UH 



INDEX TO VOL. I. 



[MATIIKMATICS. 



SECTION VII. MATHEMATICS. 



A>EVIATIOS, arithmetical marks and 

 signs used for. 451* 



Addition in algebra, sign of, 451 i illuitra- 

 tions of ; exercises in, 453, el teg. 



Addition of compound quantities, 441 ; of 

 fractions, 444 ; decimals, 448. 



Addition of fractions in algebra, exercises 

 in, 468. 



Addition, simple, on the use and applica- 

 tion of, 434. 



Algebra, addition in, with examples for 

 exercise, 453, */ ttq. 



Algebra, arithmetical and symbolical, 512. 



Algebra, arithmetical progression in, 477. 



Algebra, division in, 462 ; exponents, 

 roots, and surds, 464 ; evolution, or 

 extraction of roots, 465; exercises in, 

 466. 



Algebra, extraction inroots of the square- 

 root of a polynomial, 481 ; exercises in, 

 482 ; of the square-root of a binomial, 

 482 ; of the cube-root of a compound 

 quantity, 484 ; exercises in, 484, ft ttq. 



Algebra, fractions, 466 ; exercises in, 467 ; 

 reduction of fractions ; addition and 

 subtraction of fractions ; exercises in ; 

 n ultiplication of fractions, 468: division 

 of fractions; exercises in, 469. 



Algebra, general principles of, 451 , el teg. : 

 signs of ; the study of, requires a previous 

 knowledge of arithmetic; definitions 

 and explanations of; exercises in; 

 operations in, 452. 



Algebra, geometrical progression, 478 ; 

 exercises in, 479. 



Algebra, homogeneous and symmetrical 

 quadratics, 476. 



Algebra, multiplication in, 459 ; involu- 

 tion, 461. 



Algebra, proportion and progression, 479. 



Algebra, ratio and proportion, 476. 



Algebra, simple equations, 455, et leg. 



Algebra, solutions to exercises in, 486 

 511. 



Algebra, solution of simple equations, 

 469; quadratic equations, 472. 



Algebra, subtraction in, 454. 



Algebra, transposition ; clearing fractions, 

 456 : questions for solution and exercise, 

 457. 



"Ambiguities" arising from the use of 

 trigonometrical formulas, 619. 



Angle, circular measure of an, 612; defi- 

 nition of, 614. 



Angles, formulas for determining the 

 relations of, 616, et teg. 



Angles of a spherical triangle, sines of 

 the, 657. 



Angles, ratios of, 613, et teg. ; functions 

 of, 615 i of a corresponding character, 

 616 ; sines and cosines of, 613, 621 ; the 

 trigonometrical ratios of, 621 ; to cal- 

 culate logarithmic sines and cosines of, 

 635 ; methods of correcting, 636. 



Angles, sines and cosines of, 613 ; tables 

 of logarithmic sines, &c., of, 666, etteq.; 

 Delambre's method for solving, 640. 



Apothecaries' weight, 439. 



Arcs, circular, lengths of, 540. 



Areas, on the mensuration of, 644. 



Areas, to find the area of a rectangle ; of 

 a triangle ; of a parallelogram ; of a 

 trapexoid ; of a trapezium; of a polygon 

 and of a circle, 641, 645: of the 

 segment of a circle ; of an ellipse i of 

 a parabola, 646: of a plane figure 

 bounded by a curve, 647 ; of a right 

 prism; of a right cylinder; of the 

 curved surface of a right cone ; of the 

 fnutrum of a cone; of a portion of 

 the surface of a sphere, 648. 



Arithmetic, of compound quantities, ad- 

 dition, and subtraction, 441 1 multipli- 

 cation and division, 442. 



Arithmetic, decimal, 447 ; addition and 

 subtraction of; multiplication and 

 division of; extraction of the square- 

 root, 448. 



Arithmetic, fractional, 443; addition and 

 subtraction of, 444 ; multiplication and 

 division of, 445 ; proportion, 445 ; rule- 

 of-three, 446. 



Arithmetic, mental, 450. 



Arithmetic, simple addition ; subtraction, 

 434 : multiplication, 435 ; and division, 

 437. 



Arithmetic, tables of money, time, weight, 

 and measures, 439. 



Arithmetic, the rule of reduction, 440. 



Arithmetic, uses and objects of, 431 ; the 

 ten figures, numeration table, and the 

 reading of numbers ; decimal system 

 of; local value of figures, 433. 



Arithmetical algebra, 511. 



Arithmetical complement of a logarithm, 

 to find, 522. 



Arithmetical progression in algebra, 477. 



Arithmetical table of factors, 449. 



Arithmetical values of quantities in series, 

 517. 



Avoirdupois weight, 439. 



Axioms of Euclid, 543. 



BASE line, its measurement in surveying, 

 663. 



Binomial equation, roots of a, 631. 



