A History of Mathematics/Index

by Florian Cajori

 

INDEX.

 

 

Abacists, 126.

Abacus, 8, 13, 63, 79, 82, 119, 122, 126, 129.

Abbatt, 334.

Abel, 347, 348; ref. to, 146, 279, 291, 312, 328, 336, 337, 350, 353, 371.

Abelian functions, 292, 312, 328, 346, 348, 349, 352, 355–357, 369.

Abelian integrals, 350, 379.

Abel's theorem, 352.

Absolute geometry, 301.

Absolutely convergent series, 335, 337, 338.

Abul Gud, 111; ref. to, 112, 113.

Abul Hasan, 115.

Abul Wefa, 110; ref. to, 112, 113.

Achilles and tortoise, paradox of, 27.

Acoustics, 262, 270, 278, 386.

Action, least, 253, 366, 401; varying, 292, 318, 379.

Adams, 375; ref. to, 214.

Addition theorem of elliptic integrals, 252, 350, 396.

Adrain, 276.

Æquipollences, 322.

Agnesi, 260.

Agrimensores, 80.

Ahmes, 10–15; ref. to, 17, 18, 53, 74.

Airy, 375; ref. to, 383.

Al Battani, 109; ref. to, 110, 125.

Albertus Magnus, 134.

Albiruni, 111; ref. to, 102, 104.

Alcuin, 119.

Alembert, D'. See D'Alembert.

Alexandrian School (first), 34–54; (second), 54–62.

Alfonso's tables, 127.

Algebra: Beginnings in Egypt, 15; early Greek, 73; Diophantus, 74–77; Hindoo, 93–96; Arabic, 107, 111, 115; Middle Ages, 133, 135; Renaissance, 140, 142–150, 152; seventeenth century, 166, 187, 192; Lagrange, 267; Peacock, 284; recent, 315–331; origin of terms, 107, 115. See Notation.

Algebraic functions, 346; integrals, 377.

Algorithm, origin of term, 106; Middle Ages, 126, 129.

Al Haitam, 115; ref. to, 112.

Al Hayyami, 112; ref. to, 113.

Al Hazin, 112.

Al Hogendi, 111.

Al Karhi, 111, 113.

Al Kaschi, 114.

Al Kuhi, 111; ref. to, 112.

Allégret, 377.

Allman, IX., 36.

Al Madshriti, 115.

Almagest, 56–58; ref. to, 105, 109, 127, 134, 136, 140.

Al Mahani, 112.

Alphonso's tables, 127.

Al Sagani, 111.

Alternate numbers, 322.

Ampère, 394; ref. to, 361.

Amyclas, 33.

Analysis (in synthetic geometry), 30, 39; Descartes', 186; modern, 331–334.

Analysis situs, 226, 315.

Analytic geometry, 185–189, 191, 193, 240, 287, 307–315.

Analytical Society (in Cambridge), 283.

Anaxagoras, 18; ref. to, 28.

Anaximander, 18.

Anaximenes, 18.

Angeli, 185.

Anger, 375.

Anharmonic ratio, 178, 291, 297, 306.

Anthology, Palatine, 73, 120.

Antiphon, 26; ref. to, 27.

Apices of Boethius, 82; ref. to, 63, 103, 119, 126, 129.

Apollonian Problem, 50, 154, 188.

Apollonius, 45–50; ref. to, 35, 37, 40, 54, 61, 66, 78, 105, 108, 115, 140, 153, 154.

Appel, 346.

Applied mathematics, 373–403. See Astronomy, Mechanics.

Arabic manuscripts, 124–128.

Arabic numerals and notation, 3, 73, 87, 102, 112, 127–129, 159.

Arabs, 100–117.

Arago, XI., 332, 392.

Arbogaste, 260.

Archimedes, 40–45; ref. to, 2, 35, 37, 39, 45, 47, 49, 50, 54, 61, 65, 73, 78, 90, 105, 108, 140, 144, 169, 173, 182.

Archytas, 23; ref. to, 29, 31, 32, 43.

Areas, conservation of, 253.

Arenarius, 65.

Argand, 317; ref. to, 264.

Aristæus, 34; ref. to, 46.

Aristotle, 34; ref. to, 9, 17, 27, 43, 61, 68, 125.

Arithmetic: Pythagoreans, 20, 67–70; Platonists, 29; Euclid, 38, 70; Greek, 63–77; Hindoo, 90–92; Arabic, 106; Middle Ages, 119, 122, 123, 126, 130, 133, 134; Renaissance, 150, 151, 158–161. See Numbers, Notation.

Arithmetical machine, 220, 284.

Arithmetical triangle, 196.

Armemante, 313.

Arneth, X.

Aronhold, 327.

Aryabhatta, 86; ref. to, 88, 91, 98.

Aschieri, 305, 306.

Assumption, tentative, 75, 92. See Regula falsa.

Astrology, 155.

Astronomy: Babylonian, 8; Egyptian, 10; Greek, 18, 24, 32, 39, 51, 56; Hindoo, 86; Arabic, 100, 101, 105, 115; Middle Ages, 127; Newton, 212–216; more recent researches, 253, 257, 262, 271–274, 366, 373–377. See Mechanics.

Athelard of Bath, 125; ref. to, 135.

Athenæus, 32.

Atomic theory, 382.

Attalus, 46.

Attraction, 277. See Gravitation, Ellipsoid.

August, 296.

Ausdehnungslehre, 320, 321, 378.

Axioms (of geometry), 30, 37, 38, 281, 300, 315.

 

Babbage, 283, 356.

Babylonians, 5–9; ref. to, 19, 51.

Bachet de Méziriac. See Méziriac.

Bachmann, 371; ref. to, 365.

Bacon, R., 134.

Baker, Th., 113.

Ball, Sir R. S., 378.

Ball, W. W. R., X., 217.

Ballistic curve, 279.

Baltzer, R., 314; ref. to, 302, 325.

Barbier, 341.

Barrow, 198; ref. to, 173, 202, 203, 221, 227.

Basset, 380, 382.

Battaglini, 306.

Bauer, XII.

Baumgart, XI.

Bayes, 340.

Beaumont, XI.

Beaune, De. See De Beaune.

Bede, the Venerable, 118.

Beer, 392.

Beha Eddin, 114.

Bellavitis, 322; ref. to, 300, 304, 317.

Beltrami, 304, 305; ref. to, 315.

Ben Junus, 115.

Berkeley, 236.

Bernelinus, 122.

Bernoulli, Daniel, 238; ref. to, 255, 262, 386, 401.

Bernoulli, Nicolaus (born 1695), 238.

Bernoulli, Nicolaus (born 1687), 239, 251, 269.

Bernoulli, James (born 1654), 237, 238; ref. to, 182, 226, 229, 251.

Bernoulli, James (born 1758), 239, 356, 387.

Bernoulli, John (born 1667), 238; ref. to, 226, 229, 232, 234, 237, 243, 250, 251, 356.

Bernoulli, John (born 1710), 239.

Bernoulli, John (born 1744), 239.

Bernoullis, genealogical table of, 236.

Bernoulli's theorem, 237.

Bertini, 305.

Bertrand, 337, 340, 342, 377, 379, 380, 401.

Bessel, 373–375; ref. to, 303, 309, 351.

Bessel's functions, 374.

Bessy, 181.

Beta function, 249.

Betti, 353.

Beyer, 160.

Bézout, 260; ref. to, 250, 264.

Bézout's method of elimination, 260, 331.

Bhaskara, 87; ref. to, 92–95, 97, 152.

Bianchi, 328.

Billingsley, 138.

Binet, 324, 387.

Binomial formula, 195, 196, 202, 251, 348.

Biot, 275, 288, 393.

Biquadratic equation, 112, 146, 149.

Biquadratic residues, 366.

