Elements of Synthetic Solid Geometry |
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Page 8
... axes of space , and their planes are the rectangular co - ordi- nate planes of space . These three lines admit of length measures in three directions , each perpendicular to the other two . Hence , space is said to be of three dimen ...
... axes of space , and their planes are the rectangular co - ordi- nate planes of space . These three lines admit of length measures in three directions , each perpendicular to the other two . Hence , space is said to be of three dimen ...
Page 30
... axes of the dihedral angles are its edges ; the planes LOM , MON , NOK , and KOL are its faces ; and the angles LOM , MON , NOK , and KOL are its face - angles . The term corner or solid angle does not involve any particular length of ...
... axes of the dihedral angles are its edges ; the planes LOM , MON , NOK , and KOL are its faces ; and the angles LOM , MON , NOK , and KOL are its face - angles . The term corner or solid angle does not involve any particular length of ...
Page 86
... axes of space ( Art . 8. Def . 1 ) , OA is the pro- jection of OP on OX , OB is the projection of OP on OY , and OC , of OP on OZ . Therefore , the square on any line - segment is equal to the sum of the squares of the projections of ...
... axes of space ( Art . 8. Def . 1 ) , OA is the pro- jection of OP on OX , OB is the projection of OP on OY , and OC , of OP on OZ . Therefore , the square on any line - segment is equal to the sum of the squares of the projections of ...
Page 87
Nathan Fellowes Dupuis. with the axes ; or when we are given the length of the projections of OP upon the axes . For the projections are the direction edges of a cuboid of which OP is the diagonal . This is the fundamental principle ...
Nathan Fellowes Dupuis. with the axes ; or when we are given the length of the projections of OP upon the axes . For the projections are the direction edges of a cuboid of which OP is the diagonal . This is the fundamental principle ...
Page 95
... axes of these pencils may be denoted by L1239 L1249 L134 , and L234 ; L123 being the common line to U12 , U23 , and U31 . Cor . 3. The line L123 meets the plane U1 in one point only , and it evidently meets U24 and U in the same point ...
... axes of these pencils may be denoted by L1239 L1249 L134 , and L234 ; L123 being the common line to U12 , U23 , and U31 . Cor . 3. The line L123 meets the plane U1 in one point only , and it evidently meets U24 and U in the same point ...
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Common terms and phrases
AB² altitude axis base bisect bisector centroid chord circle circular cone common line complanar congruent conic cos² cube cuboid curve cylinder cylindroid denote diagonals diameter dihedral angles draw ellipse equal face angles form a sheaf four frustum given line given point Hence hyperbola infinity intersection isoclinal line join line-segment locus mean centre median meet middle point mon line non-complanar lines normal number of faces octahedron opposite parabola parallel lines parallelepiped parallelogram pass perpendicular planar line plane figure plane geometry point equidistant polygon polyhedra polyhedron prism prismatoid projection Proof pyramid radius rectangle regular tetrahedron right angle right section right-bisector plane secant line segment sheaf of lines sides skew quadrilateral spatial figure spheric geometry spheric line spheric triangle squares surface tangent line Theorem three-faced corner vertex vertices volume
Popular passages
Page 236 - To the many of my fellow-teachers in America who have questioned me in regard to the Non-Euclidean Geometry, I would now wish to say publicly that Dr. Smith's conception of that profound advance in pure science is entirely sound. . . . Dr. Smith has given us a book of which our country can be proud. I think it the duty of every teacher of geometry to examine it carefully."— From Prof.
Page 237 - OF EUCLID'S ELEMENTS. Including Alternative Proofs, together with additional Theorems and Exercises, classified and arranged. By HS HALL, MA, and FH STEVENS, MA, Masters of the Military and Engineering Side, Clifton College. Gl.
Page 67 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 1 - The projection of a line on a plane is the locus of the projections of all its points.
Page 234 - ... University of Ohio, of Pennsylvania, of Michigan, of Wisconsin, of Kansas, of California, of Missouri, Stanford University, etc., etc. "Those acquainted with Mr. Smith's text-books on conic sections and solid geometry will form a high expectation of this work, and we do not think they will be disappointed. Its style is clear and neat, it gives alternative proofs of most of the fundamental theorems, and abounds in practical hints, among which we may notice those on the resolution of expressions...
Page 238 - AND BESSEL'S FUNCTIONS. Crown 8vo. IQJ. 6d. WILSON (JM)— ELEMENTARY GEOMETRY. Books I. to V. Containing the Subjects of Euclid's first Six Books. Following the Syllabus of the Geometrical Association. By JM WILSON, MA, Head Master of Clifton College. New Edition. Extra fcap. 8vo. 4*.
Page 237 - RICHARDSON.— THE PROGRESSIVE EUCLID. Books I. and II. With Notes, Exercises, and Deductions. Edited by AT RICHARDSON, MA, Senior Mathematical Master at the Isle of Wight College.
Page 97 - S'-A'B'C' be two triangular pyramids having equivalent bases situated in the same plane, and equal altitudes. To prove that S-ABC =c= S'-A'B'C'. Proof. Divide the altitude into n equal parts, and through the points of division pass planes parallel to the plane of the bases, forming the sections DEF, GHI, etc., D'E'F', G'H'I', etc. In the pyramids S-ABC and S'-A'B'C' inscribe prisms whose upper bases are the sections DEF, GHI, etc., D'E'F', G'H'I', etc.
Page 234 - GEOMETRY. 12mo. $2.60. WORKS BY ISAAC TODHUNTER, FRS Late Principal Lecturer on Mathematics in St. John's College. PLANE CO-ORDINATE GEOMETRY, As Applied to the Straight Line and the Conic Sections.