Binomial, powers of a, 461 ; how to 

 extract the square-root of a, 482 ; mul- 

 tipliers which render binomial surds 

 rational, 483. 



Binomial theorem, how to state the, 513 ; 

 how to prove it, 514, et teg. 



Briggian logarithms, 519; tables of, 525 

 539. 



CALCULABLE logarithm, every number has 



a, 519. 

 Calculations facilitated by logarithms, 



518. 



Cask, to find the volume of a, 656. 

 Chords, tables of, 540. 

 Circle, area of, 645. 

 Circles, concentric, to find the area 



between, 646. 

 Circle, quadrature of the, difficulty of 



solving the problem, 577. 

 Circle, sector and segment of, to find, 



646. 

 Circle, to find the radius of an inscribed, 



625 ; to find the area of a quadrilateral 



inscribed in a, 626. 

 Circular arcs, tables of, 540. 

 Circular measures of an angle, 612. 

 Cloth, measures of, 439. 

 Coefficient, the multiplier in algebra so 



called, 452 ; illustrated, 455 ; inde- 

 terminate, 512. 

 Coins, gold and silver, 439. 

 Compasses nsed in geometry, 600. 

 Complement, arithmetical, of a logarithm, 



to find, 522. 



Composite numbers, factors of the, 449. 

 Compound algebraical quantity, cube-root 



of a, 484. 

 Compound quantities, addition of; sub. 



traction of; multiplication of ; division 



of, 441, 442. 



Concentric circles, area between, 646. 

 Cone, to find the volume of the frustrum, 



area, &c., of a, 654. 

 Conic sections, on the construction of, 



608; the ellipse, 608; the parabola, 



610; the hyperbola, 611 ; the cycloid, 

 611. 



Convergent series, meaning of a, 513. 



Cosecants, 613. 



Cosines, natural, 636; tables of, 665. 



Cosines of angles, 613; to obtain the nu- 

 merical value of, 637 ; tables of, 666. 



Cotangents, 613; calculation of, 637. 



Cube-root of a compound quantity, 484. 



Cube-root of decimals, exercises for finding 

 the, 485. 



Cube-root, tables of, 540. 



Cubes, tables of, 539. 



Cubic measure, table of, 440. 



Cycloid, construction of the, 61 1. 



Cylinder, area of the surface of a, 643. 



DECIMALS, addition and subtraction of; 

 multiplication of; division of, 448. 



Decimals, beautiful contrivance of, 433 ; 

 principles and practice of, 447; re- 

 duction of fractions to, 448. 



Decimals, exercises for finding the cube- 

 root of, 485. 



Definitions of Euclid, 541 ; of the prin- 

 ciples of algebra, 451 ; of plane trigono- 

 metry, 613, et teg..- of geometrical 

 planes, 592; of spherical geometry, 596. 



Delambre's method of solving logarithmic 

 sines of small angles, 640. 



De Moivre's theorem, 628. 



Denomination of fractions, 443. 



Denominator of fractions, 443, 467. 



Development of a binomial, 461. 



Distances, the measurement of, 644. 



Divergent series, meaning of a, 513. 



Dividend, the quantity so called, 462 ; 

 when a compound quantity, 463 ; 

 exercises in the working of a, 464. 



Division of algebra, the sign of, 451 ; the 

 dividend, the divisor, and the quotient, 

 462 ; operations in, 463. 



Division of compound quantities, 442; 

 of fractions, 444 ; of decimals, 448. 



Division of fractions in algebra, exercises 

 in, 466, et teg. 



Division, simple, on the use and applica- 

 tion of; various problems in, 437. 



Divisor, the quantity so called, 462 ; when 

 a compound quantity, 463. 



Double rule-of-three, principles and prac- 

 tice of, 447. 



Drawing-pens used in geometry, 600. 



Dry goods, measures for, 439. 



EARTHWORK, military, to find contents 

 of, 654. 



Ellipse, definition and illustration of the, 

 608; to find the area of, 646. 



Equality, algebraical sign of, 452. 



Equations, arithmetical and algebraical, 

 456, et teg.; on the solution of, 456; 

 different modes of operating; transpo- 

 sition, and clearing fractions ; how to 

 solve a simple equation containing only 

 one unknown quantity, 456 : questions 

 for solution and exercises, 457 ; rules 

 and operations for their solution with 

 unknown quantities, 469, ft teg. 



Equations, quadratic, solutions of, with 

 unknown quantities, 472, et seq. 



Equivalent forms, permanence of, 511. 



Euclid, elements of, and definitions, 541 ; 

 his postulates, 542 ; marks of abbrevia- 

 tion, 543. 



Euclid, definitions and propositions of 

 Book i., 541; comments on, 551; 

 exercises on, 559. 



Euclid, definitions and propositions of 

 Book II., 560; remarks on, 562; 

 exercises on Books I. and II., 563. 



