Elements of GeometryMacmillan Company, 1897 - Geometry |
From inside the book
Results 1-5 of 34
Page v
... student comes to the higher reaches of the subject , or when he advances to other branches of mathematics . Effort has been made to introduce new material when needed , and not before ; to appeal to the understanding ; to dis- courage ...
... student comes to the higher reaches of the subject , or when he advances to other branches of mathematics . Effort has been made to introduce new material when needed , and not before ; to appeal to the understanding ; to dis- courage ...
Page vi
... student is led , not driven ; and he is encour- aged to investigate and determine for himself . The division of the work into fourteen chapters makes a natural arrangement of parts , although the chapters are quite unequal in length ...
... student is led , not driven ; and he is encour- aged to investigate and determine for himself . The division of the work into fourteen chapters makes a natural arrangement of parts , although the chapters are quite unequal in length ...
Page vii
... students are advised to read carefully the paragraphs on Demonstrative Geometry , pages 112- 116 of the " Report of the Committee on Secondary School Studies , appointed at the meeting of the National Educational Association , July 9 ...
... students are advised to read carefully the paragraphs on Demonstrative Geometry , pages 112- 116 of the " Report of the Committee on Secondary School Studies , appointed at the meeting of the National Educational Association , July 9 ...
Page xvi
... student grows , new definitions and new axioms are appropriate . Advance in Geometry is made through an orderly arrangement of theorems and problems . A theorem is a general statement of relations . relations are established by a course ...
... student grows , new definitions and new axioms are appropriate . Advance in Geometry is made through an orderly arrangement of theorems and problems . A theorem is a general statement of relations . relations are established by a course ...
Page 15
... , to the line BC leads to conclusions which are in conflict with our axioms . Hence the supposition has been shown to be an erroneous one . The student will carefully note the method employed in §§ PERPENDICULARS . 15.
... , to the line BC leads to conclusions which are in conflict with our axioms . Hence the supposition has been shown to be an erroneous one . The student will carefully note the method employed in §§ PERPENDICULARS . 15.
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.