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 Seiten |
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Seite xviii
... latter species of varia- tions may be found from the former . SECTION III . - Theory of Correlations . — Problems are resolved by a par- ticular case of the problem taken as a type - the analysis of a geometrical pro- position resolves ...
... latter species of varia- tions may be found from the former . SECTION III . - Theory of Correlations . — Problems are resolved by a par- ticular case of the problem taken as a type - the analysis of a geometrical pro- position resolves ...
Seite xxi
... latter are every where equally distant from the circle - the angles and sides of a spheri- cal polygon have the same relations as the parts of the solid angle which the polygon subtends at the centre - relations common to all spherical ...
... latter are every where equally distant from the circle - the angles and sides of a spheri- cal polygon have the same relations as the parts of the solid angle which the polygon subtends at the centre - relations common to all spherical ...
Seite xxii
... latter - in a plane , lines equally inclined to other lines form the same angle as the latter - applies also to planes which have a common intersection— perpendiculars to the sides of a closed figure , or to planes that include a solid ...
... latter - in a plane , lines equally inclined to other lines form the same angle as the latter - applies also to planes which have a common intersection— perpendiculars to the sides of a closed figure , or to planes that include a solid ...
Seite xxv
... latter exceeds that of the equations , a complex system of surfaces - examples of simple systems . Page 555 . CHAPTER II . RELATIONS THAT EXIST BETWEEN THE LINES OR THE SURFACES OF ONE SYSTEM , AND THOSE OF ANOTHER . PRELIMINARY ...
... latter exceeds that of the equations , a complex system of surfaces - examples of simple systems . Page 555 . CHAPTER II . RELATIONS THAT EXIST BETWEEN THE LINES OR THE SURFACES OF ONE SYSTEM , AND THOSE OF ANOTHER . PRELIMINARY ...
Seite 8
... latter ; the side AC continuing to fold itself exactly upon that line , until after one convolution , the angle C falls above the point A , where the triangle was first applied . Fig . 6 . Commencing anew at C , and wrapping a second ...
... latter ; the side AC continuing to fold itself exactly upon that line , until after one convolution , the angle C falls above the point A , where the triangle was first applied . Fig . 6 . Commencing anew at C , and wrapping a second ...
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Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Keine Leseprobe verfügbar - 2017 |
Inductive Geometry: Or an Analysis of the Relations of Form and Magnitude ... Charles Bonnycastle Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 163 - Of four-sided figures, a square is that which has all its sides equal, and all its angles right angles.
Seite 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.
Seite 129 - In every triangle the sum of the three angles is equal to two right angles.
Seite 290 - A . sin b = sin a . sin B sin A . sin c — sin a . sin C sin B . sin c = sin b . sin C...
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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.