Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 51
... diameter is a chord which passes through the centre . A 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 ...
... diameter is a chord which passes through the centre . A 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 ...
Page 52
... Diameter Center Secant Chord Tangent - FIG . 62 . NOTE . All curves have secants and chords ; but comparatively a small number of curves have centres and diameters . The circle is one of this small number . 44. THEOREM . A tangent to a ...
... Diameter Center Secant Chord Tangent - FIG . 62 . NOTE . All curves have secants and chords ; but comparatively a small number of curves have centres and diameters . The circle is one of this small number . 44. THEOREM . A tangent to a ...
Page 54
... diameter of the circle that is the perpendicular bisector of AB . When revolved , MA will coincide with MB , and the point A will fall at B. The points Q and P will remain stationary . A M FIG . 64 . B The two circumferences will ...
... diameter of the circle that is the perpendicular bisector of AB . When revolved , MA will coincide with MB , and the point A will fall at B. The points Q and P will remain stationary . A M FIG . 64 . B The two circumferences will ...
Page 57
... diameter and then demonstrate . ( c ) If the centre be without the angle formed by the two chords , draw an auxiliary diameter and demonstrate . B B FIG . 66 . De FIG . 67 . The three cases are all the possible ones , and each having ...
... diameter and then demonstrate . ( c ) If the centre be without the angle formed by the two chords , draw an auxiliary diameter and demonstrate . B B FIG . 66 . De FIG . 67 . The three cases are all the possible ones , and each having ...
Page 59
... diameter perpendicular to the parallel chords . Acting upon this suggestion , draw a perpendicular through C. It will be a perpendicular bisector of both chords . Revolve one semicircle upon the diameter as an axis . All the parts of ...
... diameter perpendicular to the parallel chords . Acting upon this suggestion , draw a perpendicular through C. It will be a perpendicular bisector of both chords . Revolve one semicircle upon the diameter as an axis . All the parts of ...
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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.