Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the Differential Calculus: Fit for Those who Have Studied the Principles of Arithmetic and Algebra, and Six Books of Euclid |
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Common terms and phrases
a₁ algebra analytical units apply arithmetic assertion AUGUSTUS DE MORGAN called circle commensurable Consequently consider contained cose cosecant cosine cotangent deduced definition denoted derived function diminishes without limit distinction equal equation exceed expressed Fifth Book follows formulæ geometry given gives Hence hypothenuse incommensurable increase infinite number instance ksin LAOB length lies linear unit logarithm magnitude mean proportionals method multiple scale namely nearly negative notion operations polygon positive preceding proceed proposition proved quantity question result right angle root roots of unity secant shew shewn side sin² sine square straight line student subdivision suppose supposition symbol tangent theorem triangle Trigonometry true unity V₁ V₂ whence whole number π π
Popular passages
Page 61 - C, which is compounded of the ratios of A to B, and B to C, is the same with the ratio of D to F, which is compounded of the ratios of D to E, and E to F.
Page 86 - Axis, of a sphere is a line passing through the centre, 'and terminated both ways by the surface, as the line D E.
Page 53 - That magnitude which has a greater ratio than another has unto the same magnitude, is the greater of the two : and that magnitude to which the same has a greater ratio than it has unto another magnitude, is the lesser of the two.
Page 30 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Page 55 - ... F is greater than E, but not greater than D (V. Def. 7). Because E and D are equimultiples of B and A, and E is less than D . (Const). Therefore B is less than A (V Ax. 4) Therefore, of two magnitudes, &o QED PBOP. XI. THEOREM. Ratios that are equal to the same ratio, are equal to one another. If A is to B as C is to D ; and C is to D, as E is to F.
Page 73 - ... proficient in a symbolic calculus would naturally demand a supply of meaning."1 And again: "The first who used algebraical symbols in a general sense, Vieta, concluded that subtraction was a defect, and that expressions containing it should be in every possible manner avoided. Vitium negationis, was his phrase. Nothing could make a more easy pillow for the mind, than the rejection of all which could give any trouble; .... The next and second step, .... consisted in treating the results of algebra...