The Elements of Plane and Solid Geometry ...D. Van Nostrand Company, 1890 - 393 páginas |
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Página 287
... parallelopiped is a prism whose bases are parallelograms : hence all the faces are parallelograms . 581. A right parallelopiped is one whose lateral edges are perpendicular to the bases : hence the lateral faces are rectangles . 582. A ...
... parallelopiped is a prism whose bases are parallelograms : hence all the faces are parallelograms . 581. A right parallelopiped is one whose lateral edges are perpendicular to the bases : hence the lateral faces are rectangles . 582. A ...
Página 293
... parallelopiped is equal to the sum of the squares of the three edges meeting at any vertex . For , if AG is a rectangular parallelopiped , the rt . As ACG , ABC give AG = 2 AC2 + CG2 = AB2 + BC2 + BF2 . 599. SCH . The point O through ...
... parallelopiped is equal to the sum of the squares of the three edges meeting at any vertex . For , if AG is a rectangular parallelopiped , the rt . As ACG , ABC give AG = 2 AC2 + CG2 = AB2 + BC2 + BF2 . 599. SCH . The point O through ...
Página 295
... parallelopiped P will be divided into m , and Q into n , parallelopipeds , all equal to one another . ( 588 ) ... P : Q = m : n ; and ... P : Q = AB : CD . Q.E.D. The case in which the altitudes AB and CD are incom- mensurable , is ...
... parallelopiped P will be divided into m , and Q into n , parallelopipeds , all equal to one another . ( 588 ) ... P : Q = m : n ; and ... P : Q = AB : CD . Q.E.D. The case in which the altitudes AB and CD are incom- mensurable , is ...
Página 297
... parallelopipeds whose dimensions are a , b , c , and a ' , b ' , c ' , respectively . To prove Р abc = Q a'b'c ' Proof . Make a third rectangu- lar parallelopiped R whose dimen- sions are a ' , b ' , and c . Then , because P and R have ...
... parallelopipeds whose dimensions are a , b , c , and a ' , b ' , c ' , respectively . To prove Р abc = Q a'b'c ' Proof . Make a third rectangu- lar parallelopiped R whose dimen- sions are a ' , b ' , and c . Then , because P and R have ...
Página 298
... parallelopiped is equal to the product of its three dimensions . Hyp . Let P be the rectangular parallelopiped , a , b , and c its dimen- sions , and let Q be the cube whose edge is the linear unit . Q then is the unit of volume . To ...
... parallelopiped is equal to the product of its three dimensions . Hyp . Let P be the rectangular parallelopiped , a , b , and c its dimen- sions , and let Q be the cube whose edge is the linear unit . Q then is the unit of volume . To ...
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Otras ediciones - Ver todas
ELEMENTS OF PLANE & SOLID GEOM Edward a. (Edward Albert) 1845 Bowser Sin vista previa disponible - 2016 |
ELEMENTS OF PLANE & SOLID GEOM Edward a. (Edward Albert) 1845 Bowser Sin vista previa disponible - 2016 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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'.
Página 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.