Biquaternions, 378.

Bjerknes, C. A., XIII., 357, 383.

Bobillier, 308.

Bôcher, XIV.

Bode, 341.

Boethius, 81; ref. to, 63, 72, 103, 118, 121, 134, 135.

Bois-Reymond, P. du, XIII., 337–339, 362.

Boltzmann, 397, 403.

Bolyai, Johann, 302; ref. to, 291.

Bolyai, Wolfgang, 301, 302; ref. to, 291, 364.

Bolza, 350.

Bombelli, 146; ref. to, 152.

Bonnet, O., 314; ref. to, 337, 342.

Boole, 343; ref. to, 291, 325, 340, 341, 346.

Booth, 311.

Borchardt, 355.

Bouniakowsky, 365.

Bouquet, 344; ref. to, 346, 354.

Bour, 341, 377.

Boussinesq, 383, 391, 393.

Bowditch, 275, 323.

Boyle's law, 401.

Brachistochrone (line of swiftest descent), 234, 238.

Bradwardine, 135; ref. to, 141.

Brahe, Tycho, 110, 139, 168.

Brahmagupta, 86; ref. to, 92, 95, 98, 102.

Bredon, 135.

Bretschneider, IX., 97, 320.

Brianchion, 178, 288, 289.

Briggs, 163.

Brill, A., 297, 311, 356.

Brill, L., 307.

Bring, 328.

Brioschi, 327; ref. to, 325, 330, 334, 350, 353, 379.

Briot, 344; ref. to, 346, 354.

Brouncker, 197.

Bruno, Faà de, 327.

Bruns, 377.

Bryson of Heraclea, 27.

Buchheim, 378; ref. to, 306.

Buckley, 159.

Budan, 282.

Buddha, 89.

Buffon, 340.

Bungus, 155.

Bürgi, 160; ref. to, 165.

Burkhardt, H., XII., 328.

Burkhardt, J. K., 275.

Burmester, 300.

Busche, 365.

Buteo, 154.

Buy's-Ballot, 402.

Byrgius. See Bürgi.

 

Cæsar, Julius, 81.

Calculating machines, 220, 284.

Calculation, origin of word, 79.

Calculus. See Differential Calculus.

Calculus of operations, 292; of variations, 247, 249, 261, 265, 296, 328, 333–334, 356, 366.

Calendar, 9, 81, 141, 154, 271.

Callisthenes, 9.

Canon paschalis, 79.

Cantor, G., 339, 362, 372.

Cantor, M., IX., X., 112.

Capelli, 330.

Capillarity, 278, 366, 388, 398.

Caporali, 313.

Cardan, 144; ref. to, 149, 152, 155, 156, 159.

Carll, 334.

Carnot, Lazare, 288, 289; ref. to, 56, 236, 293.

Carnot, Sadi, 399.

Casey, 313.

Cassini, D., 257.

Cassiodorius, 83, 118.

Casting out the 9's, 91, 106.

Catalan, E., 325.

Cataldi, 159.

Catenary, 191, 234, 237.

Cattle-problem, 73.

Cauchy, 331—333; ref. to, 243, 247, 264, 322, 324, 328, 330, 335, 338, 339, 341, 342, 345, 348, 349, 350, 353, 356, 362, 368, 383, 387, 388, 390, 393.

Caustics, 238, 241.

Cavalieri, 170; ref. to, 167, 193, 221.

Cavendish, 394.

Cayley, 325, 326; ref. to, XII., XIV., 291, 296, 297, 306, 308, 311, 313, 319, 324, 330, 346, 354, 355.

Centre of gravity, 177, 191; of oscillation, 191, 243.

Centres of osculation, 49.

Centrifugal force, 183, 192, 214.

Ceulen, van. See Ludolph.

Ceva, 290.

Chapman, 324.

Characteristics, method of, 297.

Chasles, 296–298; ref. to, X., 39, 47, 49, 52, 172, 289, 294, 306, 311, 313, 377.

Chauvenet, 377.

Chess, 92.

Cheyne, 206.

Chinese, 19.

Chladni's figures, 386.

Chree, 382, 391.

Christoffel, 325, 327.

Circle, 19, 24–28, 31, 41, 52, 154, 194; degrees of, 7, 271; division of, 329, 365.

Circle-squarers, 2, 19, 190, 316.

Cissoid, 50, 191.

Clairaut, 256–258; ref. to, 244, 252, 255, 262.

Clapeyron, 399.

Clarke, 341.

Clausius, 399; ref. to, 390, 398, 400–402.

Clavius, 155; ref. to, 154.

Clebech, 312, 313; ref to, XII., 296, 309, 315, 322, 327, 328, 333, 341, 342, 358, 381, 383, 390–392.

Clifford, 305. 306; ref. to, 297, 319, 324, 358, 378, 396.

Cockle, 315.

Colburn, Z., 180.

Colding, 398.

Cole, 330.

Colebrooke, 87.

Colla, 143, 145.

Collins, 203, 223, 227, 228, 230, 232.

Colson, 204.

Combinatorial School, 247, 335.

Commandinus, 153.

Commercium epistolicum, 206, 232.

Complex quantities, 292, 317. See Imaginaries.

Complex of lines, 309.

Computus, 118, 119.

Comte, X.

Concentric spheres of Eudoxus, 32.

Conchoid, 50.

Condensation of singularities, 362.

Conform representation of surfaces, 361.

Congruencies, theory of, 365.

Congruency of lines, 309.

Conic sections, Greek, 32, 34, 40, 41, 45–49, 55; Arabs, 101, 112; Renaissance, 153; Kepler, 168; more recent researches, 176–178, 192. See Geometry.

Conon, 40; ref. to, 42.

Conservation of areas, 253; of energy, 397, 398; of vis viva, 192.

Continued fractions, 159, 197. 252, 270.

Continuity, 169, 193, 226, 293, 333, 359, 372.

Contracted vein, 384.

Contravariants, 326.

Convergence of series, 334–339.

Co-ordinates, 185, 294, 308. 314, 379; first use of term, 226.

Copernican System, 139.

Copernicus, 56, 139.

Correspondence, principle of, 293, 297.

Cosine, 165.

Coss, term for algebra, 152.

Cotangent, 141, 165.

Cotes, 242; ref. to, 243.

Coulomb, 394.

Cournot, 340.

Cousinery, 299.

Covariants, 327, 354, 369.

Cox, 306.

Craig, 306, 347, 355, 382.

Craige, 226.

Cramer, 217.

Crelle, 348; ref. to, 349.

Crelle's Journal, 295.

Cremona, 299; ref. to, 291, 294–296, 300, 313.

Cridhara, 87.

Criteria of convergence, 334–339.

Crofton, 341.

Crozet, 288.

Ctesibius, 52.

Cube, duplication of. See Duplication of the cube.

Cube numbers, 72, 111, 180.

Cubic curves, 217, 257, 297.

Cubic equations, 112, 113, 142–145, 149, 152, 153. See Algebra.

Cubic residues, 366.

Culmann, 299, 300.

Curtze, M., 299.

Curvature, measure of, 314.

Curve of swiftest descent, 234, 238.

Curves, osculating, 226; quadrature of, 42, 49, 177, 190, 193, 202, 220; theory of, 226, 240, 242, 243, 292, 321. See Cubic curves, Rectification, Geometry, Conic sections.

Cusanus, 154.

Cyclic method, 96, 97.

Cycloid, 171, 173, 176, 187, 190, 191, 225, 234, 240.

Cyzicenus, 33.

Czuber, 340.

 

D'Alembert, 254–256; ref. to, 254, 258, 262, 265, 268–270, 386.

D'Alembert's principle, 254.

Damascius, 61; ref. to, 38, 104.

Darboux, XIII., 313, 343, 346, 361, 362.

Darwin, 376; ref. to, 384, 391.

