Elements of Synthetic Solid Geometry |
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Page viii
... circular cone . The latter half of this part is given to spheric geometry . The spheric figure ( tri- angle and polygon ) is considered as the section of a corner by a sphere whose centre is at the apex viii PREFACE .
... circular cone . The latter half of this part is given to spheric geometry . The spheric figure ( tri- angle and polygon ) is considered as the section of a corner by a sphere whose centre is at the apex viii PREFACE .
Page 63
... circular cone , and the line through the centre of the circle and the centre of the cone is the axis of the cone . The circular cone is a figure of revolution , and is the most important of all cones . The word ' cone ' as hereafter ...
... circular cone , and the line through the centre of the circle and the centre of the cone is the axis of the cone . The circular cone is a figure of revolution , and is the most important of all cones . The word ' cone ' as hereafter ...
Page 65
... circular cylinder is generated by one of a pair of parallel lines while revolving at a fixed distance about the ... circular cylinder twice , and only twice . Cor . 3. Sections of a circular cylinder normal to the axis are equal circles ...
... circular cylinder is generated by one of a pair of parallel lines while revolving at a fixed distance about the ... circular cylinder twice , and only twice . Cor . 3. Sections of a circular cylinder normal to the axis are equal circles ...
Page 76
... circular cone , the figure of intersection of the sphere and cone is a circle . 4. The centre locus of a sphere which touches a plane at a given point is a normal to the plane at the given point . 5. What is the centre locus of a sphere ...
... circular cone , the figure of intersection of the sphere and cone is a circle . 4. The centre locus of a sphere which touches a plane at a given point is a normal to the plane at the given point . 5. What is the centre locus of a sphere ...
Page 125
... circular and its radius ber , its area is π2 . And if h be the altitude of the cone , the vol . = } } πr2h . 134. The frustum of a cone is the limit of the frus- tum of a pyramid , and its volume is therefore h ( B + B ' + √BB ...
... circular and its radius ber , its area is π2 . And if h be the altitude of the cone , the vol . = } } πr2h . 134. The frustum of a cone is the limit of the frus- tum of a pyramid , and its volume is therefore h ( B + B ' + √BB ...
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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.