The Elements of Solid Geometry |
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Page 4
... completely by two points . Accordingly we may state as the second postulate of Geometry : POST . 2. For any two given points there is a line passing through both which is completely determined , both as to form and position , by the two ...
... completely by two points . Accordingly we may state as the second postulate of Geometry : POST . 2. For any two given points there is a line passing through both which is completely determined , both as to form and position , by the two ...
Page 5
... completely determined by the two points and by nothing else , there would be nothing to distinguish between such lines , or they would be identically the same . A straight line must be indefinitely extended in both . senses , for to ...
... completely determined by the two points and by nothing else , there would be nothing to distinguish between such lines , or they would be identically the same . A straight line must be indefinitely extended in both . senses , for to ...
Page 7
... completely by three points ( not in the same straight line ) is the circle . 7. SURFACES . If two points are taken on a surface , of all the lines that can be drawn on the surface through the two points there must always be one , and in ...
... completely by three points ( not in the same straight line ) is the circle . 7. SURFACES . If two points are taken on a surface , of all the lines that can be drawn on the surface through the two points there must always be one , and in ...
Page 8
... completely determined by three points in it , provided they are not in the same straight line ; or in other words , there is one , and only one , plane passing through three given points , not in the same straight line . This property ...
... completely determined by three points in it , provided they are not in the same straight line ; or in other words , there is one , and only one , plane passing through three given points , not in the same straight line . This property ...
Page 9
... completely by A , B , C must occupy the same position as before , and then the part of it within the triangle PQR exactly concides with the part within ABC . 9. The two - dimensional geometry of lines and points in a plane is known as ...
... completely by A , B , C must occupy the same position as before , and then the part of it within the triangle PQR exactly concides with the part within ABC . 9. The two - dimensional geometry of lines and points in a plane is known as ...
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Common terms and phrases
ABCD angle ACB axis bisected central symmetry centre centre of symmetry circle Crown 8vo cuboid diameter dihedral angle direct line distance drawn Elementary equal bases equally inclined Euclid exterior angle finite four right angles frustrum given line given point Globe 8vo greater Hence less lines joining lines of intersection lune meets the plane middle point number of faces number of sides pair parallel planes perpendicular plane BOC plane faces plane geometry plane parallel plane triangle planes are parallel polar triangle polygon polyhedra polyhedron position prism projection Q. E. D. COR Q. E. D. THEOREM quadrant ratio regular regular polyhedron six right solid angles solid figure Solid Geometry space sphere spherical excess spherical surface spherical triangle Spherical Trigonometry straight line superposable supplementary symmetrical with respect termed tetrahedron three planes triangle ABC vertex volume
Popular passages
Page 130 - ... equal, then the angles opposite to the other pair of equal sides are either equal or supplementary, and in the former case the triangles are identically equal.
Page 120 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...