Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page xi
... sphere Plane sections of a sphere . Spherical arcs Spherical triangles Triedrals Prisms Pyramids Cylinders Cones . Surface of a sphere Zone • Lune CHAPTER X. 188 188 189 192 CHAPTER XI . 205 CHAPTER XII . 210 210 213 219 227 229 230 231 ...
... sphere Plane sections of a sphere . Spherical arcs Spherical triangles Triedrals Prisms Pyramids Cylinders Cones . Surface of a sphere Zone • Lune CHAPTER X. 188 188 189 192 CHAPTER XI . 205 CHAPTER XII . 210 210 213 219 227 229 230 231 ...
Page xiii
... Spherical triangle . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) . Q. E. F. , Quod Erat Faciendum ( which was to be done ) . Hence . INTRODUCTION . GEOMETRY had its origin , as the name.
... Spherical triangle . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) . Q. E. F. , Quod Erat Faciendum ( which was to be done ) . Hence . INTRODUCTION . GEOMETRY had its origin , as the name.
Page 172
... sphere enveloping the lesser light . The diameter of the sphere is determined by the distance apart of the luminous points and by the ratio m ÷ n . This problem is very prettily handled by the methods of the Analytic Geometry . 137 ...
... sphere enveloping the lesser light . The diameter of the sphere is determined by the distance apart of the luminous points and by the ratio m ÷ n . This problem is very prettily handled by the methods of the Analytic Geometry . 137 ...
Page 175
George Cunningham Edwards. SOLID AND SPHERICAL GEOMETRY . CHAPTER IX . The first eight chapters of this work have dealt chiefly with the relations of figures in a single plane . The remainder , making use of what has been developed in ...
George Cunningham Edwards. SOLID AND SPHERICAL GEOMETRY . CHAPTER IX . The first eight chapters of this work have dealt chiefly with the relations of figures in a single plane . The remainder , making use of what has been developed in ...
Page 188
... sphere ; it will also be in the secant plane because FP will be . The point P will therefore move over the line of intersection of the two surfaces . But the locus of a point in a plane at 188 CHAPTER X A sphere Plane sections of a sphere.
... sphere ; it will also be in the secant plane because FP will be . The point P will therefore move over the line of intersection of the two surfaces . But the locus of a point in a plane at 188 CHAPTER X A sphere Plane sections of a sphere.
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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.