Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 63
... Find the maximum and minimum chords that may be drawn through a given point in a circle . 3. Establish the converse of the theorem . 4. Find the locus of any fixed point on a chord of given length . 54. THEOREM . If two circumferences ...
... Find the maximum and minimum chords that may be drawn through a given point in a circle . 3. Establish the converse of the theorem . 4. Find the locus of any fixed point on a chord of given length . 54. THEOREM . If two circumferences ...
Page 145
... Find the locus of the middle point of a given straight line segment , the extrem- ities of which remain in two lines at right angles to each other . Let the lines OY and OX be at right angles to each other ; and let S be the given ...
... Find the locus of the middle point of a given straight line segment , the extrem- ities of which remain in two lines at right angles to each other . Let the lines OY and OX be at right angles to each other ; and let S be the given ...
Page 146
... that curve will be an ellipse , the shape of which will depend upon the point selected . 66. Find the locus of the middle points of the chords of given length in a given circle . 67. Find the locus of the point P , as 146 ELEMENTS OF ...
... that curve will be an ellipse , the shape of which will depend upon the point selected . 66. Find the locus of the middle points of the chords of given length in a given circle . 67. Find the locus of the point P , as 146 ELEMENTS OF ...
Page 147
... Find the locus of the middle points of all straight line segments in- cluded between two given parallels . 69. Find the locus of the middle points of all chords that can be drawn through a given point in a circle . M FIG . 190 . 70 ...
... Find the locus of the middle points of all straight line segments in- cluded between two given parallels . 69. Find the locus of the middle points of all chords that can be drawn through a given point in a circle . M FIG . 190 . 70 ...
Page 148
... Find the locus of P , PH2 + PK2 being constant . 78. A triangle has a given base and vertical angle . Find the locus of its vertex . 79. Find the locus of the centre of the inscribed circle ; the triangle being as described in Ex . 78 ...
... Find the locus of P , PH2 + PK2 being constant . 78. A triangle has a given base and vertical angle . Find the locus of its vertex . 79. Find the locus of the centre of the inscribed circle ; the triangle being as described in Ex . 78 ...
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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.