The Elements of Solid Geometry |
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... definitions , postulates , etc. , on which they rest , I have found it necessary to deviate somewhat from the usual sequence of propositions . Thus , I have grouped in the same section the prism and its limiting case , the cylinder ...
... definitions , postulates , etc. , on which they rest , I have found it necessary to deviate somewhat from the usual sequence of propositions . Thus , I have grouped in the same section the prism and its limiting case , the cylinder ...
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... DEFINITIONS : LINES AND PLANES PROPOSITIONS I. TO XII . DEFINITIONS : DIEDRAL ANGLES DEFINITIONS : POLYEDRAL ANGLES EXERCISES PAGE 1 2-15 9 11 16 SECTION II . SOLIDS PRISMS AND CYLINDERS . DEFINITIONS : PRISMS PROPOSITIONS XIII . TO ...
... DEFINITIONS : LINES AND PLANES PROPOSITIONS I. TO XII . DEFINITIONS : DIEDRAL ANGLES DEFINITIONS : POLYEDRAL ANGLES EXERCISES PAGE 1 2-15 9 11 16 SECTION II . SOLIDS PRISMS AND CYLINDERS . DEFINITIONS : PRISMS PROPOSITIONS XIII . TO ...
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... DEFINITIONS : PARTS OF THE SPHERE DEFINITIONS : THE LUNE , ETC. EXERCISES 54 70 74 SECTION V REGULAR POLYEDRONS . DEFINITIONS PROPOSITION XLIII .. 76 CONSTRUCTION : - REGULAR POLYEDRONS 25 76 77 SECTION VI . MENSURATION : SOLIDS AND ...
... DEFINITIONS : PARTS OF THE SPHERE DEFINITIONS : THE LUNE , ETC. EXERCISES 54 70 74 SECTION V REGULAR POLYEDRONS . DEFINITIONS PROPOSITION XLIII .. 76 CONSTRUCTION : - REGULAR POLYEDRONS 25 76 77 SECTION VI . MENSURATION : SOLIDS AND ...
Page 1
... DEFINITIONS . 1. A plane is a surface such that , if a straight line be passed through any two of its points , the line will lie wholly in the surface . When a line lies wholly in a plane , it may be said of the plane that it passes ...
... DEFINITIONS . 1. A plane is a surface such that , if a straight line be passed through any two of its points , the line will lie wholly in the surface . When a line lies wholly in a plane , it may be said of the plane that it passes ...
Page 9
... DEFINITIONS . 28. A diedral angle is the angle between two planes which intersect each other . 29. The line in which the planes intersect is called the edge of the angle ; the planes themselves are called the faces of the angle . 30 ...
... DEFINITIONS . 28. A diedral angle is the angle between two planes which intersect each other . 29. The line in which the planes intersect is called the edge of the angle ; the planes themselves are called the faces of the angle . 30 ...
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Common terms and phrases
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle EDC-O equal with respect equivalent faces is called feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA lune MN and PQ mutually equal O-ABCD oblique parallelopiped parallel planes parallelogram pass perimeter perpen perpendicular to MN plane angle plane MN plane PQ polar triangle polyedral angle prisms whose bases radii radius regular polyedrons regular polygon right angles right circular cone right prism right section SCHOLIUM sides slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tetraedron THEOREM triangles ABC triangular prism triangular pyramids triedral
Popular passages
Page 48 - Assuming that 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...
Page 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 4 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Page 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Page 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 56 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.