The Method of Fluxions Both Direct and Inverse: The Former Being a Translation from the Celebrated Marquis de L'Hospital's Analyse Des Infinements [sic] Petits: and the Latter Supply'd by the Translator, E. Stone, F.R.S.William Innys, 1730 - 212 pages |
Common terms and phrases
Abfcifs affume Afymptote alfo Angle arifes Axis Baſe becauſe Cafe Cauftick Centre of Gravity confequently Conftruction COROL Curve AMD Cycloid decreaſes defcribed Diameter Diſtance draw the right drawn Ellipfis EXAMPLE expreffed Expreffion faid fecond fhall fimilar Triangles fince find the Point firft firſt Fluent fmall Arch fought fubftituting fuch fuppofed given Point Hyperbola incident Rays increaſes infinite Number infinitely fmall interfect Involute lefs likewife luminous Point manifeft Meaſure moveable Circle muft muſt Ordinate PM Parabola parallel perpendicular Pofition Point F Point of Inflexion Progreffion Radius of Evolution Ratio Ray MF reflected Ray refracted refracted Ray Retrogreffion right Line right-angled Triangles Sector ſhall ſmall Space Subtangent Tangent MT thereof theſe thoſe thro Vertex Whence whofe xion
Popular passages
Page 179 - This amounts to the same with saying, that, in the case before us, the sine of the angle of incidence is to the sine of the angle of refraction in a given ratio.
Page 175 - 3 13602' "i"i 5-1 20 £7-r.2 5-200 z? fhall be equal to the Logarithm of the Ratio, which the Geometrical Mean between the Numbers z — i and z-\- i, has to the Arithmetical Mean, viz.
Page 5 - Index of 6, the fecond as many as there are Units in the Index of c, the third as many as there are Units in the Index of <s/, the fourth as many as there are Units in the Index 6f e, &«.
Page 3 - ... or (which is the same thing) as a polygon of an infinite number of sides, each infinitely small, which determine the curvature of the line by the angles they make with one another.
Page 164 - ... another, its direction is, in general, altered at their boundary. The well-known phenomenon of the apparent bending of a stick thrust into water is an illustration of this. The extent to which light entering minerals from the air is shifted is called their index of refraction; in mathematical terms this is the ratio between the sine of the angle of incidence and that of the angle ol refraction. In amorphous minerals and in those crystallizing in the isometric system, the index of refraction...
Page 181 - Having ascertained this point, had our tables of angular resistance been complete, the size of the surface necessary for any given weight would easily have been determined. Theory, which gives the resistance of a surface opposed to the same current in different angles, to be as the square of the sine of the angle of incidence, is of no use in this case, as it appears, from the experiments of the French Academy, that in acute angles the resistance varies much more nearly in the direct ratio of the...
Page 197 - Fig. 1. 57 pie that the resistance to a body in motion in a fluid, is a function of the square of the sine of the angle of incidence to the motion.
Page xviii - Differential (as they call it) by the letter d, the second by dd, the third by ddd. &c. ; the fluents, or Flowing Quantities, being called Integrals. But since this method in the Practice thereof, does not differ from that of Fluxions, and an Increment or Differential may be taken for a Fluxion ; out of regard to Sir Isaac Newton, who invented the same before the year 1669, 1 have altered the Notation of our Author, and instead of d, dd, d\ &c.
Page 54 - Ellipfis is equal to a Circle, whofe Diameter is a mean Proportional! between the Tranfverfe and conjugate Diameters of the Ellipfis.
Page 3 - tis the Index of the Root which is to be Extracted: I fay that this Power or Root of the Multinomial, is fuch a Series as I have1 expreft.