The Elements of Solid Geometry |
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Page vii
... figures and their relations in solid space . A short word has long been wanted for the decasyllabic " rectangular parallelepiped " : I am sanguine that the word " cuboid , " which I have here introduced , will meet with acceptance from ...
... figures and their relations in solid space . A short word has long been wanted for the decasyllabic " rectangular parallelepiped " : I am sanguine that the word " cuboid , " which I have here introduced , will meet with acceptance from ...
Page 3
... figure in the general sense of any combination of points , lines , surfaces , or solids , POST . 1. Any figure may be transferred from one position in space to another without change of shape or size . 3. If one point of a figure is ...
... figure in the general sense of any combination of points , lines , surfaces , or solids , POST . 1. Any figure may be transferred from one position in space to another without change of shape or size . 3. If one point of a figure is ...
Page 4
... figure , is determined , when the positions of three points upon it are given , but this does not exclude the possibility of some special line being determined . completely by two points . Accordingly we may state as the second ...
... figure , is determined , when the positions of three points upon it are given , but this does not exclude the possibility of some special line being determined . completely by two points . Accordingly we may state as the second ...
Page 5
... figure , being completely determined by the two points , remains unchanged in position , while the figure rotates about the two points . fixed . Hence an axis of rotation is a straight line . All the parts of a straight line are ...
... figure , being completely determined by the two points , remains unchanged in position , while the figure rotates about the two points . fixed . Hence an axis of rotation is a straight line . All the parts of a straight line are ...
Page 7
... two dimensions , and the 1 In the higher geometry such a line is termed a geodesic line . A simpler term seems desirable , at any rate in elementary geometry . geometry of points , lines , and figures on a PRELIMINARY DISCUSSION . 7.
... two dimensions , and the 1 In the higher geometry such a line is termed a geodesic line . A simpler term seems desirable , at any rate in elementary geometry . geometry of points , lines , and figures on a PRELIMINARY DISCUSSION . 7.
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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...