IN DE X; Glossarial, Explanatory, and Referential. A Abbreviation, arithmetical marks and signs used for, 48. Addition, Simple, on the use and application of, 7. of Compound quantities, 21; of Fractions, 29. of Algebra, sign of, 162 ; illustrations of, 166; exercises in, 167, 168. of Fractions in Algebra, 198; exercises in, 199. ALGEBRA (Arabic al the, and gabron reduc tion of fractions), general principles of, 161 et seq., signs of, 161; the study of, requires a previous knowledge of arithmetic, 161 ; definitions and explanations of, 162; exercises in, 164; operations in, 165. Addition of, with examples for exercise, 166 et passim. Subtraction of, 168. Transposition, 173; Clearing Fractions, ib.; questions for solution and exercise, 174, 175, 177. Multiplication of, 179; Involution, 183. Division of 187; Exponents, Roots, and Surds, 191 ; Evolution, or Extraction of Roots, 193; exercises in, 195. FRACTIONS, 196; exercises in, 197 ; Addition and Subtraction of Fractions, 198 ; exercises in, 199; Multiplication of Fractions, 199; Division of Fractions, 200; exercises in, 201. Solutions of Simple Equations, 201, 204, 206, 213; exercises in, 203, 206; Quadratic Equations, 209, 210, 213, 214; exercises in, 212, 215, Homogeneous and Symmetrical Quadratics, 217. Ratio and Proportion, 218. Geometrical Progression, 222; exercises in, 225. Algebra, Proportion and Progression, 225. Extraction of Roots,-of the Square Root of a Polynomial, 228; exercises in, 231, 234; of the Square Root of a Binomial, 232; of the cube root of a compound quantity, 235; exercises, 235 et seq. -- arithmetical and symbolical, 261, 262. “Ambiguities" arising from the use of formulas, 311. Angle, circular measure of an, 293 ; definition of, 298. Angles, ratios of, 295 et seq. ; functions of, 301 ; of a corresponding character, 303; sines and cosines of, 315; the trigonometrical ratios of, 316; to obtain the cosines of, 351; methods of correcting, 417, 419. formulas for determining the relations, 304 et seq. sines and cosines of, 310, 311; logarithmic sines of, 357, 358; Delambre's method for solving, 360. spherical triangle, sines of the, 402. Apothecaries' weight (Gr. upotheca a repository), 18. Areas, on the mensuration of, 371. to find the area of a rectangle, 371 ; of a triangle, 372; of a parallelogram, 372; of a trapezoid, 372; of a trapezium, 373; of a polygon, 373; of an ellipse, 376; of a parabola, 377; of a plane figure bounded by a curve, 378; of a right prism, 380; of a right cylinder, 380; of the curved surface of a right cone, 381 ; of the frustum of a cone, 381; of a portion of the surface of a sphere, 382. ARITHMETIC (Gr. arithmos number), intro ductory to geometry, 2; uses and objects of, 3, 4; the ten figures, 4; numeration table, and the reading of numbers, 5; decimal system of, 6; local value of figures, 6. Simple Addition, 7; Subtraction, 8; Multiplication, 10; and Division, 13, Tables of Money, Time, Weight, and Measures, 18. Arithmetic, the Rule of Reduction, 19. Compound Quantities,-Addition, 21; FRACTIONS, 26; Addition and Subtrac- DECIMALS, 36; Addition and Subtrac- general principles of, 40; table of fac- to Algebra, 161, 261. See ALGEBRA. some weight), 18. Convergent series, meaning of a, 264. rical value of, 315; to obtain the, 351. calculation of, 352. of decimals, exercises for finding the, the, 447. D B Base line, its measurement in surveying, 415, 416. powers of a, 184; how to extract the square mial surds rational, 234. to prove it, 266, 269. DECIMALS (Lat. decim ten), beautiful contrir. ance of, 6; principles and practice of, 36; re- Addition and Subtraction of, 37; Mul- exercises for finding the cube root of, ciples of Algebra, 162, 103; of plane trigono- planes, 242; of spherical geometry, 252. of small angles, 360.. compound quantity, 189; exercises in th working, 191. of compound quantities, 25; of Frac. | of Algebra, the sign of, 163; the Divi. of Fractions in Algebra, 200; exercises compound quantity, 189. с 