Data (Euclid's), 39.

Davis, E. W., 306.

Davis, W. M., 385.

De Baune, 189; ref. to, 185, 223, 225.

Dee, 138.

Decimal fractions, 159–161.

Decimal point, 161.

Dedekind, 371; ref. to, 357, 362, 372.

Deficiency of curves, 312.

Definite integrals, 169, 334, 339, 341, 351, 362.

Deinostratus. See Dinostratus.

De Lahire, 285, 290.

Delambre, 366.

Delaunay, 376; ref. to, 333, 334.

Delian problem. See Duplication of the cube.

Del Pezzo, 305.

Democritus, 28; ref. to, 16.

De Moivre, 240.

De Morgan, 316; ref. to, X., XI., 1, 2, 70, 96, 161, 205, 229, 233, 260, 277, 285, 291, 333, 337, 340, 366.

De Paolis, 306.

Derivatives, method of, 269.

Desargues, 177; ref. to, 174, 184, 240, 285, 290.

Desboves, 379.

Descartes, 183–189; ref. to, 4, 48, 60, 113, 167, 173, 174, 189, 191, 192, 216, 220, 223, 240, 317; rule of signs, 187, 193.

Descriptive geometry, 286–288, 300.

Determinants, 226, 265, 278, 313, 324, 325, 334, 363.

Devanagari-numerals, 103.

Dialytic method of elimination, 330.

Differences, finite. See Finite differences.

Differential calculus, 200, 221–227, 236–242 (see Bernoullis, Euler, Lagrange, Laplace, etc.); controversy between Newton and Leibniz, 227–233; alleged invention by Pascal, 174; philosophy of, 236, 256, 259, 268, 289. 333.

Differential equations, 239, 252, 265, 278, 314, 318, 321, 333, 341–347.

Differential invariants, 327.

Dingeldey, 315.

Dini, 337; ref. to, 362.

Dinostratus, 32; ref. to, 25.

Diocles, 50.

Diodorus, 10, 40, 58.

Diogenes Laertius, 17, 32.

Dionysodorus, 54.

Diophantus, 74–77; ref. to, 55, 61, 86, 93, 95, 96, 105, 106, 107, 110, 111, 179, 372.

Directrix, 49, 60.

Dirichlet, 367–369; ref. to, XIII., 179, 291, 334, 338, 339, 348, 356, 357, 359, 362, 371, 396.

Dissipation of energy, 400.

Divergent parabolas, 217, 257.

Divergent series, 255, 337.

Division of the circle, 7, 271, 329, 365.

Diwani-numerals, 102.

Donkin, 379.

Dositheos, 40.

Dostor, 325.

Dové, 384.

D'Ovidio, 306.

Dronke, XII.

Duality, 290, 297, 308.

Duhamel, 333, 388.

Dühring, E., X.

Duillier, 230.

Duodecimals, 124, 126.

Dupin, 288, 289; ref. to, 300, 314.

Duplication of the cube, 23–25, 31, 32, 45, 50, 153.

Durège, 354; ref. to, 309, 315.

Dürer, A., 156.

Düsing, 340.

Dyck, 315. See Groups.

Dynamics, 318, 378–381.

Dziobek, XIII., 377.

 

Earnshaw, 383.

Earth, figure of, 257, 292; rigidity of, 391; size of, 214, 215.

Eddy, 300.

Edfu, 12, 53.

Edgeworth, 340.

Egyptians, 9–16, 19.

Eisenlohr, 333.

Eisenstein, 369; ref. to, 354, 357, 365, 370, 371.

Elastic curve, 237.

Elasticity, 278, 387–392.

Electricity, 394–398.

Electro-magnetic theory of light, 394.

Elements (Euclid's), 36–39, 104, 114, 125, 127, 128, 133, 135, 136, 138. See Euclid.

Elimination, 250, 308, 310, 330, 331. See Equations.

Elizabeth, Princess, 188.

Ellipsoid (attraction of), 215, 277, 280, 285, 298, 366, 378, 379; motion of, 383.

Elliptic co-ordinates, 379.

Elliptic functions, 241, 279, 280, 296, 329, 345, 346, 347–354, 363, 367, 370.

Elliptic geometry. See Non-Euclidean geometry.

Elliptic integrals, 247, 252, 328, 349, 350.

Ely, 372.

Encke, 366.

Energy, conservation of, 397, 398.

Eneström, XI.

Enneper, 353; ref. to, XIII.

Entropy, 400.

Enumerative geometry, 297.

Epicycles, 51.

Epping, IX., 9.

Equations, solution of, 15, 149, 153, 186, 250, 260, 263, 277, 348; theory of, 75, 166, 189, 193, 216, 240, 241, 250, 328–331; numerical, 147, 264, 282. See Cubic equations, Algebra, Theory of numbers.

Eratosthenes, 44; ref. to, 25, 35, 40, 71.

Errors, theory of. See Least squares.

Espy, 384.

Ether, luminiferous, 393.

Euclid, 35–40, 70, 71; ref. to, 17, 21, 22, 26, 30, 31, 33, 34, 42, 46, 50, 53, 57, 58, 61, 72, 73, 78, 81, 97, 104, 108, 114, 125, 127, 136, 138, 144, 162, 281, 303.

Euclidean space. See Non-Euclidean geometry.

Eudemian Summary, 17, 21, 30, 32, 33, 35.

Eudemus, 17, 22, 45, 46, 69.

Eudoxus, 32, 33; ref. to, 16, 28, 31, 32, 35, 36, 51.

Euler, 248–254; ref. to, 77, 96, 179, 180, 239, 241, 246, 250, 258, 259, 261, 262, 264, 265, 267, 268, 273, 278, 279, 280, 287, 314, 317, 334, 364, 365, 367, 374, 386, 387, 401.

Eulerian integrals, 280.

Eutocius, 61; ref. to, 45, 46, 54, 65.

Evolutes, 49, 191.

Exhaustion, method of, 26, 28, 33, 36, 42, 169.

Exponents, 134, 152, 160, 162, 187, 202, 241.

 

Factor-tables, 368.

Fagnano, 241.

Fahri des Al Karhi, 111.

Falsa positio, 92, 147.

Faraday, 398.

Favaro, XII.

Faye, 377.

Fermat, 173, 179–182; ref. to, 172, 173, 177, 198, 252, 264, 265, 367.

Fermat's theorem, 180, 252.

Ferrari. 145; ref. to, 144, 264.

Ferrel, 384; ref. to, 376.

Ferro, Scipio, 142.

Fibonacci. See Leonardo of Pisa.

Fiedler, 300, 312, 328.

Figure of the earth, 257, 292.

Finæus, 159.

Fine, XII.

Finger-reckoning, 63, 118.

Finite differences, 240, 242, 251, 270, 278, 343.

Fink, XII.

Fitzgerald, 394.

Flächenabbildung, 313.

Flamsteed, 218.

Floridas, 142, 144.

Flexure, theory of, 389.

Fluents, 205, 206.

Fluxional controversy, 227–233.

Fluxions, 200, 202–213, 333.

Focus, 49, 60, 169, 170.

Fontaine, 252, 254.

Forbes, 397.

Force-function, 395. See Potential.

Forsyth, XII., 327, 344, 362.

Four-point problem, 341.

Fourier, 281–284; ref. to, 174, 255, 351, 356, 367.

Fourier's series, 283, 338, 339, 367, 386.

Fourier's theorem, 282.

Fractions, Babylonian, 7; Egyptian, 13; Greek, 26, 64, 65; Roman, 78; Hindoo, 94; Middle Ages, 120, 124; decimal, 159, 160; sexagesimal, 7, 57, 65, 67, 126; duodecimal, 124, 126; continued, 159, 197, 252, 270. See Arithmetic.

Franklin, 327, 372.

