Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page xi
... spherical triangle Areas of similar surfaces . CHAPTER XIII . Volume of a prism Volume of a pyramid Prismoidal formula Truncated prism Volume of a sphere Volumes of similar figures 236 • 241 · 245 246 • 249 • 251 PAGE 254 254 262 264 ...
... spherical triangle Areas of similar surfaces . CHAPTER XIII . Volume of a prism Volume of a pyramid Prismoidal formula Truncated prism Volume of a sphere Volumes of similar figures 236 • 241 · 245 246 • 249 • 251 PAGE 254 254 262 264 ...
Page xiii
George Cunningham Edwards. Angle . Angles . SYMBOLS . A , Plane triangle . A , Plane triangles . = Equals , or is equal ... Spherical triangle . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) ...
George Cunningham Edwards. Angle . Angles . SYMBOLS . A , Plane triangle . A , Plane triangles . = Equals , or is equal ... Spherical triangle . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) ...
Page 192
... triangle ( sph . A ) . If through the vertices ( A , B , and C ) of a spherical triangle , diameters be drawn , their other extremities ( P , Q , and R ) determine a ... sphere through A 192 ELEMENTS OF GEOMETRY . Spherical triangles.
... triangle ( sph . A ) . If through the vertices ( A , B , and C ) of a spherical triangle , diameters be drawn , their other extremities ( P , Q , and R ) determine a ... sphere through A 192 ELEMENTS OF GEOMETRY . Spherical triangles.
Page 193
... spherical triangle is isosceles , it may be brought to coincide with its symmetrical . NOTE . In general the spherical triangles that are symmetrical cannot be superimposed , because the equal parts are not arranged in the same order ...
... spherical triangle is isosceles , it may be brought to coincide with its symmetrical . NOTE . In general the spherical triangles that are symmetrical cannot be superimposed , because the equal parts are not arranged in the same order ...
Page 194
... spherical triangle . Hence the Demonstration . -The diameters through Q , M , and B determine the symmetrical sph . A Q'M'B ' . Then if the symmetrical sph . A Q'M'B ' be caused to slide over the surface of the sphere , rotating 180 ...
... spherical triangle . Hence the Demonstration . -The diameters through Q , M , and B determine the symmetrical sph . A Q'M'B ' . Then if the symmetrical sph . A Q'M'B ' be caused to slide over the surface of the sphere , rotating 180 ...
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Common terms and phrases
altitude angle bisector apothem auxiliary line axiom axis base bisect called centre changes of direction chord circumference coincide complete rotation congruent construct convex corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equal angles equally distant figure Find the locus fixed point frustum Geometry given circle given line given point greater hyperbola hypothenuse infinite number inscribed polygon interior angles isosceles joining lines be drawn lines forming Lune middle point NOTE number of sides oblique parabola parallelogram parallelopiped pass perimeter perpen perpendicular bisector Plane Geometry point of intersection position prism PROBLEM pyramid Q. E. D. Exercises quadrangle radii radius ratio rectangle regular polygon relations represent right angle right circular cone right triangle secant plane Show side opposite sphere spherical triangle square subtended surface THEOREM three sides triangular prism triedral vertex vertices volume
Popular passages
Page 25 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 26 - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.
Page 17 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 293 - SUITABLE FOR USE IN PREPARATORY SCHOOLS. SELECTED FROM THE LISTS OF THE MACMILLAN COMPANY, Publishers. ARITHMETIC FOR SCHOOLS. By JB LOCK, Author of " Trigonometry for Beginners" "Elementary Trigonometry" etc Edited and Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math.
Page 172 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 172 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x- and z-axes equals 4.
Page 100 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.