Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... Cylinder 147 The Cone 148 Polar Triangles The Sphere Spherical Polygons Symmetrical Spherical Polygons Reciprocal Theorems 150 156 157 160 161 · BOOK VIII . MEASUREMENT OF SOLIDS . Prisms and Cylinders Pyramids and Cones Surface of the ...
... Cylinder 147 The Cone 148 Polar Triangles The Sphere Spherical Polygons Symmetrical Spherical Polygons Reciprocal Theorems 150 156 157 160 161 · BOOK VIII . MEASUREMENT OF SOLIDS . Prisms and Cylinders Pyramids and Cones Surface of the ...
Σελίδα 146
... + ( I. , 35 , Cor . 1 ) . nz . ― • 4Rf = 2R ( 2e ) - 4Rf ( 10 , Cor . ) ; or , But hence S4R ( e - ƒ ) . e - f = v - 2 ( 10 ) : S4R ( v - 2 ) . BOOK VII . THE THREE ROUND BODIES . THE CYLINDER 146 [ BOOK VI . ELEMENTS OF GEOMETRY .
... + ( I. , 35 , Cor . 1 ) . nz . ― • 4Rf = 2R ( 2e ) - 4Rf ( 10 , Cor . ) ; or , But hence S4R ( e - ƒ ) . e - f = v - 2 ( 10 ) : S4R ( v - 2 ) . BOOK VII . THE THREE ROUND BODIES . THE CYLINDER 146 [ BOOK VI . ELEMENTS OF GEOMETRY .
Σελίδα 147
... CYLINDER . I. DEF . 1. The locus of the parallel lines drawn from all the points in the circumference of a circle to a plane parallel to that circle is a cylindrical surface ; * and the solid enclosed is a cylinder . DEF . 2. Any one of ...
... CYLINDER . I. DEF . 1. The locus of the parallel lines drawn from all the points in the circumference of a circle to a plane parallel to that circle is a cylindrical surface ; * and the solid enclosed is a cylinder . DEF . 2. Any one of ...
Σελίδα 148
... cylinder cut off by this plane . M m COR . 4. Every section of a cylinder made by a plane passing through an element is a parallelogram ; for a plane passing through an element , Aa , will cut the cir- cumference of the base in a second ...
... cylinder cut off by this plane . M m COR . 4. Every section of a cylinder made by a plane passing through an element is a parallelogram ; for a plane passing through an element , Aa , will cut the cir- cumference of the base in a second ...
Σελίδα 170
... ( cylinder ) is equal to the product of its base by its altitude . E / PROOF . A triangular prism is half a parallelopiped having a double base and the same altitude ( 2 , Cor . 1 ) hence the volume of a triangular prism is equal to the ...
... ( cylinder ) is equal to the product of its base by its altitude . E / PROOF . A triangular prism is half a parallelopiped having a double base and the same altitude ( 2 , Cor . 1 ) hence the volume of a triangular prism is equal to the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² adjacent angles altitude angles are equal anharmonic ratio bisect called centre chord circle circumference circumscribed polygon cone congruent construct cylinder diagonals diameter dihedrals distance divided draw equal altitudes equal bases equally distant equations equiangular EXERCISE exterior angle face angles formed frustum Geometry harmonically hence homologous HYPOTH infinite number inscribed angle intersection lateral edges line joining lines drawn locus middle point number of sides Olney's opposite sides P₁ parallel lines parallelogram parallelopiped pass perpendicular plane angle point of contact polar pole polyhedral polyhedron prism Problem PROOF proportional PROVED pyramid quadrilateral radical axis radii radius rectangle regular polygon right angles SCHOLIUM segments solid angle sphere spherical excess spherical polygon spherical triangle square straight line symmetrical tangent Theorem triangle ABC trihedrals vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 19 - IF two triangles have two sides of the one equal to two sides of the...
Σελίδα 34 - 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.
Σελίδα 14 - 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, &c.
Σελίδα 75 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Σελίδα 170 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.
Σελίδα 69 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.