Geometrical Exercises in Paper FoldingAddison & Company, 1893 - 114 ページ |
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多く使われている語句
ABCD altitude apothegm arcs axis bisectors bisects the angle centre of inversion centre of symmetry CHAP CHAPTER chords circle CDE circumference collinear common point concurrent congruent conjugate corners corresponding points curve DECAGON diagonal diameter directrix distance draw ellipse equation equilateral triangle fixed point geometrical given lines given square Harmonic hexagon hyperbola isogonal conjugates KLMN Latus Rectum LEMNISCATE OF BERNOULLI mean centre medial section middle point midpoint natural numbers nine-points circle nonagon number of equal number of points number of sides OA=R obtain octagon ordinate paper folding parabola parallel pentagon perpendicular piece of paper plane point of intersection points of section polar radical axis radii radius Rect rectangle regular polygons respectively right angles Simson's line straight line tangent theorem trisected vertex ОА ليا
人気のある引用
111 ページ - Cycloid. The cycloid is a curve generated by a point on the circumference of a circle which rolls on a straight line tangent to the circle.
iv ページ - I have sought not only to aid the teaching of geometry in schools and colleges, but also to afford mathematical recreation to young and old, in an attractive and cheap form. "Old boys" like myself may find the book useful to revive their old lessons, and to have a peep into modern developments which, although very interesting and instructive, have been ignored by university teachers.
84 ページ - These are the limiting points, and in this point of view we see that each limiting point is to be regarded as an infinitely small circle. The two infinite systems of circles are to be regarded as one coaxal system, the circles of which range from infinitely large to infinitely small — the radical axis being the infinitely large circle, and the limiting points the infinitely small. Cor. 1.
104 ページ - An hyperbola is a curve which is the locus of a point that moves in a plane so that the difference of its distances from two fixed points in the plane is constant.
66 ページ - Nay, that the three angles of a triangle are together equal to two right angles, is not a primitive judgment, for it needs other truths coming between to carry our conviction.
69 ページ - is oo is 1. « 173. The following simple contrivance may be used for dividing a line into a number of equal parts. Take a rectangular piece of paper, and mark off n equal segments on each or one of two adjacent sides. Fold through the points of section so as to obtain perpendiculars to the sides. Mark the points of section and the corners 0, 1, 2, ...... Suppose it is required to divide the edge of another piece of paper AB into n equal parts.
92 ページ - NA' in a constant ratio, PN being the distance of P from the line joining two fixed points A and A', and N not being between A and A', the locus of P is an hyperbola of which AA
39 ページ - Philoporus, it is asserted that the Athenians in 430 BC, when suffering from the plague of eruptive typhoid fever, consulted the oracle at Delos as to how they could stop it. Apollo replied that they must double the size of his altar which was in the form of a cube. To the unlearned suppliants nothing seemed more easy, and a new altar was constructed either having each of its edges double that of the old one (from which it followed that the volume was increased eightfold) or by placing a similar...
104 ページ - Fig. 82. the curve is rr' = £*, where r and r' are the distances of any point on the curve from the foci and k is a constant. Let F and F' be the foci. Fold through F and F'. Bisect FF' in C, and fold BCB' perpendicular to FF'. Find points B and B' such that FB and FB' are each =k. Then B and B' are evidently points on the curve.