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 ScienceC.P. M'Kennie, 1834 - 631 σελίδες |
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Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
angles formed apply arrangement assigned assuming Chap circle Classification closed figures co-ordinates cosine curve deduced denoted Detailed analysis determine distance ellipse equa equal equation example expressed finite number formulæ generatrix geometrical investigation geometry given plane given point greater number hyperbola inclination 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 result right angled triangle science obtained Sect sides sine singular points solid angle sphere spherical straight line substituting three divergent lines tion values varieties of form whence wherein whilst zero
Δημοφιλή αποσπάσματα
Σελίδα 415 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 163 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Σελίδα 395 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side. DEM.— Let ABC be any spherical triangle; then l3 BO' < BA + AC, and BC - AC < BA ; and the same is true of the sides in any order.
Σελίδα 129 - In every triangle the sum of the three angles is equal to two right angles.
Σελίδα 290 - A . sin b = sin a . sin B sin A . sin c — sin a . sin C sin B . sin c = sin b . sin C...
Σελίδα xxi - ... 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.
Σελίδα 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...
Σελίδα 123 - ... are identical with angles of the triangle, and the third, b, 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...
Σελίδα 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.
Σελίδα 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.