Elements of GeometryMacmillan Company, 1897 - Geometry |
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Page 60
... increased , AB will be diminished by a like amount . When the position AD ' shall have been reached , the will be measured by the half of CD ' . + Ai B FIG . 72 . D ' D ' If a further movement be made , under the same condi- tions , and ...
... increased , AB will be diminished by a like amount . When the position AD ' shall have been reached , the will be measured by the half of CD ' . + Ai B FIG . 72 . D ' D ' If a further movement be made , under the same condi- tions , and ...
Page 70
... step we should come nearer the point . is said to be the LIMIT toward which we approach as we increase the number of decimal places in .6666 ..... 57. We know from § 19 that parallel lines are 70 ELEMENTS OF GEOMETRY .
... step we should come nearer the point . is said to be the LIMIT toward which we approach as we increase the number of decimal places in .6666 ..... 57. We know from § 19 that parallel lines are 70 ELEMENTS OF GEOMETRY .
Page 72
... increased commensurable area , which will be a nearer approximation to the area bh . This subdivision of the unit after the manner above indicated may be carried as far as we please , and a com- mensurable area be expressed in the terms ...
... increased commensurable area , which will be a nearer approximation to the area bh . This subdivision of the unit after the manner above indicated may be carried as far as we please , and a com- mensurable area be expressed in the terms ...
Page 122
... increasing the number of terms in the decimal . If a secant AB rotate about the point A as a pivot , B will approach ... increase in the number of terms . Let this problem be proposed : At what time between 2 and 3 o'clock will the hour ...
... increasing the number of terms in the decimal . If a secant AB rotate about the point A as a pivot , B will approach ... increase in the number of terms . Let this problem be proposed : At what time between 2 and 3 o'clock will the hour ...
Page 123
... increases , 180 ° as its limit . will decrease , and approaches n If we have a series of numerical terms represented by a + bh + ch2 + dh3 + eh1 + ... , the limit toward which this series will approach as we diminish the value of h will ...
... increases , 180 ° as its limit . will decrease , and approaches n If we have a series of numerical terms represented by a + bh + ch2 + dh3 + eh1 + ... , the limit toward which this series will approach as we diminish the value of h will ...
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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.