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 sider |
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Side vi
... inquiry that has in view the combination of these elements , or , in other words , the whole body of geometrical science , was at once reduced to a known problem of algebra . That some sacrifice of clearness and brevity would , in a few ...
... inquiry that has in view the combination of these elements , or , in other words , the whole body of geometrical science , was at once reduced to a known problem of algebra . That some sacrifice of clearness and brevity would , in a few ...
Side viii
... inquiry not confined to the gradual acquisition of general results from a comparison of the phenomena observed in the external world , but extend- ing to the acquirement of knowledge from a comparison of any phenomena , whether mental ...
... inquiry not confined to the gradual acquisition of general results from a comparison of the phenomena observed in the external world , but extend- ing to the acquirement of knowledge from a comparison of any phenomena , whether mental ...
Side ix
... inquiry , is evident from what is here said of them , and the omissions noticed in regard to synthesis become more important from the fact , that the premises , in many cases , conduct to a result having apparently such little connec ...
... inquiry , is evident from what is here said of them , and the omissions noticed in regard to synthesis become more important from the fact , that the premises , in many cases , conduct to a result having apparently such little connec ...
Side xiv
... inquiry - relations of form and magnitude reduced to the relations of number - recapitulation - elements peculiar to the subject . Page 42 . FIRST APPENDIX TO PART I. — Of some Simple Forms . Page 86 . SECOND APPENDIX TO PART I ...
... inquiry - relations of form and magnitude reduced to the relations of number - recapitulation - elements peculiar to the subject . Page 42 . FIRST APPENDIX TO PART I. — Of some Simple Forms . Page 86 . SECOND APPENDIX TO PART I ...
Side xvi
... Inquiry suggested by these Reflections . By considering , then , lines as the boundaries of planes , should we not obtain an idea of superficial quantity ; and by considering planes as the boundaries of solids , an idea of solid ...
... Inquiry suggested by these Reflections . By considering , then , lines as the boundaries of planes , should we not obtain an idea of superficial quantity ; and by considering planes as the boundaries of solids , an idea of solid ...
Andre utgaver - Vis alle
Inductive Geometry, Or, An Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Uten tilgangsbegrensning - 1834 |
Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Ingen forhåndsvisning tilgjengelig - 2017 |
Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 163 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Side 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.
Side 129 - In every triangle the sum of the three angles is equal to two right angles.
Side 290 - A . sin b = sin a . sin B sin A . sin c — sin a . sin C sin B . sin c = sin b . sin C...
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.