Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page xiii
... . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) . Q. E. F. , Quod Erat Faciendum ( which was to be done ) . Hence . INTRODUCTION . GEOMETRY had its origin , as the name.
... . The straight line segment PQ . The arc PQ . Quod Erat Demonstrandum ( which was to be proved ) . Q. E. F. , Quod Erat Faciendum ( which was to be done ) . Hence . INTRODUCTION . GEOMETRY had its origin , as the name.
Page 7
... drawn through this point so as to reach every point of both planes ; in which case the two planes would have every point in common . Hence the statement or THEOREM . Two planes may be made to coincide . MORE ABOUT PLANES . 7.
... drawn through this point so as to reach every point of both planes ; in which case the two planes would have every point in common . Hence the statement or THEOREM . Two planes may be made to coincide . MORE ABOUT PLANES . 7.
Page 10
... Hence the two angles thus generated must be equal . Each is one - half of the angle generated by a complete rotation ; and may be expressed as 180 degrees ( 180 ° ) , or 200 grades ( 2008 ) . The dotted line in the accompanying figure ...
... Hence the two angles thus generated must be equal . Each is one - half of the angle generated by a complete rotation ; and may be expressed as 180 degrees ( 180 ° ) , or 200 grades ( 2008 ) . The dotted line in the accompanying figure ...
Page 14
... Hence the Theorem is established . NOTE . - The T square is a me- chanical device , used in drawing , for the purpose of erecting perpen- diculars at any points of a line ; and , as we shall see in the next article , for letting fall ...
... Hence the Theorem is established . NOTE . - The T square is a me- chanical device , used in drawing , for the purpose of erecting perpen- diculars at any points of a line ; and , as we shall see in the next article , for letting fall ...
Page 15
... Hence the theorem is established . ― NOTE . The supposition that there could be a perpendicular through A , other than AF , to the line BC leads to conclusions which are in conflict with our axioms . Hence the supposition has been shown ...
... Hence the theorem is established . ― NOTE . The supposition that there could be a perpendicular through A , other than AF , to the line BC leads to conclusions which are in conflict with our axioms . Hence the supposition has been shown ...
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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.