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Seltman M. (ed.), Goulding R. (ed.) — Thomas Harriot's Artis Analyticae PRAXIS: An English Translation with Commentary
Seltman M. (ed.), Goulding R. (ed.) — Thomas Harriot's Artis Analyticae PRAXIS: An English Translation with Commentary

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Название: Thomas Harriot's Artis Analyticae PRAXIS: An English Translation with Commentary

Авторы: Seltman M. (ed.), Goulding R. (ed.)


The present work is the first ever English translation of the original text of Thomas Harriot's Artis Analyticae Praxis, first published in 1631 in Latin. Thomas Harriot's Praxis is an essential work in the history of algebra. Even though Harriot's contemporary, Viete, was among the first to use literal symbols to stand for known and unknown quantities, it was Harriot who took the crucial step of creating an entirely symbolic algebra. This allowed reasoning to be reduced to a quasi-mechanical manipulation of symbols. Although Harriot's algebra was still limited in scope (he insisted, for example, on strict homogeneity, so only terms of the same powers could be added or equated to one another), it is recognizably modern. While Harriot's book was highly influential in the development of analysis in England before Newton, it has recently become clear that the posthumously published Praxis contains only an incomplete account of Harriot's achievement: his editor substantially rearranged the work before publishing it, and omitted sections that were apparently beyond comprehension, such as negative and complex roots of equations. The commentary included with this translation relates the contents of the Praxis to the corresponding pages in his manuscript papers, which enables much of Harriot's most novel and advanced mathematics to be explored. This publication will become an important contribution to the history of mathematics, and it will provide the basis for a reassessment of the development of algebra.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 299

