Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page v
... exercises , every one of which the student must work out as he comes to them . At the end of the Plane Geometry and at the end of the Solid Geometry there will be found a sufficiently large number of exercises to give a review of the ...
... exercises , every one of which the student must work out as he comes to them . At the end of the Plane Geometry and at the end of the Solid Geometry there will be found a sufficiently large number of exercises to give a review of the ...
Page vi
George Cunningham Edwards. attack in the mind of the student . The exercises which have been taken from other authors are limited to such as appear in at least two of them . Simplicity in wording and in demonstration have been sought ...
George Cunningham Edwards. attack in the mind of the student . The exercises which have been taken from other authors are limited to such as appear in at least two of them . Simplicity in wording and in demonstration have been sought ...
Page 12
... ° . By Equality Axiom ( a ) , Z BAC + CAF = △ BAC + ZBAG . Then subtracting / BAC from each member of the equation , we have : CAF = ≤ BAG . Q. E. D. Exercise . Establish the fact that BAC = Z FAG 12 ELEMENTS OF GEOMETRY . Equality ...
... ° . By Equality Axiom ( a ) , Z BAC + CAF = △ BAC + ZBAG . Then subtracting / BAC from each member of the equation , we have : CAF = ≤ BAG . Q. E. D. Exercise . Establish the fact that BAC = Z FAG 12 ELEMENTS OF GEOMETRY . Equality ...
Page 13
George Cunningham Edwards. Exercise . Establish the fact that BAC = Z FAG , by rotat- ing one of them until it coincides with the other . - Proof . Under the authority given by the axiom in § 8 , the BAC may ( without changing the ...
George Cunningham Edwards. Exercise . Establish the fact that BAC = Z FAG , by rotat- ing one of them until it coincides with the other . - Proof . Under the authority given by the axiom in § 8 , the BAC may ( without changing the ...
Page 16
... Exercise . Use the above figure to establish the fact that the least distance from any point to a straight line will be the segment AF of the perpendicular . This last distance named is the one always to be understood as the distance of ...
... Exercise . Use the above figure to establish the fact that the least distance from any point to a straight line will be the segment AF of the perpendicular . This last distance named is the one always to be understood as the distance 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.