Elements of Geometry |
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Page 2
... also be an infinite number of points . The rays of light from an arc - light or from a fixed star are fairly good illus- trations . FIG . 2 . 3. If a point move from an assumed position , 2 ELEMENTS OF GEOMETRY . Direction axiom.
... also be an infinite number of points . The rays of light from an arc - light or from a fixed star are fairly good illus- trations . FIG . 2 . 3. If a point move from an assumed position , 2 ELEMENTS OF GEOMETRY . Direction axiom.
Page 3
... fixed point has a fixed direction from another fixed point , only one straight line can join two points . 4. Our idea of distance involves the ideas of motion DEFINITIONS . 3.
... fixed point has a fixed direction from another fixed point , only one straight line can join two points . 4. Our idea of distance involves the ideas of motion DEFINITIONS . 3.
Page 25
... fixed points always equals unity . A CIRCLE . 21. Definitions . The locus of a moving point , the dis- tance of which from a given point is fixed , is called a circumference . Ө FIG . 23 . B If the line AB rotate about A as a pivot ...
... fixed points always equals unity . A CIRCLE . 21. Definitions . The locus of a moving point , the dis- tance of which from a given point is fixed , is called a circumference . Ө FIG . 23 . B If the line AB rotate about A as a pivot ...
Page 63
... fixed point on a chord of given length . 54. THEOREM . If two circumferences intersect , the line of centres will be the perpendicular bisector of their common chord . - Analysis . If the line OO ' be the perpendicular bisector of the ...
... fixed point on a chord of given length . 54. THEOREM . If two circumferences intersect , the line of centres will be the perpendicular bisector of their common chord . - Analysis . If the line OO ' be the perpendicular bisector of the ...
Page 65
... to the point of tangency . If then we had CT drawn , Z CTP would be 90 ° . If we had a line CP , joining the two fixed points , a right triangle would be F formed having CP for its hypothenuse ; and if a CIRCLES . 65.
... to the point of tangency . If then we had CT drawn , Z CTP would be 90 ° . If we had a line CP , joining the two fixed points , a right triangle would be F formed having CP for its hypothenuse ; and if a CIRCLES . 65.
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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.