Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 7
... joining those points . Every possible position of a plane which contains two given points , may be reached by causing a selected plane which contains them to rotate about the line joining them as an axis , until it returns to the ...
... joining those points . Every possible position of a plane which contains two given points , may be reached by causing a selected plane which contains them to rotate about the line joining them as an axis , until it returns to the ...
Page 61
... joining their extremities with the centre will be equal , because angles at the centre are measured by the inter- cepted arcs . Proof . Draw the auxiliary lines indicated . The AABC and DEC are equal , having the three sides of one ...
... joining their extremities with the centre will be equal , because angles at the centre are measured by the inter- cepted arcs . Proof . Draw the auxiliary lines indicated . The AABC and DEC are equal , having the three sides of one ...
Page 65
... a radius drawn to the point of tangency . If then we had CT drawn , Z CTP would be 90 ° . If we had a line CP , joining the two fixed points , a right triangle would be F formed having CP for its hypothenuse ; and if a CIRCLES . 65.
... a radius drawn to the point of tangency . If then we had CT drawn , Z CTP would be 90 ° . If we had a line CP , joining the two fixed points , a right triangle would be F formed having CP for its hypothenuse ; and if a CIRCLES . 65.
Page 67
... joining the given point with the centre of the given circle . F Ө P F N C FIG . 84 . 3. Show that of all the points on the circumference of a circle , the nearest and the furthest from another circumference will be on the line joining ...
... joining the given point with the centre of the given circle . F Ө P F N C FIG . 84 . 3. Show that of all the points on the circumference of a circle , the nearest and the furthest from another circumference will be on the line joining ...
Page 75
... joining the middle points of the non - parallel sides of a trapezoid will equal the half - sum of the parallel sides . FIG . 95 . 62. THEOREM . If a line be drawn parallel to PROPORTIONAL DIVISION . 75 Proportional division.
... joining the middle points of the non - parallel sides of a trapezoid will equal the half - sum of the parallel sides . FIG . 95 . 62. THEOREM . If a line be drawn parallel to PROPORTIONAL DIVISION . 75 Proportional division.
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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.