Seite vi
... Spherical Geometry on the lines of my teaching , which I have followed in Book IX . The figures , which I think give this geometry a special advantage , owe all their beauty to my colleague , Professor A. V. Lane , who has given them ...
... Spherical Geometry on the lines of my teaching , which I have followed in Book IX . The figures , which I think give this geometry a special advantage , owe all their beauty to my colleague , Professor A. V. Lane , who has given them ...
Seite xiii
... sphere • · PAGE 243 , 244 • 245 246-248 Intersecting spheres Sphere and tetrahedron . Globe and globe - segment de- fined · · • 631 , 632 . 240 633-639 . .240 640 , 641 . 613 , 614. Plane and sphere 615,616 . Great circle and small ...
... sphere • · PAGE 243 , 244 • 245 246-248 Intersecting spheres Sphere and tetrahedron . Globe and globe - segment de- fined · · • 631 , 632 . 240 633-639 . .240 640 , 641 . 613 , 614. Plane and sphere 615,616 . Great circle and small ...
Seite xiv
... sphere .. 258 705-707 . 657-662 . Fundamental properties , 258,259 663-666 . Definitions 708-719 . Polar triangles . . Spherical triangles · 272 , 273 • 274-280 259 720 , 721 . Loci 280 , 281 667-675 . Assumptions with corolla- 722,723 ...
... sphere .. 258 705-707 . 657-662 . Fundamental properties , 258,259 663-666 . Definitions 708-719 . Polar triangles . . Spherical triangles · 272 , 273 • 274-280 259 720 , 721 . Loci 280 , 281 667-675 . Assumptions with corolla- 722,723 ...
Seite xv
... sphere . Zone • · • • • PAGE 323-325 • · 325 • 326 326-329 • 330 331 · 322 · ARTICLE CHAPTER IV . SPACE ANGLES . 836 ... spherical triangle or 842. Spherical pyramid • 333 polygon . · 336 • • 855 , 856 . 857 . 858 , CONTENTS . XV.
... sphere . Zone • · • • • PAGE 323-325 • · 325 • 326 326-329 • 330 331 · 322 · ARTICLE CHAPTER IV . SPACE ANGLES . 836 ... spherical triangle or 842. Spherical pyramid • 333 polygon . · 336 • • 855 , 856 . 857 . 858 , CONTENTS . XV.
Seite 241
... sphere , perpendicular to its plane , passes through the cen- ter of the sphere . 615. A Great Circle of a sphere is any section of the sphere made by a plane which passes through the center . All other circles on the sphere are called ...
... sphere , perpendicular to its plane , passes through the cen- ter of the sphere . 615. A Great Circle of a sphere is any section of the sphere made by a plane which passes through the center . All other circles on the sphere are called ...
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Häufige Begriffe und Wortgruppen
ABCD alternate angles altitude angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY cross-ratio describe diagonals diameter divided draw equal are congruent equal sects equiangular equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior intersecting lines isosceles triangle less locus magnitudes meet mid-point multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN prismatoid PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal rhombus right angle Rule of Inversion sect joining segment sides equal sphere spherical polygon square straight angle subtended supplemental surface symmetrical tangent THEOREM THEOREM VIII three sides transversal triangles are congruent vertex
Beliebte Passagen
Seite 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Seite 112 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Seite 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Seite 190 - 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.
Seite 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Seite 13 - An Acute Angle is one which is less than a right angle.
Seite 104 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Seite 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Seite 103 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.