Elementary GeometryJ.B. Lippincott Company, 1893 |
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Σελίδα 238
... PYRAMIDS . S 36. Definitions . A pyramid is a polyedron bounded by a polygon and triangular faces formed by the intersections of planes passed through the sides of the polygon and a common point out of its plane ; as S - ABCDE . The ...
... PYRAMIDS . S 36. Definitions . A pyramid is a polyedron bounded by a polygon and triangular faces formed by the intersections of planes passed through the sides of the polygon and a common point out of its plane ; as S - ABCDE . The ...
Σελίδα 241
... pyramids have equal altitudes and equivalent bases , sections made by planes parallel to their bases and at equal distances from their vertices are equivalent . PROPOSITION XIV . - THEOREM . 42. The lateral area of a regular pyramid is ...
... pyramids have equal altitudes and equivalent bases , sections made by planes parallel to their bases and at equal distances from their vertices are equivalent . PROPOSITION XIV . - THEOREM . 42. The lateral area of a regular pyramid is ...
Σελίδα 244
... pyramids . In the pyramid S - ABC inscribe a series of prisms whose upper bases are the sections DEF , GHI , etc. , and in the pyramid S ' - A'B'C ' inscribe a series of prisms whose upper bases are the sections D'E'F ' , G'H'I ' , etc ...
... pyramids . In the pyramid S - ABC inscribe a series of prisms whose upper bases are the sections DEF , GHI , etc. , and in the pyramid S ' - A'B'C ' inscribe a series of prisms whose upper bases are the sections D'E'F ' , G'H'I ' , etc ...
Σελίδα 245
... pyramid S ' - A'B'C ' , as its limit ( Proposition XV . ) . Therefore , by III . , Theorem of Limits , these volumes are equal . PROPOSITION XVII . - THEOREM . Jean си 46. A triangular pyramid is one - third of a triangular prism of the ...
... pyramid S ' - A'B'C ' , as its limit ( Proposition XV . ) . Therefore , by III . , Theorem of Limits , these volumes are equal . PROPOSITION XVII . - THEOREM . Jean си 46. A triangular pyramid is one - third of a triangular prism of the ...
Σελίδα 246
... pyramid is equal to one - third of the product of its base by its altitude . For any pyramid , S - ABCDE , may be di- vided into triangular pyramids by passing planes through an edge SA and the diagonals AD , AC , etc. , of its base ...
... pyramid is equal to one - third of the product of its base by its altitude . For any pyramid , S - ABCDE , may be di- vided into triangular pyramids by passing planes through an edge SA and the diagonals AD , AC , etc. , of its base ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Δημοφιλή αποσπάσματα
Σελίδα 127 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Σελίδα 131 - Two triangles having 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 245 - 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 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Σελίδα 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Σελίδα 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Σελίδα 34 - The sum of the three angles of any triangle is equal to two right angles.