Frantz, XIII.

Fresnel, 392.

Fresnel's wave-surface, 209, 314.

Frézier, 286.

Fricke, 354.

Friction, theory of, 382.

Frobenius, 325, 344, 345.

Frost, 315.

Froude, 381, 384.

Fuchs, 343; ref. to, 344, 345.

Fuchsian functions, 345, 360.

Fuchsian groups, 345.

Functions, definition of, 356; theory of, 268, 269, 345, 356–362; arbitrary, 262, 283. See Elliptic functions, Abelian functions, Hyperelliptic functions, Theta functions, Beta function, Gamma function, Omega function, Sigma function, Bessel's function, Potential.

Funicular polygons, 299.

 

Gabir ben Aflah, 115; ref. to, 127.

Galileo, 182; ref. to, 43, 139, 161, 168, 170, 171, 188.

Galois, 329.

Gamma function, 249.

Garbieri, 324.

Gases, Kinetic theory of, 401–403.

Gauss, 363–367; ref. to, 77, 158, 247, 248, 251, 264, 276, 291, 294, 302, 303, 304, 313, 314, 315, 317, 320, 324, 325, 239, 330, 333, 335, 343, 348, 350, 351, 357, 362, 373, 398.

Gauss' Analogies, 366.

Geber. See Gabir ben Aflah.

Geber's theorem, 116.

Geminus, 53; ref. to, 46, 50, 57.

Gellibrand, 165.

Genocchi, 365.

Geodesics, 249, 379.

Geodesy, 366.

Geometry, Babylonian, 8; Egyptian, 10–13; Greek, 17–62, 69; Hindoo, 97, 98; Roman, 80; Arabic, 104, 108, 110, 113, 114; Middle Ages, 121, 125, 127, 128, 130, 131; Renaissance, 138, 153, 154, 158, 167; analytic, 186–189, 191, 193, 287, 307–315; modern synthetic, 240, 285–290, 293–307; descriptive, 286–288, 300. See Curves, Surfaces, Curvature, Quadrature, Rectification, Circle.

Gerard of Cremona, 126.

Gerbert, 120–124.

Gergonne, 297; ref. to, 178, 290.

Gerhardt, XI., 227, 230, 233.

Gerling, 366.

Germain, Sophie, 387; ref. to, 386.

German Magnetic Union, 366.

Gerstner, 389.

Gibbs, 400; ref. to, XII., 319.

Giovanni Campano, 127.

Girard, 166; ref. to, 127, 161.

Glaisher, 372; ref. to, XIII., 325, 328, 374, 368.

Glazebrook, 397; ref. to, XIV.

Gobar numerals, 82, 103.

Godfrey, 218.

Golden section, 33.

Göpel, 355.

Gordan, 312, 327, 330.

Gournerie, 300, 311.

Goursat. 343; ref. to, 350.

Gow, IX., 35.

Graham, XII.

Grammateus, 151.

Grandi, 251.

Graphical statics, 292, 299.

Grassmann, 320–321; ref. to, 294, 304, 317, 318, 378.

Gravitation, theory of, 213, 258, 271, 275.

Greeks, 16–77.

Green, 395; ref. to, 358, 383, 388, 390, 393, 395.

Greenhill, 354. 382.

Gregorian Calendar, 154.

Gregory, David F., 215, 284, 315.

Gregory, James, 228, 243.

Gromatici, 80.

Groups, theory of, 328–330, 344–346. Papers by W. Dyck (Math. Ann., 20 and 22) and by O. Hölder (Math. Ann., 34) should have been mentioned on p. 330.

Grunert, 314; ref. to, 320.

Gua, de, 240.

Gubar-numerals, 82, 103.

Gudermann, 353.

Guldin, 167; ref. to, 59, 171.

Guldinus. See Guldin.

Gunter, E., 165.

Günther, S., IX., X., XI., 325.

Gützlaff, 353.

 

Haan, 334.

Haas, XII.

Hachette, 288, 300.

Hadamard, 368.

Hadley, 218.

Hagen, 276.

Halifax, 134; ref. to, 136.

Halley, 45, 213, 214, 261.

Halley's Comet, 258, 374.

Halphen, 311; ref. to, 297, 315, 327, 344, 345, 354.

Halsted, X., 303.

Hamilton, W., 184, 316.

Hamilton, W. R., 318, 319; ref. to, 266, 291, 292, 314, 316, 317, 321, 324, 328, 341, 378, 379, 393, 401.

Hamilton's numbers, 329.

Hammond, J., 327.

Hankel, 322; ref. to, IX., X., 28, 93, 96, 285, 325, 339, 362.

Hann, 385.

Hansen, 375.

Hanus, 325.

Hardy. 174.

Harkness, 362.

Harmonics, 55.

Haroun-al-Raschid, 104.

Harrington, 377.

Harriot, 166; ref. to, 147, 152, 162, 187, 192.

Hathaway, XI.

Heat, theory of, 399–401.

Heath, 306.

Heaviside, 319, 397, 398.

Hebrews, 19.

Hegel, 373.

Heine, 339; ref. to, 362, 372.

Helen of geometers, 187.

Helicon, 32.

Heliotrope, 363.

Helmholtz, 397, 398; ref. to, 304, 305, 382, 385, 386, 393, 396, 400, 401.

Henrici, XIII.

Henry, 396.

Heraclides, 45.

Hermite, 353; ref. to. XIII., 328, 330, 343, 347, 350, 355, 362, 372.

Hermotimus, 33.

Herodianic signs, 63.

Heron the Elder, 52; ref. to, 50, 54, 65, 80, 98, 105, 131, 140.

Herschel, J. F. W.. 386; ref. to, X., 276, 283, 284, 356.

Hesse, 309–311; ref. to, 295, 309, 312, 325, 329, 330, 333, 342, 377.

Hessian, 295, 310, 327.

Heuraet, 190.

Hexagrammum mysticum, 178, 296.

Hicks, 382, 384.

Hilbert, 327.

Hill, 376.

Hindoos, 84–100; ref. to, 3.

Hipparchus, 51; ref. to, 54, 56.

Hippasus, 22.

Hippias of Elis, 25.

Hippocrates of Chios, 25, 28, 30.

Hippopede, 51.

Hirn, 400.

History of mathematics, its value, 1–4.

Hodgkinson, 389.

Hölder, O. See Groups.

Holmboe, 336, 347, 350.

Homogeneity, 293, 308.

Homological figures, 178.

Honein ben Ishak, 104.

Hooke, 213.

Hoppe, 306.

Horner, 147, 330.

Hospital, l', 239, 240.

Hoüel, 319.

Hovarezmi, 106; ref. to, 107, 110, 114, 125, 127.

Hudde, 189; ref. to, 203.

Hurwitz, 358.

Hussey, 377.

Huygens, 190–192; ref. to, 177, 182, 188, 213, 214, 219, 234, 257, 392.

Hyde, 321.

Hydrodynamics, 239, 255, 380, 381–384. See Mechanics.

Hydrostatics, 44, 255. See Mechanics.

Hypatia, 61; ref. to, 37.

Hyperbolic geometry. See Non-Euclidean geometry.

Hyperelliptic functions, 292, 328, 348, 354, 360.

Hyperelliptic integrals, 352.

Hypergeometric series, 335, 361.

Hyperspace, 304, 305.

Hypsicles, 51; ref. to, 7, 38, 71, 104.

 

Iamblichus, 72; ref. to, 10, 22, 69.

Ibbetson, 392.

Ideal numbers, 371.

Ideler, 32.

Iehuda ben Mose Cohen, 127.

Ignoration of co-ordinates, 380.

Images, theory of, 381.

Imaginary geometry, 301.

Imaginary points, lines, etc., 298.

Imaginary quantities, 146, 166, 241, 287, 349, 363, 372.

