Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude: Commencing with the Elementary Ideas Derived Through the Senses, and Proceeding by a Train of Inductive Reasoning to Develope the Present State of the Science (Google eBook)
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algebraic angles formed apply arrangement assigned assumed becomes Chap circle Classification closed figures co-ordinates cosine curve deduced denoted Detailed analysis determine distance ellipse equa equal equation example expressed finite number formula generatrix geometrical investigation geometry given plane given point greater number hyperbola inclination infinite inquiry intersection lations peculiar latter lines and surfaces magnitude measured method number of points parabola parallel parameters pass peculiar to three perpendicular place is referred plane angles plane curves plane space polygon position preceding primordial elements principles problem proposition quantity radius ratios rectangular pyramid regard relations of direction relations of points Relations of three remark result right angled triangle science obtained secants Sect sides sine singular points solid angle sphere spherical straight line substituting tangent plane theorem three divergent lines tion values varieties of form whence wherein whilst zero
Page 163 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Page 330 - A — cos B cos C — sin B sin C cos a ; and changing the signs of the terms, we obtain, cos A = sin B sin C cos a — cos B cos C.
Page 392 - ... set of prime numbers cannot be finite — since the product of any set of finite numbers plus one gives a new prime number — is as aesthetically neat in our times as it was in Euclid's. But a problem takes on extra luster if, in addition to its logical elegance, it provides useful knowledge. That the shortest distance between two points on a sphere is the arc of a great circle is an agreeable curiosity ; that ships on earth actually follow such paths enhances its interest.
Page 310 - In practice however, there will generally be some circumstances which will determine whether the angle required is acute or obtuse. If the side opposite the given angle be longer than the other given side...
Page 123 - ... which forms a space indefinitely extended, differs from the opening we call the angle C merely by the small space included in the triangle. "This last, by bringing the triangle nearer to C, may be rendered as small as we please ; and thus a triangle can always be assigned whose angles shall differ from a...
Page 167 - In other words, if the fundamental rule that the whole is equal to the sum of its parts and that the deduction of any part decreases the whole is adhered to, the depreciation problem is solved.
Page 619 - Y will be identical, and all points will lie on a line passing through the origin and making an angle of 45° with the two axes.
Page 129 - The square of the hypotenuse of a right triangle is equal to the sums of the squares of the other two sides, ie (MO)2 = (MN)2 + (WO)2.