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 xx
... divergent lines . Subdivisions . SECOND DIVISION . Relations of any number of points in space . Subdi- visions . Dependent on the number of points . These general principles of arrangement admit of modification whenever principles of a ...
... divergent lines . Subdivisions . SECOND DIVISION . Relations of any number of points in space . Subdi- visions . Dependent on the number of points . These general principles of arrangement admit of modification whenever principles of a ...
Seite xxi
... divergent lines - particular rela- tions of three divergent lines - ambiguous cases - appendix . Page 324 . APPENDIX TO SECTION III . - Examples . Page 355 . SECTION IV . - Relations of two Points restricted to a Given Distance and a ...
... divergent lines - particular rela- tions of three divergent lines - ambiguous cases - appendix . Page 324 . APPENDIX TO SECTION III . - Examples . Page 355 . SECTION IV . - Relations of two Points restricted to a Given Distance and a ...
Seite xxii
... Divergent Lines . — Relations of divergent lines agree with those of spherical polygons -- equations relative to the inclinations of divergent lines obtained from the sides of closed figures , by equating with zero the common ...
... Divergent Lines . — Relations of divergent lines agree with those of spherical polygons -- equations relative to the inclinations of divergent lines obtained from the sides of closed figures , by equating with zero the common ...
Seite 111
... lines diverging as from a centre - nor does there seem , on a casual observation , any connection between the angles included by these divergent lines , and the relations that form the subject of this chapter . But a little reflection ...
... lines diverging as from a centre - nor does there seem , on a casual observation , any connection between the angles included by these divergent lines , and the relations that form the subject of this chapter . But a little reflection ...
Seite 285
... lines are drawn parallel to them from a given point , the angles formed by these lines will be equal to the angles ... divergent lines . SECOND DIVISION . Relations of any number of points 286 in space . points . Subdivisions . Dependent on.
... lines are drawn parallel to them from a given point , the angles formed by these lines will be equal to the angles ... divergent lines . SECOND DIVISION . Relations of any number of points 286 in space . points . Subdivisions . Dependent on.
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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.