Imschenetzky, 342.

Incommensurables, 36, 38, 70. See Irrationals.

Indeterminate analysis, 95, 101, 111. See Theory of numbers.

Indeterminate coefficients, 186.

Indeterminate equations, 95, 101, 111. See Theory of numbers.

Indian mathematics. See Hindoos.

Indian numerals. See Arabic numerals.

Indices. See Exponents.

Indivisibles, 170–173, 176, 193.

Induction, 340.

Infinite products, 349, 354.

Infinite series, 197, 203, 208, 220, 247, 250, 255, 259, 269, 283, 334–339, 348, 349, 361, 363.

Infinitesimal calculus, See Differential calculus.

Infinitesimals, 135, 169, 207, 208, 211.

Infinity, 27, 135, 169, 178, 193, 269, 293, 304, 308; symbol for, 193.

Insurance, 239, 340.

Integral calculus, 171, 223, 348, 350, 368, 371; origin of term, 237.

Interpolation, 194.

Invariant, 293, 310, 325, 328, 344, 354.

Inverse probability, 340.

Inverse tangents (problem of), 169, 189, 220, 222, 223.

Involution of points, 60, 177.

Ionic School, 17–19.

Irrationals, 22, 26, 69, 94, 107, 362, 372. See Incommensurables.

Irregular integrals, 344.

Ishak ben Honein, 104.

Isidorus of Seville, 118; ref. to, 61.

Isochronous curve, 234.

Isoperimetrical figures, 51, 237, 249, 261. See Calculus of variations.

Ivory, 285; ref. to, 276.

Ivory's theorem, 285.

 

Jacobi, 351–352; ref. to, 279, 291, 295, 308, 309, 315, 324, 330, 333, 341, 347, 349, 350, 353, 357, 365, 367, 370, 374, 377, 378, 379, 381.

Jellet, 334; ref. to, 381, 390.

Jerrard, 328.

Jets, 382, 386.

Jevons, 340.

Joachim. See Rhæticus.

Jochmann, 402.

John of Seville, 126, 159.

Johnson, 347.

Jordan, 329; ref. to, 341, 343, 346.

Jordanus Nemorarius, 134.

Joubert, 353.

Joule, 399; ref. to, 401, 403.

Julian calendar, 81.

Jurin, 236.

 

Kaestner, 363; ref. to, 217.

Kant, 274, 376.

Kauffmann. See Mercator, N.

Keill, 231, 232, 235.

Kelland, 383, 397.

Kelvin, Lord, 395–396; ref. to, 283, 315, 358, 381, 382, 383, 388, 391, 393, 394, 395, 399, 400, 403. See Thomson, W.

Kempe, 326.

Kepler, 168–170; ref. to, 139, 156, 158, 161, 167, 171, 174, 202, 213, 263.

Kepler's laws, 168, 213.

Kerbedz, XIII.

Ketteler, 393.

Killing, 306.

Kinckhuysen, 204.

Kinetic theory of gases, 401–403.

Kirchhoff, 396; ref. to, 309, 381, 382, 383, 388, 393, 396.

Klein, 343; ref. to, XII., 305, 306, 307, 309, 313, 328, 330, 345, 346, 347, 354.

Kleinian groups, 345.

Kleinian functions, 360.

Kohlrausch, 394.

Kohn, 337.

König, 401.

Königsberger, 353; ref. to, 344, 350, 354, 355.

Köpcke, 382.

Korkine, 372; ref. to, 341.

Korndörfer, 313.

Kowalevsky, 380; ref. to, 345, 352, 378.

Krause, 355.

Krazer, 355.

Kronecker, 329; ref. to, 328, 330, 359, 365.

Krönig, 401.

Kühn, H., 317.

Kuhn, J., 219.

Kummer, 370, 371; ref. to, XIII., 179, 314, 337, 338, 343, 355, 365.

 

Lacroix, 284, 286, 287, 320.

Laertius, 10.

Lagrange, 260–270; ref. to, 4, 77, 174, 179, 183, 244, 246, 247, 248, 254, 255, 259, 273, 277, 278, 279, 280, 293, 296, 304, 309, 313, 314, 325, 362, 363, 364, 367, 378, 383, 386, 387, 401.

Laguerre, 306.

Lahire, de, 240.

Laisant, 319.

La Louère, 177.

Lamb, 378, 382, 383, 396.

Lambert, 258–259; ref. to, 2, 290, 303, 313.

Lamé, 389; ref. to, 367, 389, 392.

Lamé's functions, 389.

Landen, 259; ref. to, 268, 279.

Laplace, 270–278; ref. to, 174, 215, 245, 246, 256, 263, 279, 285, 320, 336, 340, 362, 363, 373, 375, 376, 384, 386, 392, 395, 398.

Laplace's coefficients, 277.

Latitude, periodic changes in, 392.

Latus rectum, 48.

Laws of Laplace, 273.

Laws of motion, 183, 188, 213.

Least action, 253, 266, 401.

Least squares, 276, 281, 285, 363.

Lebesgue, 325, 333, 365.

Legendre, 278–281; ref. to, 247, 252, 259, 266, 276, 301, 349, 350, 351, 353, 365, 367.

Legendre's function, 280.

Leibniz, 219–235; ref. to, 4, 158, 176, 200, 208, 209, 210, 237, 241, 250, 251, 252, 268, 315, 334, 356.

Lemoine, 341.

Lemonnier, 267.

Leodamas, 33.

Leon, 33.

Leonardo of Pisa, 128; ref. to, 133, 137.

Leslie, X.

Le Verrier, 375; ref. to, 376.

Levy, 300, 391.

Lewis, 382.

Lexis, 340.

Leyden jar, 396.

L'Hospital, 239, 240; ref. to, 229, 234.

Lie, 346; ref. to, 341, 350.

Light, theory of, 218, 390.

Limits, method of, 212, 268.

Lindelöf, 334.

Lindemann, 315; ref. to, 2, 306, 356.

Linear associative algebra, 323.

Lintearia, 237.

Liouville, 369; ref. to, 314, 356, 365, 370, 379.

Lipschitz, 306; ref. to, 338, 375, 382.

Listing, 315.

Lloyd, 393.

Lobatchewsky, 301; ref. to, 291, 303.

Local probability, 340.

Logarithmic criteria of convergence, 337.

Logarithmic series, 197.

Logarithms, 158, 161–165, 168, 197, 242, 250.

Logic, 37, 316, 323, 343.

Lommel, 375, 393.

Long wave, 383.

Loomis, 384.

Lorenz, 393.

Loria, XI.

Loud, 298.

Lucas de Burgo. See Pacioli.

Ludolph, 154.

Ludolph's number, 154.

Lune, squaring of, 25.

Lüroth, 358; ref. to, 362.

 

MacCullagh, 311; ref. to, 393.

Macfarlane, 319.

Machine, arithmetical, 220, 284.

Maclaurin, 243; ref. to, 236, 244, 280, 285, 290.

Macmahon, 327.

Magic squares, 92, 135, 241.

Magister matheseos, 136.

Main, 377.

Mainardi, 334.

Malfatti, 296, 328.

Malfatti's problem, 296, 312.

Mansion, 341.

Marie, Abbé, 279.

Marie, C. F. M., 298.

Marie, M., X., 52, 172.

Mathieu, 391; ref. to, 353, 377, 392, 398.

Matrices, 321, 324.

Matthiessen, X.

Maudith, 135; ref. to, 141.

Maupertius, 253, 257, 401.

Maurolycus, 153; ref. to, 155.

Maxima and minima, 49, 174, 186, 189, 208, 244, 333, 334, 339, 342.

Maxwell, 387; ref. to, 300, 376, 382, 390, 394, 396, 398, 400, 401, 402, 403.

Mayer, 398; ref. to, 376.

