MATHEMATICS.] 



INDEX TO VOL. I. 



1237 



Euclid, definitions of Book III., 564 ; 

 remarks on, 571 j exercises on Books 

 I.. II., III., 572. 



EuHid, definitions of Book IV., 572 ; 

 remarks on, 576 ; exercises on the four 

 books of, 577. 



Euclid, proportion in place of Book V., 

 578. 



Euclid, Book VI., 584. 



Euclid, propositions on planes, Book XI., 

 592. 



Euclid, problems in practical geometry, 

 600. 



Euclid, spherical geometry, 596 ; defi- 

 nitions and propositions, 596, ft teg. 



Evolution in algebra, 465 ; exercises, 466. 



Exercises in the rules of algebra, 452, 

 tt teg. : in addition of algebra, 453 ; in 

 subtraction, 455 ; in equations, 457, 

 458; in multiplication of algebra, 459; 

 in involution, 461 ; in division, 463 ; in 

 extraction of roots, 466 ; in fractions, 

 467 ; in addition and subtraction of 

 fractions, 468 ; in multiplication of 

 fractions ; in division of fractions, 469 : 

 in the solution of simple equations, 471 ; 

 in quadratic equations, 474 ; in arith- 

 metical and geometrical progressions, 

 479 ; in extracting the square-root of a 

 polynomial, 482; of a binomial, 483; 

 in the cube-root of decimals, 485. 



Exercises in the problems and theorems of 

 Euclid, Book I., 559 ; Books I. and II., 

 563; Books I , II., and III., 572; on 

 the four first books, 577. 



Exercises, solutions to algebraical, 486 

 511. 



Exponential, to obtain lines, &c., in 

 terms of, 629. 



Exponents in algebra. Illustrations of, 464. 



Expression, meaning of the term in algebra, 

 452. 



Extraction of algebraical rooti, 465 ; rules 

 for ; exercises in, 466. 



Extraction of the square-root, 448. 



FACTOR, meaning of the term, 435. 



Factors of the composite numbers, table 

 of the, 449. 



Factors, operations of, when they are 

 simple quantities, 459. 



Figures of arithmetic, 433 ; local value of, 

 433 ; use of in arithmetic and algebra, 

 451. 



Formulas of spherical trigonometry, 657, 

 tt teq. 



Formulas, trigonometrical, for determining 

 the relations of different angles, 614, 

 tt ng. : " ambiguities" arising from the 

 use of, 619; adapted for logarithmic 

 calculation, 624. 



Fractions in algebra, addition and sub- 

 traction of, 468. 



Fractions in algebra, division of; exercises 

 in, 469. 



Fractions in algebra, multiplication of, 

 468 ; exercises in, 469. 



Fractions in algebra, operations of, 4 66 ; 

 exercises in, 467 ; how to reduce them 

 to a common denominator, 467. 



Fractions, principles and practice of, 443 ; 

 additioa and subtraction of; multipli- 

 cation and division of, 444; reduction 

 of to decimals, 448. 



Fru-trum of I cone, to determine the 

 volume of a, 654. 



Functions, trigonometrical, of angles, 615, 

 ttltq. 



GEODETICAL operations, on the formulas 

 peculiar to, 662, */ itq. 



Geometrical progression in algebra, 478. 



Geometry, 541. 



Geometry, plane, introduction to; de- 

 finitions of, 541 (See Euclid). 



Geometry, practical, general treatise on, 

 600, tt teq. ; the instruments in general 

 use, 600; construction of conic sections, 

 608 ; the ellipse, 608 ; the parabola, 

 610; the hyperbola, 611; the cycloid, 

 611. 



Geometry, spherical, introduction to ; de- 

 finitions of; propositions for solution, 

 596599. 



HEIGHTS, the measurement of, 643. 

 Homogeneous quadratics, definition and 



illustration of, 476. 

 Hyperbola, definition of the, 611. 



IMPOSSIBLE expressions, 512. 

 Indeterminate coefficients, 512. 

 Indices, theory of, 512. 

 Infinite series, arithmetical values of, 517. 

 Instruments used in practical geometry 



compasses, ruler, pencil, and drawing. 



pen, 600. 

 Involution of simple quantities, 461 ; 



exercises in ; the powers of a binomial, 



462. 



LENGTH, tables of, 439. 



Letters, use of in algebra, 451. 



Lines and ratios, trigonometrical, 613. 



Liquids, measures for, 439. 



Logarithmic sines, &c., calculation of, 637. 



Logarithmic tables of natural numbers, 

 525539. 



Logarithms, Briggs', 519. 



Logarithms, multiplication, division, in- 

 volution, and evolution by, 523, tt teq. 



Logarithms, Napierian, 5.17; table* of, 

 539. 



