Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page x
... tangents . 103 CHAPTER VIII . Inscribed and circumscribed polygons 117 Variable and limit 121 Limit axioms 124 Area of a circle . 126 PROBLEMS . 137 Intersections of planes Perpendiculars to planes Parallels to planes CHAPTER X CONTENTS.
... tangents . 103 CHAPTER VIII . Inscribed and circumscribed polygons 117 Variable and limit 121 Limit axioms 124 Area of a circle . 126 PROBLEMS . 137 Intersections of planes Perpendiculars to planes Parallels to planes CHAPTER 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 . C 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 . C 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 . Q. E. D. 45. THEOREM . 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 . Q. E. D. 45. THEOREM . 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
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.