Добавлена в каталог: 13.05.2008

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Предметный указатель
Acephalic square      258
Adventitious equation      244
Affected power      262
Algebra, algebraic logic      6
Algebra, completely symbolic notation      9
Algebra, Harriot’s role      1
Algebra, purely symbolic notation      1
Algebra, Renaissance to the modern world      15
Algebra, zero, introduction of      6
Algorithmic methods      15
Analytical geometry      211
Antithesis      215
Apollonius      212
Application      215—216
Archimedes      212
Artis Analyticae Praxis, achievements      11—14
Artis Analyticae Praxis, analysis exclusively algebraic      10—11
Artis Analyticae Praxis, Canonical equations generated from binomial roots      11 12
Artis Analyticae Praxis, clear symbolism      13
Artis Analyticae Praxis, comparisons with MS and Torporley’s copy      214
Artis Analyticae Praxis, contents compared with Harriot manuscript pages      287—291
Artis Analyticae Praxis, contents overview      11—14
Artis Analyticae Praxis, Definitions - author      10
Artis Analyticae Praxis, Definitions - purpose of providing      12
Artis Analyticae Praxis, equations solved, comparative table      263—269
Artis Analyticae Praxis, errata      v 271—278
Artis Analyticae Praxis, exponential notation lacking      15
Artis Analyticae Praxis, first published      v
Artis Analyticae Praxis, first published algebraic work to be purely symbolic      15
Artis Analyticae Praxis, focus on the structure of equations      15
Artis Analyticae Praxis, generalization through lists of examples      215
Artis Analyticae Praxis, Harriot’s intentions      v
Artis Analyticae Praxis, Lemmas in section five      233—238
Artis Analyticae Praxis, model polynomials      253
Artis Analyticae Praxis, numerical exegesis      254—255
Artis Analyticae Praxis, numerical solution of equations by successive approximation      13
Artis Analyticae Praxis, ordering of sections      13
Artis Analyticae Praxis, polynomial equations with numerical coefficients      11
Artis Analyticae Praxis, Preface      10
Artis Analyticae Praxis, purely symbolic notation      1
Artis Analyticae Praxis, Rules for Guidance      13
Artis Analyticae Praxis, section contents summarised      29
Artis Analyticae Praxis, significance      14—16
Artis Analyticae Praxis, structure of book      13
Artis Analyticae Praxis, superior notation demonstrated      258 259
Artis Analyticae Praxis, text and surviving Harriot manuscripts      4
Artis Analyticae Praxis, Torporley, Nathaniel      4
Artis Analyticae Praxis, Warner, Walter as editor      4
Artis Analyticae Praxis, Warner, Walter changes      286—287
avulsed powers      259 261
Backward composition      256 257 260
Bibliography      293—294
Biquadratic equations, general method to find roots      13—14
Biquadratic equations, reduction      247
Biquadratic equations, removing the term of second highest degree      239
Biquadratic equations, table of derivation from ‘originals’      221—222
Bombelli, Raffaelo      7
Canonical equations, background by Warner      22
Canonical equations, definitions      5n2 217
Canonical equations, generated by binomial factors      11 243
Canonical equations, primary reduced to secondary      223
Canonical equations, roots of Primary and Secondary      219
Canonical equations, secondary      254
Canonical equations, treatment      217
Canonical forms, pattern of formation      228
Canonical polynomial, definition      5 note 2
Cardano, Girolamo      6 20 234 242
Cavendish, Charles      4
Chuquet, Nicolas      7
Clavious, Christopher      13
Comma used as bracket      214
Common equations      223
Complex roots of equations      219—221 235
Conceiving and imagining      9
Conjugate complex numbers      6 246—247
Conjugate equations, pairs of      247 248
Copernicanism      2
Corrective device      258—259
Cossic notation      13 15 213
Cossic numbers      6
Cubic equations, derivation from ‘originals’      222
Cubic equations, fully solved      239 242
Cubic equations, general method to find roots      13—14
Cubic equations, negative coefficients      240
Cubic equations, pure cube      260
Cubic equations, reciprocal      222
Cubic equations, removing the term of second highest degree      14 239
Cubic equations, symbolic solution      245
De Radicalibus      215 287
Dee, John      2
Definitions in Artis Analyticae Praxis, analysis      24 211—212
Definitions in Artis Analyticae Praxis, canonical equations      28—29
Definitions in Artis Analyticae Praxis, common or adventitious equation      27
Definitions in Artis Analyticae Praxis, composition, resolution      24
Definitions in Artis Analyticae Praxis, equation      23
Definitions in Artis Analyticae Praxis, Exegetic [analysis]      25 212
Definitions in Artis Analyticae Praxis, numerical Exegesis      26
Definitions in Artis Analyticae Praxis, originals of canonical equations      27
Definitions in Artis Analyticae Praxis, Poristic [analysis]      25 212
Definitions in Artis Analyticae Praxis, primary canonical equations      27—28
Definitions in Artis Analyticae Praxis, reciprocal equation      29
Definitions in Artis Analyticae Praxis, root, value      26—27
Definitions in Artis Analyticae Praxis, secondary canonical equations      28
Definitions in Artis Analyticae Praxis, secondary Exegesis      26
Definitions in Artis Analyticae Praxis, specious Exegesis      25—26
Definitions in Artis Analyticae Praxis, specious logistic      23 209—211
Definitions in Artis Analyticae Praxis, synthesis      23—24 211
Definitions in Artis Analyticae Praxis, Zetetic [analysis]      24—25 212
Degree of an equation, equality with number of roots      15 219
Descartes, Rene, algebraic geometry      10
Descartes, Rene, geometrism      15—16
Descartes, Rene, La Geometrie      2 7 9
Descartes, Rene, Pappus’ locus problem      210
Descartes, Rene, Rule of Signs      15 235 236
Descartes, Rene, unity      9—10
Digges, Leonard      2
Digges, Thomas      2
Diophantus      6—7 8 20
Discriminant of the cubic      235
Dividing through an equation by known quantity      216
Dividing through an equation by the unknown      216
Epanorthosis      261
Equations with numerical coefficients      254
Equipollence      233 235 236 287
Exegesis [use of word]      253
Explicated root of equation      229
Fractions reduced to lowest terms      214
Girard Albert      7
Grenville, Sir Richard      3
Hakluyt, Richard      2
Halley, Edmund      14 237
Harriot, Thomas - papers, Add. MS, 6782 contents list      279—271
Harriot, Thomas - papers, Add. MS, 6783 contents list      281—282
Harriot, Thomas - papers, Add. MS, 6784 contents list      282
Harriot, Thomas - papers, comments on numbering      286—287