McClintock, 328.

McColl, 341.

McCowan, 383.

McCullagh, 311, 393.

McMahon, 328.

Mechanics: Greek, 23, 34, 43; Stevin and Galileo, 158, 182; Descartes, Wallis Wren, Huygens, Newton, 188, 191, 192, 212–216; Leibniz, 227; Bernoullis, 237, 238; Taylor, 243; Euler, 253; Lagrange, 266; Laplace, 274; more recent work, 290, 328, 346, 377–381, 401. See Dynamics, Hydrodynamics, Hydrostatics, Graphic statics, Laws of motion, Astronomy, D'Alembert's principle.

Meissel, 353.

Menæchmus, 32; ref. to, 31, 34, 46, 113.

Menelaus, 55; ref. to, 57, 157.

Mercator, G., 313.

Mercator, N., 197; ref. to, 220.

Méré, 182.

Mersenne, 180, 191.

Mertens, 336, 367.

Meteorology, 384–386.

Method of characteristics, 297.

Method of exhaustion, 28; ref. to, 33, 36, 42, 169.

Metius, 154.

Meunier, 314.

Meyer, A., 340, 341.

Meyer, G. F., 334.

Meyer, O. E., 382, 392, 402.

Méziriac, 179; ref. to, 265.

Michelson, 394.

Middle Ages, 117–137.

Midorge, 174.

Minchin, 381.

Minding, 314.

Minkowsky, 370.

Mittag-Leffler, 359.

Möbius, 294; ref. to, 293, 320, 321, 366, 375, 377.

Modern Europe, 138 et seq.

Modular equations, 329, 353.

Modular functions, 354.

Mohammed ben Musa Hovarezmi, 106; ref. to, 107, 110, 114, 125, 127.

Mohr, 300.

Moigno, 334.

Moivre, de, 245.

Mollweide, 366.

Moments in fluxionary calculus, 205, 206.

Monge, 286–288; ref. to, 248, 259, 282, 293, 300, 314, 341.

Montmort, de, 240.

Montucla, X., 172.

Moon. See Astronomy.

Moore, 330.

Moors, 115, 116, 125.

Moral expectation, 239.

Morley, 362.

Moschopulus, 135.

Motion, laws of, 183, 188, 213.

Mouton, 219.

Muir, XII., 325.

Müller, X.

Müller, J. See Regiomontanus.

Multi-constancy, 390, 391.

Multiplication of series, 335, 336.

Musa ben Sakir, 108.

Musical proportion, 8.

Mydorge, 177.

 

Nachreiner, 325.

Nägelbach, 324.

Napier, J., 162, 163; ref. to, 156, 161, 164, 165.

Napier, M., X.

Napier's rule of circular parts, 165.

Nasir Eddin, 114.

Nautical almanac, United States, 376.

Navier, 387; ref. to, 382, 390.

Nebular hypothesis, 274.

Negative quantities, 93, 152, 187, 256, 372. See Algebra.

Negative roots, 93, 112, 146, 149, 152, 166. See Algebra.

Neil, 190; ref. to, 198.

Neocleides, 33.

Neptune, discovery of, 375.

Nesselmann, 76.

Netto, 330.

Neumann, C., 375; ref. to, 309, 315, 393.

Neumann, F. E., 398; ref. to, 309, 312, 390, 392, 396, 401.

Newcomb, 376; ref. to, 306, 307, 392.

Newton, 201–218; ref. to, 4, 50, 60, 147, 173, 186, 191, 192, 195, 200, 238, 243, 244, 252, 254, 257, 258, 262, 268, 282, 285, 290, 297, 302, 317, 330, 334, 372, 380, 386.

Newton, controversy with Leibniz, 227–233.

Newton's discovery of binomial theorem, 195, 196.

Newton's discovery of universal gravitation, 213.

Newton's parallelogram, 217.

Newton's Principia, 191, 208, 212–215, 229, 233, 242.

Nicolai, 366.

Nicole, 240.

Nicolo of Brescia. See Tartaglia.

Nicomachus, 72; ref. to, 58, 81.

Nicomedes, 50.

Nieuwentyt, 235.

Nines, casting out the, 106.

Niven, 396.

Nolan, 376.

Non-Euclidean geometry, 38, 300–307.

Nonius, 153; ref. to, 154.

Notation: in algebra, 15, 75, 93, 133, 134, 149, 150, 151, 160, 167; Babylonian numbers, 5–7; Egyptian numbers, 13; Greek numbers, 64; Arabic notation, 3, 73, 87, 102, 112, 127–129, 159; Roman, 78; decimal fractions, 160; trigonometry, 249; differential calculus, 205, 221, 222, 260, 269, 283. See Exponents, Algebra.

Nöther, 311, 313, 330, 356.

Numbers: amicable, 68, 108, 115; excessive, 68; heteromecic, 68; perfect, 68; defective, 68; triangular, 180; definitions of numbers, 372; theory of numbers, 55, 76, 95, 108, 119, 131, 178–182, 252, 264, 280, 362–372.

Numbers of Bernoulli, 238.

Numerals: Egyptian, 13; Babylonian, 5–7; Greek, 64; Arabic, 87, 102, 103, 112. See Apices.

 

Oberbeck, 386.

Œnopides, 19; ref. to, 16.

Ohm, M., 317.

Ohrtmann, X.

Olbers, 364, 373.

Oldenburg, 228.

Olivier, 300.

Omega-function, 353.

Operations, calculus of, 292.

Oppolzer, 377.

Optics, 39.

Oresme, 134; ref. to, 160.

Orontius, 154.

Oscillation, centre of, 191, 243.

Ostrogradsky, 333, 379.

Otho, 142.

Oughtred, 167; ref. to, 147, 161, 202.

Ovals of Descartes, 187.

 

$\scriptstyle {\pi }$: values for; Babylonian and Hebrew, 8; Egyptian, 11; Archimedean, 41; Hindoo, 98; Arabic, 108; Ludolph's, 154; Wallis', 194, 195; Brouncker's, 197; Fagnano's, 241; Leibniz's, 220; selection of letter $\scriptstyle {\pi }$, 250; proved to be irrational, 259, 281; proved to be transcendental, 2.

Pacioli, 135; ref. to, 134, 142, 152, 155, 158, 196.

Padmanabha, 87.

Palatine anthology, 73, 120.

Pappus, 58–61; ref. to, 35, 39, 45, 49, 50, 55, 65, 66, 153, 178, 186.

Parabola, 42, 70, 198; semi-cubical, 190. See Geometry.

Parabolic geometry. See Non-Euclidean geometry.

Parallelogram of forces, 183.

Parallels, 38, 281, 300, 301, 303, 306.

Parameter, 48.

Partial differential equations, 208, 255, 287, 341 et seq., 379.

Partition of numbers, 372.

Pascal, 175–177; ref. to, 178, 182, 196, 220, 240, 284, 285, 290, 310.

Pascal's theorem, 178.

Peacock, 284; ref. to, X., 130, 133, 161, 283, 315.

Pearson, 391.

Peaucellier, 326.

Peirce, B., 323; ref. to, 291, 317, 376, 381.

Peirce, C. S., 323; ref. to, 37, 307, 321.

Peletarius, 166.

Pell, 147, 151, 181, 219.

Pell's problem, 97, 181.

Pemberton, 201.

Pendulum, 191.

Pepin, 365.

Perier, Madame, X.

Periodicity of functions, 349, 350.

Pernter, J. M., 385.

Perseus, 50.

Perspective, 177. See Geometry.

Perturbations, 273.

Petersen, 365.

Pfaff, 341, 342; ref. to, 362.

Pfaffian problem, 341, 342.

Pherecydes, 20.

Philippus, 33.

Philolaus, 22; ref. to, 28, 68.

Philonides, 46.

