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 vii
Commencing with the Elementary Ideas Derived Through the Senses, and Proceeding by a Train of Inductive Reasoning to ... idea , it became necessary to displace the circle and the sphere from the forced positions wherein they had hitherto ...
Commencing with the Elementary Ideas Derived Through the Senses, and Proceeding by a Train of Inductive Reasoning to ... idea , it became necessary to displace the circle and the sphere from the forced positions wherein they had hitherto ...
Seite xiv
... idea of an angle results from comparing the directions of three points - idea of a triangle obtained from the same source -relations of four points - straight lines that cross without meeting - idea of a plane obtained from the ...
... idea of an angle results from comparing the directions of three points - idea of a triangle obtained from the same source -relations of four points - straight lines that cross without meeting - idea of a plane obtained from the ...
Seite xvi
... idea of superficial quantity ; and by considering planes as the boundaries of solids , an idea of solid quantity ? These three species of quantity , being alike parts of space ; ought they not to have some relation to each other ...
... idea of superficial quantity ; and by considering planes as the boundaries of solids , an idea of solid quantity ? These three species of quantity , being alike parts of space ; ought they not to have some relation to each other ...
Seite xxiv
Commencing with the Elementary Ideas Derived Through the Senses, and Proceeding by a Train of Inductive Reasoning to Develope ... idea of a curve , or of a mathematical line of any kind , is derived , as explained in Part I. , from the ...
Commencing with the Elementary Ideas Derived Through the Senses, and Proceeding by a Train of Inductive Reasoning to Develope ... idea of a curve , or of a mathematical line of any kind , is derived , as explained in Part I. , from the ...
Seite 11
... idea of a plane , it requires but a slight power of abstrac- tion to consider the latter as , an object by itself , uncon- nected with any particular solid . But the study of tangible objects must not be dis- missed until we have ...
... idea of a plane , it requires but a slight power of abstrac- tion to consider the latter as , an object by itself , uncon- nected with any particular solid . But the study of tangible objects must not be dis- missed until we have ...
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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.