A history of elementary mathematics |
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Page 29
... trian- gular , perfect , excessive , defective , amicable . The Pythag- 1 Gow , p . 69 . 2 For their definitions see Gow , p . 70 , or C. H. M. , p . 68 . oreans paid much attention to the subject of proportion . GREECE 29.
... trian- gular , perfect , excessive , defective , amicable . The Pythag- 1 Gow , p . 69 . 2 For their definitions see Gow , p . 70 , or C. H. M. , p . 68 . oreans paid much attention to the subject of proportion . GREECE 29.
Page 30
... definition 21 , book VII.1 " Plane and solid numbers are similar when their sides are proportional . " Again , num- bers are not written in numerals , nor are they designated by anything like our modern algebraic notation ; they are ...
... definition 21 , book VII.1 " Plane and solid numbers are similar when their sides are proportional . " Again , num- bers are not written in numerals , nor are they designated by anything like our modern algebraic notation ; they are ...
Page 41
... definition , " broken number , " given in old English arithmetics . One of the last Roman writers was Boethius ( died 524 ) , who is to be mentioned in this connection as the author of a work , De Institutione Arithmetica , essentially ...
... definition , " broken number , " given in old English arithmetics . One of the last Roman writers was Boethius ( died 524 ) , who is to be mentioned in this connection as the author of a work , De Institutione Arithmetica , essentially ...
Page 61
... definitions and the consideration of postulates and axioms . The Pythagorean definition , " a point is unity in position , " embodying a philo- sophical theory , was rejected by the Platonists ; a point was defined as " the beginning of ...
... definitions and the consideration of postulates and axioms . The Pythagorean definition , " a point is unity in position , " embodying a philo- sophical theory , was rejected by the Platonists ; a point was defined as " the beginning of ...
Page 62
... definition of analysis as op- posed to synthesis is given in Euclid , XIII . , 5 , which was most likely framed by Eudoxus : " Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth ...
... definition of analysis as op- posed to synthesis is given in Euclid , XIII . , 5 , which was most likely framed by Eudoxus : " Analysis is the obtaining of the thing sought by assuming it and so reasoning up to an admitted truth ...
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A History of Elementary Mathematics, with Hints on Methods of Teaching Florian Cajori No preview available - 2019 |
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abacists abacus Ahmes algebra angles appears Arabic Archimedes arith arithmetic Arithmetick astronomer axioms Boethius Bolyai Brahmagupta Briggs called CANTOR century circle Cocker computation construction cube Cyclopædia Desargues digits Diophantus discovery divided division divisor early edition Egyptian elementary England English equal equations Euclid Euclid's Elements figures G. B. HALSTED geom geometry Gerbert German given gives Greek Greek mathematical HANKEL Heron Hindu numerals invention Italian later Latin Leonardo of Pisa logarithms London LORIA Math mathematical mathematicians method metic modern Morgan multiplication Napier notation numbers origin Pacioli PEACOCK plane Plato polygon postulate pound problem proof proportion published pupil Pythagoreans Regiomontanus right triangle Robert Simson Roman roots rule of three says sexagesimal sides sines sixteenth solution square straight line subtraction symbol Tartaglia teacher teaching text-book theorem theory tion translation treatise trigonometry unit-fractions Vieta vigesimal weights and measures word write written wrote
Popular passages
Page 130 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 68 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 71 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Page 284 - The Connexion of Number and Magnitude; An attempt to explain the fifth book of Euclid.
Page 160 - Napier lord of Markinston, hath set my head and hands at work with his new and admirable logarithms. I hope to see him this summer, if it please God ; for I never saw a book which pleased me better, and made me more wonder.
Page 229 - He spoke of imaginary quantities, and inferred by induction that every equation has as many roots as there are units in the number expressing its degree.
Page 100 - These problems are proposed simply for pleasure; the wise man can invent a thousand others, or he can solve the problems of others by the rules given here. As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.
Page 134 - The square of a diagonal of a rectangular parallelopiped is equal to the sum of the squares of the three dimensions.
Page 236 - The neglect which he had shown of the elementary truths of geometry he afterwards regarded as a mistake in his mathematical studies ; and on a future occasion he expressed to Dr. Pemberton his regret that " he had applied himself to the works of Descartes, and other algebraic writers, before he had considered the Elements of Euclid with that attention which so excellent a writer deserved."3 The study of Descartes...
Page 101 - the second value is in this case not to be taken, for it is inadequate ; people do not approve of negative roots.