Harriot, Thomas - papers, contents and comparison with Torporley      283—285
Harriot, Thomas - papers, contents and numbering      285—286
Harriot, Thomas - papers, disposal after death      3—4 3
Harriot, Thomas - papers, Torporley access      11
Harriot, Thomas - papers, ‘waste’      3
Harriot, Thomas, accomplishments      2
Harriot, Thomas, accomplishments set out by D.T. Whiteside      2
Harriot, Thomas, algebra transformed      1
Harriot, Thomas, analytical geometry      211
Harriot, Thomas, background      2
Harriot, Thomas, background by Warner      19—20 22
Harriot, Thomas, career      3
Harriot, Thomas, comparison with Viete      8—11
Harriot, Thomas, completely symbolic notation      9
Harriot, Thomas, conceptual connection with Viete      10
Harriot, Thomas, equating all the terms of an equation to zero      13
Harriot, Thomas, equations with numerical coefficients      254
Harriot, Thomas, exegesis [use of word]      253
Harriot, Thomas, exponential notation      15
Harriot, Thomas, facility in symbolic thinking      224
Harriot, Thomas, influence on later English mathematicians      4
Harriot, Thomas, manuscript papers      254
Harriot, Thomas, notation revolutionary      1
Harriot, Thomas, polynomial equations generated by product of binomial factors      1
Harriot, Thomas, polynomial equations with terms equated to zero      1
Harriot, Thomas, purely symbolic notation      1 15
Harriot, Thomas, reputation      1
Harriot, Thomas, superior notation demonstrated      258 259
Harriot, Thomas, telescopes      2
Harriot, Thomas, two chief discoveries      5
Harriot, Thomas, use of Vie`te’s examples      253
Harriot, Thomas, Will      3
Headless quadratic method      258
Homogeneity, laws of      260
Homogeneity, problems of      9
Homogeneous term      13 217 247 248
Homogenous form of equations      213
Hues, Robert      3
Hypobibasm      215 216
Imaginary roots of equations      12 219—220 249
Imagining and conceiving      9
Kepler, J.      2
Lagrange, J.L.      6 14 235
Lower, William      6
Macraelius      217
Magnitudes, algebra of      9
Magnitudes, Descartes      10
Magnitudes, of dimension      10
Magnitudes, Viete, Francois      8 209—210
Mercantile capitalism      2
Negative roots changed to positive roots      247 249
Negative roots of equations      6 12 219—220 229
Negative roots of equations, existence recognised but usefulness challenged      222
Noetic      221
Northumberland, 9th Earl of      3
Notation, completely symbolic notation      9
Notation, Cossic      6 13 15 213
Notation, cube root      245
Notation, Diophantine      6—7
Notation, division line      223
Notation, dots      v 215
Notation, equal signs      216
Notation, equality signs      214 229
Notation, exponents      7 15
Notation, Harriot’s unique      15
Notation, inequality sign      v 1
Notation, inequality signs      214 216
Notation, letters for positive numbers      213
Notation, literal      4
Notation, literal sign for a general number      6
Notation, logic embodied in notation      1
Notation, multiplication sign      13 213 215 218
Notation, negative sign      7 258
Notation, purely symbolic      1 15
Notation, revolutionary      1
Notation, separate signs for unknown and each power      6—7
Notation, square number      7—8
Notation, superscripts for collecting like terms      224 227
Notation, Viete, Franc?ois      4—5 7 8
Numerical Exegesis      21 22
Numerical logistic, Viete’s definition      8—9 209
Operation rules, Franc?ois Vie`te      209—210
Pacioli, Luca      6
Pappus      8
Pappus’ locus problem      210
Parabolismus      215 216
Pell, John      4
Pepper, Jon V      1
Plato      211
Polynomial equations with numerical coefficients, solution by successive approximations      11
Polynomial equations with numerical coefficients, use by Harriot of Vie`te’s work      9
Poristic verification      259 260 261
Posited root of equation      229
Positive roots changed to negative roots      247 249
Positive roots of equations      219
Privative roots of equations      229
Problems (section 3) related to corresponding propositions (section 4) table including roots of equations      230—232
Problems vs propositions      217
Proclus      215—216
Propositions (section 4) related to corresponding problems (section 3) table including roots of equations      230—232
Propositions vs problems      217
Pure powers      256 257
Quadratum acephalum method      258
RADIX      229
Ralegh (Raleigh), Walter      3
Real roots from conjugate complex numbers      246—247
Rectification      261
Specious arithmetic      21
Specious logistic      8—9 10
Square root of negative quantity      245
Stedall, Jacqueline A.      4
Stevin, Simon      7 21
Stifel, Michael      6
Successive approximations method      255—257
Sylvester, J.J.      6
Symbolic arithmetic      21
Symbolic logistic, Viete’s definition      9 209
Symmetric functions of roots of an equation      219 260 261
Tanner, R C H      1 4 14
Tartaglia, Niccolo      20
Theon      211 212
Torporley, Nathaniel      3
Torporley, Nathaniel, access to Harriot papers      11
Torporley, Nathaniel, contents and comparison with Harriot papers      283—285
Transposition under opposite signs      216
Trial divisor      255 257
Unaffected equation      256
Unity, conceived as a number      7
Unity, dimension of      9—10
Unity, problem of homogeneity      9
Verification by substitution      257
Viete, Francois, analysis identified with algebra as well as geometry      8
Viete, Francois, comparison with Harriot      8—11
Viete, Francois, generality of algebra      8
Viete, Francois, literal sign for a general number      6
Viete, Francois, magnitudes      8
Viete, Francois, notation      4—5 7 8
Wallis, John      4 9 233 236 238
Warner, Walter, changes made to Harriot material      287—288
Warner, Walter, conceptual connection with Vie`te      10
Warner, Walter, connection with Harriot      3
Warner, Walter, debt due to him      16
Warner, Walter, editor of Artis Analyticae Praxis      4 10—12
Warner, Walter, eulogy to Harriot      11
Warner, Walter, Harriot’s two chief discoveries      5
Warner, Walter, order of sections of Artis Analyticae Praxis      13
Whiteside, D.T.      1 2
Witmer, T Richard      9
Zero, equating all the terms of an equation to zero      13 218—219
Zero, introduced into algebra      6
Zero, use as a calculable quantity      241
Zero, use by Harriot      213
‘A quadratum’      7—8
‘Anticipation’      258
‘Four-root law’      249
‘Originals’, biquadratic equations derived from them      221—222
‘Originals’, cubic equations derived from them      218 222
‘Originals’, treatment      217 218
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