34. Drawing-pens used in geometry, 421. E Ellipse (Gr. elleipsis deficiency), definition and Calculable logarithm, every number has a, 279. Quadrature of the, difficulty of solving the multiplier in algebra so called, 163; illus- trated, 164. sited), factors of the, 41. traction of, 22; Multiplication of, 23; Division of, 25. volume of the frustum of a, 395. ellipse, 439; the parabola, 444; the hyperbola, illustration of the, 439. of the, 340. F EQUATIONS, arithmetical and algebraical, 172 et seq.; on the solution of, 172; different modes Quadratic, solutions of, with unknown 212. Propositions of Book I., 48—67; com- Definitions and Propositions of Book of Book III., 96-112; remarks of Book IV., 116-124; re- on, 124; exercises on the Four Books his Plane Geometry, 241 ; his proposi. his Spherical Geometry, 251; defini- Problems in practical geometry, 423– ing), in algebra, 193; exercises, 195. clid, Book I., 85; Books I. and II., 95; Books in the rules of ALGEBRA, 164 et seq. ; cube root of decimals, 238. 335. illustrations of, 191. cises in, 195. Factor (Lat. factor a working agent), meaning of the term, 165. quantities, 179; to express sin. x, in a series of the Composite numbers, table of the, use of in arithmetic and algebra, 161. determining the relations of different angles, Fundamental, of sperical trigonometry, principles and practice of, 26; addition and in Algebra, operations of, 196; exer- Addition and Subtraction of, Multiplication of, 199; exer- -- Division of, 200; exer in, prism, to determine the volume of, 389. G Geodetical operations (Gr. ge land, and daio to divide), on the formulas peculiar to, 414 et seq. ing), arithmetic introductory to, 2; illustra- Plane, introduction to, 241 ; definitions Spherical, introduction to, 251 ; defini- Practical, general treatise on, 421 et Letters, use of in algebra, 161. on numbers), treatise on, 261 et seq.; on the P M MATHEMATICS (Gr. mathema learning), intro- Parabola, definition of the, 432 ; illustrations of the, 444, to, 241 et seq. TRIGONOMETRY). -250. how to extract the square root of a, 228, of, 422. solution) of Euclid, 48 et seq. ; 423-417; (see PROPOSITIONS). ductory remarks on, I et seq.; different sub- GEOMETRY, ALGEBRA, &c.) tise on, 367 et seq. ; heights and distances, measure of solids, 383—400. 222; Geometrical, 222. they are concerned, 225. a, 394. Moivre's trigonometrical theorem, 332. nomen a name), how to extract a proposed root of a, 194; exercises, 195. of Compound Quantities, 23; of Frac- Proportion, rule of, 30. in Plane Geometry, 243—250. in Plane Trigonometry, 299, 305-307. Quadratic Equations (Lat. quadratus fourfold), solutions of with unknown quantities, 209, 210, 213, 214; exercises in, 212. 117. squaring of anything), problem of the, 126, 127. latera sides), to find its area inscribed in a circle, 328. 179; in calculating the arithmetical values of, in Algebra, simple and compound, 163; Unknown, solution of simple equations equations, 209, 213, 214. Mixed, reduction of to an improper tity so called, 187, Series, treatise on, 261 et seq. ; what is meant by a Convergent and Divergent Series, 264. (See LOGARITHMS). practical illustrations of, 164. Logarithmic, tables of, 355. Natural, tables of, 353. 396. tional, 402; solution of the, 408 ; Napier's rule for solving, 409. 398. of a polynomial, 228. various algebraic exercises for extract. of a binomial, 232. of Compound Quantities, 22; of Frac- of Algebra, sign of, 162 ; illustrations of Fractions in Algebra, 198; exercises illustrations of, 191. R et seq. Radius of an inscribed circle, to find the, 327. Symbolical Algebra, 261. 393. T Ratio and Proportion, in algebra, 218. - Inverse Trigonometrical, explained, 318. 19-21. for, 194; exercises in, 195. Double, illustrations of, 34. Tangents, the calculation of, 352. S Science (Lat. scientia the knowledge of things), 18. requiring demonstration), 49 et seq. (See PRO- POSITIONS.) 368. angles, 322; methods of treating, 418, 419. on the study of, 3. |