Elements of Geometry |
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Page xi
... Prisms Pyramids Cylinders Cones . Surface of a sphere Zone Lune Area of a spherical triangle Areas of similar surfaces CHAPTER XIII . Volume of a prism 236 Volume of a pyramid 241 Prismoidal formula 245 Truncated prism 246 Volume of a ...
... Prisms Pyramids Cylinders Cones . Surface of a sphere Zone Lune Area of a spherical triangle Areas of similar surfaces CHAPTER XIII . Volume of a prism 236 Volume of a pyramid 241 Prismoidal formula 245 Truncated prism 246 Volume of a ...
Page 210
... prism . 4. If any number of planes intersect in . parallel lines , and these parallel lines be inter- FIG . 292 . sected by two parallel planes , the enclosed portion of 210 CHAPTER XII Prisms Pyramids.
... prism . 4. If any number of planes intersect in . parallel lines , and these parallel lines be inter- FIG . 292 . sected by two parallel planes , the enclosed portion of 210 CHAPTER XII Prisms Pyramids.
Page 214
... prism will be formed ; the vol- ume of which will be less than the volume of the cylinder ; and the area of the bases of which will be less than the area of the bases of the cylinder . 7. If under the same con- FIG . 301 . ditions as in ...
... prism will be formed ; the vol- ume of which will be less than the volume of the cylinder ; and the area of the bases of which will be less than the area of the bases of the cylinder . 7. If under the same con- FIG . 301 . ditions as in ...
Page 216
... prisms are in- scribed , will be the limit toward which these prisms approach , both in superficial area and in volume , as the number of lateral faces of the prisms is made to increase . 133. Definitions . We have in § 3 described a ...
... prisms are in- scribed , will be the limit toward which these prisms approach , both in superficial area and in volume , as the number of lateral faces of the prisms is made to increase . 133. Definitions . We have in § 3 described a ...
Page 237
... prism is equivalent to a right prism , the base of which is a right section of the oblique prism , and the altitude of which is equal to an edge of the oblique prism . Let A - I represent the oblique prism , and K - N a right section ...
... prism is equivalent to a right prism , the base of which is a right section of the oblique prism , and the altitude of which is equal to an edge of the oblique prism . Let A - I represent the oblique prism , and K - N a right section ...
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Common terms and phrases
AB² altitude Analysis apothem approach auxiliary line axis base bisect called centre chord circumference circumscribed polygon coincide cone convex convex polygon corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equally distant figure Find the locus fixed point frustum Geometry given circle given line given point given segment greater Hence hypothenuse inscribed polygon interior angles isosceles joining lines be drawn middle point move NOTE number of sides oblique parabola parallel parallelogram parallelopiped pass perimeter perpen perpendicular bisector point of intersection position prism PROBLEM pyramids Q. E. D. Exercises quadrangle radii radius ratio re-entrant polygon rectangle regular polygon represent right angles right circular cone right triangle rotation secant Show side opposite similar 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.