Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 10
... fall in the direction AF ; the BAJ will coincide with FAJ ; and so must be equal to it . Hence ( .. ) the 180 ° of change of direction from A B FIG . 7 . AF to AB will be bisected by AJ . Thus we see that if two lines intersect so as to ...
... fall in the direction AF ; the BAJ will coincide with FAJ ; and so must be equal to it . Hence ( .. ) the 180 ° of change of direction from A B FIG . 7 . AF to AB will be bisected by AJ . Thus we see that if two lines intersect so as to ...
Page 14
... fall perpen- diculars to a line from points not in the line . FIG . 12 . 14. THEOREM . From a point not on a given straight line one , and only one , perpendicular may be drawn to the line . ( a ) Since at any point of a line a ...
... fall perpen- diculars to a line from points not in the line . FIG . 12 . 14. THEOREM . From a point not on a given straight line one , and only one , perpendicular may be drawn to the line . ( a ) Since at any point of a line a ...
Page 23
... fall at A , and the line BC ( being perpendicular to MB ) will in its revolved position take the direction AD . Because NC is perpendicular to MN , it will when rotated lie in the direction ND . The point C will then lie somewhere in ...
... fall at A , and the line BC ( being perpendicular to MB ) will in its revolved position take the direction AD . Because NC is perpendicular to MN , it will when rotated lie in the direction ND . The point C will then lie somewhere in ...
Page 24
... fall at A ; P will remain stationary ; and the segment PB will coincide with the segment PA , and must there- fore be equal to it . Q. E. D. Exercises . 1. Show that any point not on the perpendicular bisector will not be equally ...
... fall at A ; P will remain stationary ; and the segment PB will coincide with the segment PA , and must there- fore be equal to it . Q. E. D. Exercises . 1. Show that any point not on the perpendicular bisector will not be equally ...
Page 27
... fall at A ; the segments ED and AB will coin- cide ; the same will be true of EF and AC ; DF and BC will remain in coincidence ; and all the parts of one triangle ( perimeter , angles , and surface ) will coincide . with the parts of ...
... fall at A ; the segments ED and AB will coin- cide ; the same will be true of EF and AC ; DF and BC will remain in coincidence ; and all the parts of one triangle ( perimeter , angles , and surface ) will coincide . with 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.