Elements of GeometryMacmillan Company, 1897 - Geometry |
From inside the book
Results 1-5 of 16
Page xi
... Cones . Surface of a sphere Zone • Lune CHAPTER X. 188 188 189 192 CHAPTER XI . 205 CHAPTER XII . 210 210 213 219 227 229 230 231 232 Area of a spherical triangle Areas of similar surfaces . CHAPTER XIII . Volume of a prism Volume of a ...
... Cones . Surface of a sphere Zone • Lune CHAPTER X. 188 188 189 192 CHAPTER XI . 205 CHAPTER XII . 210 210 213 219 227 229 230 231 232 Area of a spherical triangle Areas of similar surfaces . CHAPTER XIII . Volume of a prism Volume of a ...
Page 220
... cone , * and the perpendicular is called the axis of the cone . In all cones the surface is not limited in extent , but for certain purposes limited por- tions may be considered . FIG . 312 . Any plane section may be taken as the base ...
... cone , * and the perpendicular is called the axis of the cone . In all cones the surface is not limited in extent , but for certain purposes limited por- tions may be considered . FIG . 312 . Any plane section may be taken as the base ...
Page 221
... cone will pass through the ver- tex , and if one nappe is entirely on one side of the tan- gent plane , the other nappe will be on the other side . Exercise . Show that all plane sections parallel to the base of a right circular cone ...
... cone will pass through the ver- tex , and if one nappe is entirely on one side of the tan- gent plane , the other nappe will be on the other side . Exercise . Show that all plane sections parallel to the base of a right circular cone ...
Page 223
... middle section , and that the area of the frustum may be described as the circumference of the middle section by the slant height : * ( " + R ) s . F = 2π 2 3. Find an algebraic expression ( formula ) for the THE CONE . 223.
... middle section , and that the area of the frustum may be described as the circumference of the middle section by the slant height : * ( " + R ) s . F = 2π 2 3. Find an algebraic expression ( formula ) for the THE CONE . 223.
Page 225
... cone or of a frustum of a cone may be considered as generated by a circle , the plane of which moves parallel to itself and the radius of which varies as its distance from a given point . For if we have a right circular cone or frustum ...
... cone or of a frustum of a cone may be considered as generated by a circle , the plane of which moves parallel to itself and the radius of which varies as its distance from a given point . For if we have a right circular cone or frustum ...
Other editions - View all
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.