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... tangents . 103 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 .
... tangents . 103 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 51
... tangent to a curve is a straight line having a point in common with the curve , and having the same direction that the generating point of the curve has , at the common point . The common point is called the point of contact . H B K FIG ...
... tangent to a curve is a straight line having a point in common with the curve , and having the same direction that the generating point of the curve has , at the common point . The common point is called the point of contact . H B K FIG ...
Page 52
... tangent ; for the straight line will at that instant have the same direction that a point in motion along the curve will have at A. A tangent is sometimes said to be the limit toward which the secant approaches as the points of ...
... tangent ; for the straight line will at that instant have the same direction that a point in motion along the curve will have at A. A tangent is sometimes said to be the limit toward which the secant approaches as the points of ...
Page 53
... tangent . 45. THEOREM . Q. E. D. The perpendicular bisector of a chord of a circle will pass through the centre and will bisect the arcs subtended by the chord . Section 20 furnishes the proof for the first part of the theorem . P For ...
... tangent . 45. THEOREM . Q. E. D. The perpendicular bisector of a chord of a circle will pass through the centre and will bisect the arcs subtended by the chord . Section 20 furnishes the proof for the first part of the theorem . P For ...
Page 54
... tangent at a given point of a circumfer- ence . 3. Having given a circumference , show how to find the centre . 46. Recalling the matter in §§ 7 , 11 , and 21 , and again observing the generation of an angle by the rotation of a line ...
... tangent at a given point of a circumfer- ence . 3. Having given a circumference , show how to find the centre . 46. Recalling the matter in §§ 7 , 11 , and 21 , and again observing the generation of an angle by the rotation of a line ...
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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.