Logarithms of sines, cosines, tangents, &c., 

 666688. 



Logarithms, on the calculations of, 51 7 ; 

 principle on which, they may be used 

 to facilitate calculations, 518; every 

 number has a calculable logarithm ; 

 numerical values of may be calculated, 

 519 : use of, 521, ft teq. 



MANTISSA of a logarithm, 521. 



Mathematics, introductory remark) on ; 

 different subjects connected with ; on 

 the study of, as a science, 431, 432. 



Measurement of a base line, 663. 



Measures, tables of, 439. 



Mensuration, 643, tt teq. ; heights and 

 distances, 643, */ teq. ; the measure of 

 areas, 644 ; the measure of solids, 649. 



Mental arithmetic, 450. 



Military earthwork, to find the solid 

 contents of a, 654. 



Money, tables of, 439. 



Monomial quantity, how to extract the 

 root of a; exercises, 466. 



Multiples of angles, sines, &c., of, 619. 



Multiplication in algebra, the sign of, 451 ; 

 the rule of, when the factors are simple 

 quantities, 459; exercises in, 461. 



Multiplication of fractions in algebra, 

 468; exercises in, 469. 



Multiplication of compound quantities, 

 442; of fractions, 444; of decimals, 

 448. 



Multiplication, simple, use and application 

 of; table of, 435; various workings in, 

 436. 



Multiplier, algebraically called the co- 

 efficient, 452 ; in algebra a factor, 452. 



Muliipliers, which render binomial surds 

 rational, 483. 



NAPIER, logarithms of, 517, 539. 

 Napierian logarithms, tables of, 539. 

 Natural sines and cosines, calculation of, 

 636 ; tables of, 665. 

 Negative and positive values in quadratic 

 equations, 475. 



Negative angles, 614. 



Negative sign, use of, to denote position, 

 614. 



Notation, algebraical, 451. 



Notation, arithmetical, 433. 



Notation, decimal, 447. 



Notation, fractional, 443. 



Number, methods of finding the logarithm 

 of a ; use of a table of logarithms ; 

 method of finding the characteristic, 

 521, 522. 



Numbers, reading of, 433. 



Numeration table, 433. 



Numerator of fractions, 443, 467. 



Numerical solution of right-angled tri- 

 angles, 641, tt teij. 



Numerical value of logarithms, 522 ; of 

 sines and cosines of angles, 621. 



, VALUE of, 591 , 630. 



Parabola, definition of the, 610; area of 

 the, 646 ; to find the area of a, 646. 



Parallel! peds, mensuration of, 650. 



Parallelogram, to find the area of a, 645. 



Pence table, 439. 



Pencils used in geometry, 600. 



Pens used in geometry, 600. 



Permanence of equivalent forms, 511. 



Plane geometry, introduction to, 541. 



Plane trigonometry, 612 (See Trigo- 

 nometry ). 



Planes, definitions of, 592; propositions 

 in, 592595. 



Polygon inscribed in a circle, area of, 591, 

 626. 



Polygon, to find the area of a, 645. 



Polynomial, how to extract the square- 

 root of a, 481. 



Positive values in equations, 475. 



Postulates of Euclid ; problems illustrative 

 of, 542. 



Practical geometry, 600. 



Prismoid, to find the volume of a, 653. 



Prisms, various, measurement of, 648,651. 



Problems (See Propositions). 



Progression, arithmetical, 477; exercise* 

 in, 478; geometrical, 479. 



Proportion and progression, questions in 

 which they are concerned, 479. 



Proportion in algebra, 476. 



Proportion, rule of arithmetical, 445. 



Proportional parts, use of a table of, 521. 



Propositions ill geometry of planes, 592. 



Propositions in plane trigonometry, 612, 

 tt ttq. 



Propositions in spherical geometry, 596. 



Propositions in spherical trigonometry, G57. 



Propositions of Euclid, 541 595. 



Pyramids, mensuration of, 651. 



QUADRANT, trigonometrical signs of each, 



of a circle, 616. 

 Quadratic equations, solutions of, with 



unknown quantities, 472, et teg. . 



exercises in, 475. 



Quadratics, homogeneous and symme- 

 trical, 476. 

 Quadrature of the circle, problem of the, 



577. 

 Quadrilateral, inscribed in circle, to find 



it* area, 626. 

 Quantities in algebra, simple and com. 



pound ; illustrations of, 452. 

 Quantities, simple, operation of the factors 



in, 459. 

 Quantities, unknown, solution of simple 



equations with, 469, et teg. ; of 



quadratic equations with, 472, */ ttg. 

 Quantity, murks and symbols of, 452. 

 Quantity, mixed, reduction of to an 



improper fraction, 466. 

 Quotient, the quantity so called, 462. 



RADIUS of an inscribed circle, to find Uu 

 625. 



