Plane and Solid Geometry |
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Σελίδα 251
The edge is the line of intersection , and the faces are the intersecting planes .
Thus , in the diedral angle formed by the planes AC and BE , BC is the edge and
AC and BE are the faces . 493 . A diedral angle may be designated by two letters
...
The edge is the line of intersection , and the faces are the intersecting planes .
Thus , in the diedral angle formed by the planes AC and BE , BC is the edge and
AC and BE are the faces . 493 . A diedral angle may be designated by two letters
...
Σελίδα 252
The plane angle of a diedral angle is the angle formed by perpendiculars to the
edge at some point , one in each face . ... The size of a diedral angle does not
depend upon the extent of its faces , but upon the difference of their positions .
495 .
The plane angle of a diedral angle is the angle formed by perpendiculars to the
edge at some point , one in each face . ... The size of a diedral angle does not
depend upon the extent of its faces , but upon the difference of their positions .
495 .
Σελίδα 258
Every point in a plane bisecting a diedral angle is equidistant from the faces of
the angle . Hyp . Plane CB bisects diedral Z ABED , and FG and FH are the
respective distances of a point F in BC , from AB and BD . To prove FH = FG .
Proof .
Every point in a plane bisecting a diedral angle is equidistant from the faces of
the angle . Hyp . Plane CB bisects diedral Z ABED , and FG and FH are the
respective distances of a point F in BC , from AB and BD . To prove FH = FG .
Proof .
Σελίδα 262
516 . Der . The vertex of a polyedral angle is the common point in which the
planes meet ; the edges are the intersections of the planes ; the faces are the
planes bounded by the edges ; and the face angles are the angles formed by the
edges .
516 . Der . The vertex of a polyedral angle is the common point in which the
planes meet ; the edges are the intersections of the planes ; the faces are the
planes bounded by the edges ; and the face angles are the angles formed by the
edges .
Σελίδα 263
Two polyedral angles are equal if the face and diedral angles of the one are
respectively equal to the face and diedral angles of the other one , and all the
parts are arranged in the same order ( for evidently they can be made to coincide
) .
Two polyedral angles are equal if the face and diedral angles of the one are
respectively equal to the face and diedral angles of the other one , and all the
parts are arranged in the same order ( for evidently they can be made to coincide
) .
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle angles are equal base bisect bisector called chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divide draw drawn equal equidistant equivalent exterior angle faces figure Find formed four frustum geometrical given circle given line given point greater Hence homologous hypotenuse inches included inscribed intersecting isosceles triangle lateral edges length less limit line joining measured median meet midpoints opposite sides parallel parallel lines parallelogram passing perimeter perpendicular plane polyedron polygon prism PROBLEM Proof PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle School segments sides similar sphere spherical triangle square straight line surface tangent THEOREM third transform triangle triangle are equal vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 45 - 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.
Σελίδα 119 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 180 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Σελίδα 250 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 297 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 105 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference, intersecting the given circumference in B and C.
Σελίδα 276 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =s= GM'. Proof. The lateral edges of GM
Πληροφορίες βιβλιογραφίας
| Τίτλος | Plane and Solid Geometry Plane and Solid Geometry, Frank Louis Sevenoak |
| Συγγραφείς | Arthur Schultze, Frank Louis Sevenoak |
| Εκδότης | Macmillan, 1902 |
| Μέγεθος | 370 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |