The Elements of Plane and Solid Geometry ...D. Van Nostrand Company, 1890 - 393 Seiten |
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Seite 286
... volume of a solid is its numerical measure ( 229 ) , referred to some other solid called the unit of vol- ите . 572. Two solids are equivalent when they have equal volumes . 573. Two polygons are said to be parallel when their sides are ...
... volume of a solid is its numerical measure ( 229 ) , referred to some other solid called the unit of vol- ите . 572. Two solids are equivalent when they have equal volumes . 573. Two polygons are said to be parallel when their sides are ...
Seite 297
... 'c ' Q.E.D. EXERCISE . Find the ratio of two rectangular parallelopipeds whose dimensions are 4 , 7 , 9 , and 6 , 14 , 15 , respectively . Proposition 11. Theorem . 606. The volume of a rectangular BOOK VII . - PARALLELOPIPEDS . 297.
... 'c ' Q.E.D. EXERCISE . Find the ratio of two rectangular parallelopipeds whose dimensions are 4 , 7 , 9 , and 6 , 14 , 15 , respectively . Proposition 11. Theorem . 606. The volume of a rectangular BOOK VII . - PARALLELOPIPEDS . 297.
Seite 298
... volume . To prove Proof . P = abc . Р ( 584 ) ахъхс p C P 1 = Q = abc . 1 x 1 x 1 ( 605 ) But since Q is the unit of volume , P Q = the volume of P. volume of P = abc . ( 571 ) Q. E.D. 607. SCH . The statement of this theorem is an ...
... volume . To prove Proof . P = abc . Р ( 584 ) ахъхс p C P 1 = Q = abc . 1 x 1 x 1 ( 605 ) But since Q is the unit of volume , P Q = the volume of P. volume of P = abc . ( 571 ) Q. E.D. 607. SCH . The statement of this theorem is an ...
Seite 299
... volume of a rectangular parallelopiped is equal to the product of its base and altitude . 609. COR . 2. The volume of a cube is the third power of its edge , being the product of three equal factors ; if the edge is 1 , the volume is 1 ...
... volume of a rectangular parallelopiped is equal to the product of its base and altitude . 609. COR . 2. The volume of a cube is the third power of its edge , being the product of three equal factors ; if the edge is 1 , the volume is 1 ...
Seite 301
... volume of the given prism is the sum of the volumes of the triangular prisms , that is , the sum of their bases , or ... VOLUME OF A PRISM . 301.
... volume of the given prism is the sum of the volumes of the triangular prisms , that is , the sum of their bases , or ... VOLUME OF A PRISM . 301.
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Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD adjacent angles altitude angles are equal base bisect bisector centre chord circumference circumscribed coincide cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equilateral triangle equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 prove Proof pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Beliebte Passagen
Seite 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Seite 188 - 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.
Seite 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Seite 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Seite 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Seite 57 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Seite 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Seite 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.
Seite 378 - The circumferences of the sections made by the planes are called the bases of the zone, and the distance between the planes is the altitude of the zone.