Elements of GeometryMacmillan Company, 1897 - Geometry |
From inside the book
Results 1-5 of 11
Page xii
... parabola Line relations CHAPTER XIV . • Area of a parabola Particular cases . The ellipse . Line relations Area of an ellipse Particular cases The hyperbola Line relations Particular cases . PROBLEMS . xii CONTENTS .
... parabola Line relations CHAPTER XIV . • Area of a parabola Particular cases . The ellipse . Line relations Area of an ellipse Particular cases The hyperbola Line relations Particular cases . PROBLEMS . xii CONTENTS .
Page 132
... parabola . If through any point ( P ) a line ( PP1 ) parallel to the given line ( MM1 ) be drawn , the area included between the curve and PP1 will be exactly equal to the rectangle PQQ1P1 . This fact will be established in § 163 ...
... parabola . If through any point ( P ) a line ( PP1 ) parallel to the given line ( MM1 ) be drawn , the area included between the curve and PP1 will be exactly equal to the rectangle PQQ1P1 . This fact will be established in § 163 ...
Page 255
... parabola , are both perpendicular to the plane of the picture ; and so ( § 111 , Ex . 4 ) their line of intersection ( DM ) is perpendicular to the plane of the picture . Let P be any point on the parabola . Join it to F ( the point of ...
... parabola , are both perpendicular to the plane of the picture ; and so ( § 111 , Ex . 4 ) their line of intersection ( DM ) is perpendicular to the plane of the picture . Let P be any point on the parabola . Join it to F ( the point of ...
Page 256
... parabola have been deduced . Most of the properties of the Conic Sections are best developed by the methods of Analytic Geometry and Calculus ; but because of their importance in Nature and in Art , a few of the simpler properties are ...
... parabola have been deduced . Most of the properties of the Conic Sections are best developed by the methods of Analytic Geometry and Calculus ; but because of their importance in Nature and in Art , a few of the simpler properties are ...
Page 257
... parabola . Repeat the process , using the second line in the same way as the first was used , thus determining the points E and G. In the same way H and K and any number of points may be determined . Through these points draw a smooth ...
... parabola . Repeat the process , using the second line in the same way as the first was used , thus determining the points E and G. In the same way H and K and any number of points may be determined . Through these points draw a smooth ...
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.