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 x
... taken by the writer in regard to this question , the peculiar advantages of both are capable of being com- bined : every possible aid - by diagrams - by solid and skele- ton models and by reiterated explanation , should , in his opinion ...
... taken by the writer in regard to this question , the peculiar advantages of both are capable of being com- bined : every possible aid - by diagrams - by solid and skele- ton models and by reiterated explanation , should , in his opinion ...
Seite xvii
... taken with reference to these primordial ele- ments , co - ordinates , how shall we express the relations of points in terms of their co - ordinates ? SECTION I. Various Systems of Primordial Elements . Data involved in the position of ...
... taken with reference to these primordial ele- ments , co - ordinates , how shall we express the relations of points in terms of their co - ordinates ? SECTION I. Various Systems of Primordial Elements . Data involved in the position of ...
Seite xviii
... taken as a type - the analysis of a geometrical pro- position resolves itself into two parts ; first , the analysis of a type peculiar to the proposition , secondly , an inquiry into the changes which the type under- goes the first ...
... taken as a type - the analysis of a geometrical pro- position resolves itself into two parts ; first , the analysis of a type peculiar to the proposition , secondly , an inquiry into the changes which the type under- goes the first ...
Seite 11
... taken in treating , successively , the sphere , the cone and the plane , as the most simple cases of surfaces that differ in their capacity to enclose a solid . The plane is ob- viously the least perfect in this respect , but after an ...
... taken in treating , successively , the sphere , the cone and the plane , as the most simple cases of surfaces that differ in their capacity to enclose a solid . The plane is ob- viously the least perfect in this respect , but after an ...
Seite 12
... taken of the sub- ject we are investigating . The thread , examined with attention , will , indeed , be recognized as a cylinder whose breadth and thickness bear a small proportion to the length ; but since the two former dimensions may ...
... taken of the sub- ject we are investigating . The thread , examined with attention , will , indeed , be recognized as a cylinder whose breadth and thickness bear a small proportion to the length ; but since the two former dimensions may ...
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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.