Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 18
... extremities and have its partial rotations coin- cide with the changes of direction , and its complete rotation be the sum of the three changes of direction . Let ( ST ) be any segment of one of the lines forming the triangle . Move it ...
... extremities and have its partial rotations coin- cide with the changes of direction , and its complete rotation be the sum of the three changes of direction . Let ( ST ) be any segment of one of the lines forming the triangle . Move it ...
Page 24
... extremities of the bisected segment . 2. Show that if a line have two of its points equally distant from the ends of the segment , it will be the bisector of the segment . Solution . If a perpendicular bisector of the segment were 24 ...
... extremities of the bisected segment . 2. Show that if a line have two of its points equally distant from the ends of the segment , it will be the bisector of the segment . Solution . If a perpendicular bisector of the segment were 24 ...
Page 25
... extremities of the segment . For this reason it would pass through the two points mentioned in the hypothesis ; but " two points determine the position of a straight line . " Therefore the line which by hypothesis passed through two ...
... extremities of the segment . For this reason it would pass through the two points mentioned in the hypothesis ; but " two points determine the position of a straight line . " Therefore the line which by hypothesis passed through two ...
Page 31
... extremities . с b A FIG . 30 . The student will show that there are two constructions , but the resulting triangles are congruent . 28. FOURTH CASE . That in which two sides and an angle opposite one of them are given . C b A a α FIG ...
... extremities . с b A FIG . 30 . The student will show that there are two constructions , but the resulting triangles are congruent . 28. FOURTH CASE . That in which two sides and an angle opposite one of them are given . C b A a α FIG ...
Page 33
... extremities of the third side . a + b > c + d d + ef a + b + e > c + f 6. Show that if from any point in a perpendicular , oblique lines be drawn to the base of any two , the one which meets the base at the greater distance from the ...
... extremities of the third side . a + b > c + d d + ef a + b + e > c + f 6. Show that if from any point in a perpendicular , oblique lines be drawn to the base of any two , the one which meets the base at the greater distance from the ...
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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.