Elements of GeometryMacmillan Company, 1897 - Geometry |
From inside the book
Results 1-5 of 38
Page 4
... They may be brought to coincide ; in which case all the points of the two lines are in common . The lines are then said to be congruent . PLANE GEOMETRY . 6. A plane is a surface such 4 ELEMENTS OF GEOMETRY . Rotation axiom.
... They may be brought to coincide ; in which case all the points of the two lines are in common . The lines are then said to be congruent . PLANE GEOMETRY . 6. A plane is a surface such 4 ELEMENTS OF GEOMETRY . Rotation axiom.
Page 6
... a plane may be moved so as to cause any one of its points to coincide with the given point . Any infinite number of planes may be made to pass 6 ELEMENTS OF GEOMETRY . Figures Translation axiom A circle Angles and arcs.
... a plane may be moved so as to cause any one of its points to coincide with the given point . Any infinite number of planes may be made to pass 6 ELEMENTS OF GEOMETRY . Figures Translation axiom A circle Angles and arcs.
Page 7
... coincide , and then one of the planes be rotated about this line until at least one point , not in the common line , shall be common to the two planes , any line which may be drawn through this point and any point of the common line ...
... coincide , and then one of the planes be rotated about this line until at least one point , not in the common line , shall be common to the two planes , any line which may be drawn through this point and any point of the common line ...
Page 8
... coincide with . its first position , AB . If the direction AB be positive , the direction AF is negative . When the positive direction has been changed to AC , the negative has been changed to AI . When the positive has been changed to ...
... coincide with . its first position , AB . If the direction AB be positive , the direction AF is negative . When the positive direction has been changed to AC , the negative has been changed to AI . When the positive has been changed to ...
Page 9
... FB be revolved on that line as an axis , it may be brought to coincide with that which is above the same line ( § 10 ) ; and in that position , if the line AB be rotated about A as a pivot until it reach the direction AF , ANGLES . 9.
... FB be revolved on that line as an axis , it may be brought to coincide with that which is above the same line ( § 10 ) ; and in that position , if the line AB be rotated about A as a pivot until it reach the direction AF , ANGLES . 9.
Other editions - View all
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.