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 xxiii
... Reflections . To discover the curve , or surface , formed by all those points the relations of which to known elements shall be expressed in an equation of the second degree . SECTION III . — Of Plane Lines of the Second ANALYSIS . xxiii.
... Reflections . To discover the curve , or surface , formed by all those points the relations of which to known elements shall be expressed in an equation of the second degree . SECTION III . — Of Plane Lines of the Second ANALYSIS . xxiii.
Side xxiv
... curve by the de- gree of its equation , applies only to the curves the equations of which are alge- braic . But the idea of a curve , or of a mathematical line of any kind , is derived , as explained in Part I. , from the intersection ...
... curve by the de- gree of its equation , applies only to the curves the equations of which are alge- braic . But the idea of a curve , or of a mathematical line of any kind , is derived , as explained in Part I. , from the intersection ...
Side xxv
... curves and curve surfaces admit of tangents and tangent planes ? SECTION I. - Of Tangents and Normals of Plane Curves . - Definition of a tangent - equations of the tangents of a plane curve - examples -- polar equations of tangents ...
... curves and curve surfaces admit of tangents and tangent planes ? SECTION I. - Of Tangents and Normals of Plane Curves . - Definition of a tangent - equations of the tangents of a plane curve - examples -- polar equations of tangents ...
Side xxvi
... curve is concave or convex - points of inflexion - points of reflexion - conjugate points - serpentine points - examples . Page 600 . + SECTION V. - Of Curves Tangential and Normal to Systems , and of the Singular Points of Systems .-- ...
... curve is concave or convex - points of inflexion - points of reflexion - conjugate points - serpentine points - examples . Page 600 . + SECTION V. - Of Curves Tangential and Normal to Systems , and of the Singular Points of Systems .-- ...
Side 7
... curve , that , ascending by equal advances from the base of the solid towards its opposite extremity , re- sembles , indeed , the thread of a screw , but appears different from any rectilinear figure that could be traced upon a plane ...
... curve , that , ascending by equal advances from the base of the solid towards its opposite extremity , re- sembles , indeed , the thread of a screw , but appears different from any rectilinear figure that could be traced upon a plane ...
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.