Physics, mathematical. See Applied mathematics.

Piazzi, 373.

Picard. E., 347, 350, 360.

Picard, J., 214, 215.

Piddington, 384.

Piola, 388.

Pitiscus, 142.

Plana, 375, 387, 396.

Planudes, M., 135.

Plateau, 382.

Plato, 29–31; ref. to, 3, 10, 16, 23, 32, 33, 34, 35, 63, 68.

Plato of Tivoli, 109, 125.

Plato Tiburtinus. See Plato of Tivoli.

Platonic figures, 39.

Platonic School, 29–34.

Playfair, X., 156.

Plectoidal surface, 60.

Plücker, 307–309; ref. to, 304, 308, 313.

Plus and minus, signs for, 150.

Pohlke, 300.

Poincaré, 343; ref. to, XIII., 345, 346, 347, 352, 359, 368, 384, 400.

Poinsot, 378; ref. to, 377.

Poisson, 387; ref. to, 175, 298, 330, 333, 351, 375, 378, 382, 383, 386, 387, 390, 392, 395, 396.

Poncelet, 289, 290; ref. to, 178, 288, 293, 306, 308, 389.

Poncelet's paradox, 308.

Porisms, 39.

Porphyrius, 55.

Potential, 277, 358, 395.

Poynting, 397, 398.

Preston, 400.

Primary factors, Weierstrass' theory of, 354, 360.

Prime and ultimate ratios, 198, 212, 268.

Prime numbers, 38, 45, 71, 179, 180, 368.

Princess Elizabeth, 188.

Principia (Newton's), 191, 208, 212–215, 229, 233, 242.

Pringsheim, 336–338.

Probability, 158, 182, 192, 237, 239, 240, 245, 252, 270, 276, 285, 340, 341.

Problem of Pappus, 60.

Problem of three bodies, 253, 256, 377.

Proclus, 61; ref. to, 17, 19, 33, 35, 38, 39, 50, 54, 58.

Progressions, first appearance of arithmetical and geometrical, 8.

Projective geometry, 307.

Proportion, 17, 22, 23, 26, 33, 36, 38, 67, 68.

Propositiones ad acuendos iuvenes, 119, 120.

Prym, 355.

Ptolemæus. See Ptolemy.

Ptolemaic System, 56.

Ptolemy, 56–58; ref. to, 7, 9, 54, 55, 98, 104, 106, 108, 109, 115, 139, 313.

Puiseux. 356.

Pulveriser, 95.

Purbach, 134; ref. to, 140.

Pythagoras, 19–23, 67–70; ref. to, 3, 16, 18, 24, 29, 36, 63, 82, 97, 135.

Pythagorean School, 19–23.

 

Quadratic equations, 76, 93, 107, 111, 112. See Algebra, Equations.

Quadratic reciprocity, 252, 280, 365.

Quadratrix, 25, 32, 59, 60.

Quadrature of the circle. See Circle; also see Circle-squarers, $\scriptstyle {\pi }$.

Quadrature of curves, 42, 49, 177, 190, 193, 220, 222.

Quaternions, 318, 319; ref. to, 317.

Quercu, a, 154.

Quetelet, 340; ref. to, X.

 

Raabe, 337.

Radau, 377.

Radiometer, 403.

Rahn, 151.

Ramus, 153.

Rankine, 399; ref. to, 400.

Rari-constancy, 390.

Ratios, 372.

Rayleigh, Lord, 386; ref. to, 374, 383, 384, 397, 398.

Reaction polygons, 300.

Reciprocal polars, 290.

Reciprocants, 327, 361.

Recorde, 151; ref. to, 158.

Rectification of curves, 169, 177, 190, 198. See Curves.

Redfield, 384.

Reductio ad absurdum, 28.

Reech, 381.

Regiomontanus, 140, 141; ref. to, 139, 149, 153, 154, 155, 158, 160.

Regula aurea. See Falsa positio.

Regula duorum falsorum, 106.

Regula falsa, 106.

Regular solids, 21, 31, 34, 38, 51, 110, 168.

Reid, 384.

Reiff, XI.

Renaissance, 139–156.

Resal, 377.

Reye, 299; ref. to, 305.

Reynolds, 383.

Rhæticus, 141; ref. to, 139, 142.

Rheticus. See Rhæticus.

Rhind papyrus, 10–15.

Riccati. 241; ref. to, 239.

Richard of Wallingford, 135.

Richelot, 353; ref. to, 309, 312.

Riemann, 357–359; ref. to, 304, 305, 312, 315, 339, 342, 354, 355, 356, 362, 368, 384, 392, 398.

Riemann's surfaces, 358; ref. to, 356.

Roberts, 313.

Roberval, 172; ref. to, 172, 187, 191.

Rolle, 241; ref. to, 236.

Roman mathematics in Occident, 117–124.

Romans, 77–83.

Romanus, 154; ref. to, 142, 148, 154.

Römer, 199.

Rosenberger, XIV.

Rosenhain, 355; ref. to, 353.

Roulette, 171.

Routh, 380; ref. to, 381, 397.

Rowland, 382, 394, 397, 398.

Rudolff, 151.

Ruffini, 328.

Rühlmann, 400.

Rule of signs, 187, 193.

Rule of three, 92, 106.

 

Saccheri, 303.

Sachse, XIII.

Sacro Bosco. See Halifax.

Saint-Venant, 390; ref. to, 322, 382, 389, 393.

Salmon, XII., 295, 311–313, 330.

Sand-counter, 65, 90.

Sarrau, 393.

Sarrus, 333.

Saturn's rings, 192, 376.

Saurin, 240.

Savart, 387.

Scaliger, 154.

Schellbach, 296.

Schepp, 362.

Schering, 306; ref. to, 357, 365.

Schiaparelli, 32.

Schläfli, 306; ref. to, 338, 353.

Schlegel, 322; ref. to, XII., 306.

Schlessinger, 300.

Schlömilch, 375.

Schmidt, XII.

Schooten, van, 189; ref. to, 190, 202.

Schreiber, 288, 300.

Schröter, H., 313; ref. to, 296, 353.

Schröter, J. H., 374.

Schubert, 297.

Schumacher, 366; ref. to, 348.

Schuster, XIII.

Schwarz, 361; ref. to, 297, 339, 345, 347, 362.

Schwarzian derivatiye, 361.

Scott, 325.

Screws, theory of, 378.

Secants, 142.

Sectio aurea, 33.

Section, the golden, 33.

Seeber, 371.

Segre, 305.

Seidel, 339.

Seitz, 341.

Selling; 371.

Sellmeyer, 393.

Semi-convergent series, 336.

Semi-cubical parabola, 190.

Semi-invariants, 328.

Serenus, 55.

Series, 111, 245. See Infinite series, Trigonometric series, Divergent series, Absolutely convergent series, Semi-convergent series, Fourier's series, Uniformly convergent series.

Serret, 313; ref. to, 341, 342, 377, 379.

Servois, 284, 288, 290.

Sexagesimal System, 7, 57, 65, 67, 126.

Sextant, 218.

Sextus Julius Africanus, 58.

Siemens, 385.

Sigma-function, 354.

Signs, rule of, 187, 193.

Similitude (mechanical), 380.

Simony, 315.

Simplicius, 61.

Simpson, 249.

Simson, 290; ref. to, 37, 39.

Sine, 99, 102. 109, 116, 125, 140, 141; origin of term, 109.

Singular solutions, 226, 265, 277.

Sluze, 189; ref. to, 222, 224.

Smith, A., 381.

Smith, H., 369, 370; ref. to, XIII., 353, 372.

Smith, R., 242.

Sohnke, 353.

Solid of least resistance [Prin. II., 25], 215.

Solitary wave, 383.

Somoff, 381.

Sophist School, 23–29.

Sosigenes, 81.

