Elements of Geometry: And the First Principles of Modern GeometrySheldon & Company, 1878 - 209 σελίδες |
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Σελίδα
... Polar Polyhedrals 132 BOOK VI . POLYHEDRONS 138 The Prism 139 Pyramids 141 Regular Polyhedrons . 143 BOOK VII . THE THREE ROUND BODIES . The Cylinder 147 The Cone 148 Polar Triangles The Sphere Spherical Polygons Symmetrical Spherical ...
... Polar Polyhedrals 132 BOOK VI . POLYHEDRONS 138 The Prism 139 Pyramids 141 Regular Polyhedrons . 143 BOOK VII . THE THREE ROUND BODIES . The Cylinder 147 The Cone 148 Polar Triangles The Sphere Spherical Polygons Symmetrical Spherical ...
Σελίδα 132
... polar polyhedral . COR . 2. The edges of a polyhedral are perpendicular to the faces of its polar angle ; for any edge , BM , is perpendicular to the plane passed through the lines that are drawn perpen- dicular to the faces , AMB and ...
... polar polyhedral . COR . 2. The edges of a polyhedral are perpendicular to the faces of its polar angle ; for any edge , BM , is perpendicular to the plane passed through the lines that are drawn perpen- dicular to the faces , AMB and ...
Σελίδα 134
... polar polyhedrals , the face angles of the one are the supplements of the dihedrals formed by the corre- sponding planes of the other . For if , at a point , M , in the edge , EF , of two faces of a poly- hedral , MA and MB be drawn ...
... polar polyhedrals , the face angles of the one are the supplements of the dihedrals formed by the corre- sponding planes of the other . For if , at a point , M , in the edge , EF , of two faces of a poly- hedral , MA and MB be drawn ...
Σελίδα 136
... polar trihedrals are equal each to each , being supplements of the equal dihedrals . ( 30 ) ; hence the dihedrals of the polar trihedrals are also equal ( 34 ) ; and the face angles of the given trihedrals are equal , being supplements ...
... polar trihedrals are equal each to each , being supplements of the equal dihedrals . ( 30 ) ; hence the dihedrals of the polar trihedrals are also equal ( 34 ) ; and the face angles of the given trihedrals are equal , being supplements ...
Σελίδα 159
... shown that the symmetrical spherical pyra- B mids , O - ABC and O - A'B'C ' , are equal : hence two symmetrical spherical pyramids are equal . POLAR TRIANGLES . B A XVI . DEF . If BOOK VII . ] 159 THE THREE ROUND BODIES .
... shown that the symmetrical spherical pyra- B mids , O - ABC and O - A'B'C ' , are equal : hence two symmetrical spherical pyramids are equal . POLAR TRIANGLES . B A XVI . DEF . If BOOK VII . ] 159 THE THREE ROUND BODIES .
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.