A history of elementary mathematics |
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Page 55
... straight lines , he discovered a transcendental curve ( i.e. one which cannot be represented by an algebraic ... line and circle more than anything else , and properly separates them for the purpose of elementary geometry ? Their self - ...
... straight lines , he discovered a transcendental curve ( i.e. one which cannot be represented by an algebraic ... line and circle more than anything else , and properly separates them for the purpose of elementary geometry ? Their self - ...
Page 58
... line , or other magnitude . Zeno's position was practically taken by Antiphon in his assumption that straight and curved lines are ultimately reducible to the same indivisible elements.1 Zeno reasoned by reductio ad absurdum against the ...
... line , or other magnitude . Zeno's position was practically taken by Antiphon in his assumption that straight and curved lines are ultimately reducible to the same indivisible elements.1 Zeno reasoned by reductio ad absurdum against the ...
Page 61
... straight line " or " an indivisible line . " According to Aristotle the following definitions were also current : The point , the line , the surface , are respectively the boundaries of the line , the surface , and the solid ; a solid ...
... straight line " or " an indivisible line . " According to Aristotle the following definitions were also current : The point , the line , the surface , are respectively the boundaries of the line , the surface , and the solid ; a solid ...
Page 68
... straight lines to one another , which meet together , but are not in the same straight line , " but leaves the idea of angle magnitude somewhat indefinite by his failure to give a test for equality of two angles or to state what ...
... straight lines to one another , which meet together , but are not in the same straight line , " but leaves the idea of angle magnitude somewhat indefinite by his failure to give a test for equality of two angles or to state what ...
Page 71
... straight line meet two straight lines , so as to make the two interior angles on the same side of it taken to- gether less than two right angles , these straight lines , being continually produced , shall at length meet on that side on ...
... straight line meet two straight lines , so as to make the two interior angles on the same side of it taken to- gether less than two right angles , these straight lines , being continually produced , shall at length meet on that side on ...
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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.