Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 20
... auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the first and second . NOTE . In order to ...
... auxiliary line connecting two points of inter- section and then apply Ex . 1. Two applications will be necessary . 3. Establish the theorem when the third and fourth lines intersect between the first and second . NOTE . In order to ...
Page 23
... auxiliary line MN be drawn perpendicular to AB ( § 13 ) it will be perpendicular to DC ( § 19 , Ex . 1 ) . But we do not as yet know whether it will bisect DC or not . If we revolve the portion of the figure that lies on the right of ...
... auxiliary line MN be drawn perpendicular to AB ( § 13 ) it will be perpendicular to DC ( § 19 , Ex . 1 ) . But we do not as yet know whether it will bisect DC or not . If we revolve the portion of the figure that lies on the right of ...
Page 27
... auxiliary line AE . By § 20 , Ex . 2 , the line CB will be the perpendicular bisector of the segment AE . BL K FIG . 25 . ( r ) If the figures to the right of the line CK be revolved on CK as an axis , the point E will fall at A ; the ...
... auxiliary line AE . By § 20 , Ex . 2 , the line CB will be the perpendicular bisector of the segment AE . BL K FIG . 25 . ( r ) If the figures to the right of the line CK be revolved on CK as an axis , the point E will fall at A ; the ...
Page 38
... auxiliary line DB . It will separate the angle to which it is drawn into two parts , one of which equals the CAB . The B is the larger . AC = AD + DC = BD + DC > BC . Q. E. D. Exercises . - 1 . Prove the same by using AE as an auxiliary ...
... auxiliary line DB . It will separate the angle to which it is drawn into two parts , one of which equals the CAB . The B is the larger . AC = AD + DC = BD + DC > BC . Q. E. D. Exercises . - 1 . Prove the same by using AE as an auxiliary ...
Page 40
... each other , and the segments AB and AF would be equal . If the auxiliary line BF were drawn , AP would be a perpendicular bisector to it . This determination of relations that would exist if the angle 40 ELEMENTS OF GEOMETRY .
... each other , and the segments AB and AF would be equal . If the auxiliary line BF were drawn , AP would be a perpendicular bisector to it . This determination of relations that would exist if the angle 40 ELEMENTS OF GEOMETRY .
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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.