Sound, velocity of, 270, 278. See Acoustics.

Speidell, 165.

Spherical Harmonics, 247.

Spherical trigonometry, 56, 115, 280, 294.

Spheroid (liquid), 384.

Spirals, 42, 60, 237.

Spitzer, 333.

Spottiswoode, 325; ref. to, XII., 292.

Square root, 65, 94, 159.

Squaring the circle. See Quadrature of the circle.

Stahl, 306.

Star-polygons, 22, 135, 156.

Statics, 44, 182. See Mechanics.

Statistics, 340.

Staudt, von. See Von Staudt.

Steele, 381.

Stefano, 382.

Steiner, 295, 296; ref. to, 293, 297, 298, 308, 311, 312, 320, 348, 357.

Stereometry, 31, 33, 38, 168.

Stern, 357, 365.

Stevin, 160; ref. to, 134, 162, 182.

Stevinus. See Stevin.

Stewart, 290.

Stifel, 151; ref. to, 149, 151, 155, 162.

Stirling, 244.

Stokes, 381; ref. to, 339, 382, 383, 386, 388, 390, 393, 398.

Story, 306.

Strassmaier, IX.

Strauch, 334.

Strings, vibrating, 242, 255, 262.

Stringham, 306.

Strutt, J. W., 386. See Rayleigh.

Struve, 366.

Sturm, J. C. F., 330; ref. to, 178, 282, 379, 381.

Sturm, R., 296.

Sturm's theorem, 330.

St. Vincent, Gregory, 190, 197.

Substitutions, theory of, 292.

Surfaces, theory of, 250, 287, 295, 299, 309, 310, 314.

Suter, X.

Swedenborg, 274.

Sylow, 330; ref. to, 350.

Sylvester, 326; ref. to, XIII., 216, 296, 310, 311, 312, 319, 324, 325, 328, 330, 341, 361, 368, 370, 378, 396.

Sylvester II. (Gerbert), 120–124.

Symmetric functions, 250, 328, 330.

Synthetic geometry, 293–307.

Synthesis, 30, 31.

 

Taber, 324.

Tabit ben Korra, 108; ref. to, 105.

Tait, 283, 319, 381, 388, 400.

Tangents, in geometry, 62, 173, 186; in trigonometry, 110, 141, 142.

Tangents, direct problem of, 198, 223; inverse problem of, 169, 189, 220, 222, 223.

Tannery, 343; ref. to, 362.

Tartaglia, 143–145; ref. to, 152, 153.

Tautochronous curve, 191.

Taylor, B., 242; ref. to, 234, 255.

Taylor's theorem, 243, 268, 269, 333, 342.

Tchebycheff, 368.

Tchirnhausen, 241; ref. to, 224, 226, 264, 328.

Tentative assumption, 75, 92. See Regula falsa.

Thales, 17, 18; ref. to, 16, 20, 21.

Theætetus, 33; ref. to, 35, 36, 70.

Theodorus, 70; ref. to, 29.

Theodosius, 54; ref. to, 108, 125, 127.

Theon of Alexandria, 61; ref. to, 37, 51, 55, 65, 82.

Theon of Smyrna, 55, 58, 72.

Theory of equations. See Equations.

Theory of functions, 268, 269, 344, 345, 346, 347–362. See Functions.

Theory of numbers, 55, 76, 95, 108, 119, 131, 178–182, 252, 264, 280, 362–372.

Theory of substitutions, 329, 364.

Thermodynamics, 385, 398–401.

Theta-functions, 352, 353, 355, 380.

Theta-fuchsians, 345.

Theudius, 33.

Thomae, 353, 362.

Thomé, 344; ref. to, 345.

Thomson, J., 385.

Thomson, J. J., 382; ref. to, 396, 397.

Thomson, Sir William, 395, 396; ref. to, 283, 315, 358, 381, 382, 383, 388, 391, 393, 394, 395, 399, 400, 403. See Kelvin (Lord).

Thomson's theorem, 359.

Three bodies, problem of, 253, 256, 377.

Thymaridas, 73.

Tides, 278, 383.

Timæus of Locri, 29.

Tisserand, 377.

Todhunter, 334; ref. to, I., XIII., 375.

Tonstall, 158.

Torricelli, 171.

Trajectories, 234, 238.

Triangulum characteristicum, 220.

Trigonometric series, 283, 339, 357. See Fourier's series.

Trigonometry, 51, 56, 98–100, 109, 110, 115, 135, 140, 141, 154, 160, 161, 165, 238, 242, 245, 249, 259; spherical, 57, 115, 280, 294.

Trisection of angles, 24, 31, 50, 153.

Trochoid, 171.

Trouton, 394.

Trudi, 324.

Tucker, XIII.

Twisted Cartesian, 312.

Tycho Brahe, 110, 139, 168.

 

Ubaldo, 183.

Ultimate multiplier, theory of, 379.

Ulug Beg, 114.

Undulatory theory of light, 192, 339, 379, 392–394.

Universities of Cologne, Leipzig, Oxford, Paris, and Prague, 136.

 

Valson, XIII.

Van Ceulen. See Ludolph.

Vandermonde, 278; ref. to, 264, 278.

Van Schooten, 189; ref. to, 190, 202.

Variation of arbitrary consonants, 378.

Varignon, 240; ref. to, 236.

Varying action, principle of, 292, 318, 379.

Venturi, 52.

Veronese, 305; ref. to, 307.

Versed sine, 99.

Vibrating rods, 387.

Vibrating strings, 242, 255, 262.

Vicat, 389; ref. to, 390.

Victorius, 79.

Vieta, 147; ref. to, 50, 142, 152, 153, 154, 167, 196, 202, 217, 264.

Vincent, Gregory St., 190, 197.

Virtual velocities, 34, 265.

Viviani, 172.

Vlacq, 165.

Voigt, XIII., 365, 393.

Volaria, 237.

Von Helmholtz. See Helmholtz.

Von Staudt, 298, 299; ref. to, 292, 294, 295.

Vortex motion, 382.

Vortex rings, 382.

Voss, 306; ref. to, 336.

 

Waldo, 385.

Walker, 323.

Wallis, 192–195; ref. to, 98, 161, 177, 179, 187, 188, 197, 202, 229.

Waltershausen, XI.

Wand, 400.

Wantzel, 328.

Warring. 264, 330.

Watson, J. C, 377.

Watson, S., 341.

Wave theory. See Undulatory theory.

Waves, 382–385.

Weber, H. H., 355.

Weber, W. E., 394; ref. to, 357, 363, 388, 396, 398.

Weierstrass, 359; ref. to, 328, 339, 352, 353, 354, 359, 361, 362, 372.

Weigel, 219.

Weiler, 341.

Werner, 153.

Wertheim, 390.

Westergaard, 340.

Wheatstone, 386.

Whewell, IX., 43, 253.

Whiston, 216.

Whitney, 87.

Widmann, 150.

Wiener, XI.

Williams, 267.

Wilson, 264.

Wilson's theorem, 264.

Winds, 384–386.

Winkler, 392.

Witch of Agnesi, 260.

Wittstein, XII.

Woepcke, 83, 103.

Wolf, C., 241; ref. to, 167.

Wolf, R., XI.

Wolstenholme, 341.

Woodhouse, 334.

Wren, 177; ref. to, 188, 198, 213, 287.

Wronski, 324.

 

Xenocrates, 29.

Xylander, 153.

 

Young, 392; ref. to, 386, 387.

 

Zag, 127.

Zahn, XII.

Zehfuss, 325.

Zeller, 365.

Zeno, 27.

Zenodorus, 51.

Zero (symbol for), 7, 88; origin of term, 129.

Zeuthen, 313; ref. to, IX., 297.

Zeuxippus, 40.

Zolotareff, 371; ref. to, 372.