Elements of Geometry |
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Page x
... CHAPTER VIII . Inscribed and circumscribed polygons Variable and limit Limit axioms Area of a circle . PROBLEMS 117 · 121 124 126 137 Intersections of planes Perpendiculars to planes CHAPTER IX . Parallels X CONTENTS .
... CHAPTER VIII . Inscribed and circumscribed polygons Variable and limit Limit axioms Area of a circle . PROBLEMS 117 · 121 124 126 137 Intersections of planes Perpendiculars to planes CHAPTER IX . Parallels X CONTENTS .
Page 64
... of their radii . 55. Definitions . A triangle is inscribed within a circle when its vertices are on the circumference and its sides FIG . 80 . B are chords . The circle is said to be circumscribed 64 ELEMENTS OF GEOMETRY .
... of their radii . 55. Definitions . A triangle is inscribed within a circle when its vertices are on the circumference and its sides FIG . 80 . B are chords . The circle is said to be circumscribed 64 ELEMENTS OF GEOMETRY .
Page 65
George Cunningham Edwards. are chords . The circle is said to be circumscribed about the triangle . A circle is inscribed within a triangle when the sides of the triangle are tangent to the circumference and the circle lies within the ...
George Cunningham Edwards. are chords . The circle is said to be circumscribed about the triangle . A circle is inscribed within a triangle when the sides of the triangle are tangent to the circumference and the circle lies within the ...
Page 86
... circumscribed circles . 7. Show that the same relation exists between the radii of the corresponding escribed circles . 8. Show that the corresponding altitudes are to each other as the corresponding medians . 9. Show that the ...
... circumscribed circles . 7. Show that the same relation exists between the radii of the corresponding escribed circles . 8. Show that the corresponding altitudes are to each other as the corresponding medians . 9. Show that the ...
Page 105
... Circumscribe a circle about the triangle , and draw the auxiliary line AK . AKAD and CHD are similar . b + g . с = α b b2 + bg = ac , b2 = ac - bg . bg = mn . But by § 85 , ... b2 = ac mn . m Hn K FIG . 137 . If it be desired to find m ...
... Circumscribe a circle about the triangle , and draw the auxiliary line AK . AKAD and CHD are similar . b + g . с = α b b2 + bg = ac , b2 = ac - bg . bg = mn . But by § 85 , ... b2 = ac mn . m Hn K FIG . 137 . If it be desired to find m ...
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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.