A history of elementary mathematics |
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Page 5
... history , by the prince of mathematical historians of this century , will be in three volumes , when completed , and will be cited hereafter as CANTOR . by the early Sumerians . A vertical wedge stood for NUMBER - SYSTEMS AND NUMERALS 5 LQ.
... history , by the prince of mathematical historians of this century , will be in three volumes , when completed , and will be cited hereafter as CANTOR . by the early Sumerians . A vertical wedge stood for NUMBER - SYSTEMS AND NUMERALS 5 LQ.
Page 11
... century after Christ we owe the re - discovery of this principle and the invention and adoption of the zero , the symbol for the absence of quantity . Of all mathematical dis- coveries , no one has contributed more to the general ...
... century after Christ we owe the re - discovery of this principle and the invention and adoption of the zero , the symbol for the absence of quantity . Of all mathematical dis- coveries , no one has contributed more to the general ...
Page 12
... century . The Hindus possessed several different modes of designating numbers . For a fuller account of these we refer the reader to Cantor . Aryabhatta in his celebrated mathematical work ( written about the beginning of the sixth century ) ...
... century . The Hindus possessed several different modes of designating numbers . For a fuller account of these we refer the reader to Cantor . Aryabhatta in his celebrated mathematical work ( written about the beginning of the sixth century ) ...
Page 13
... century . It was transmitted to the Occi- dent through the Arabs , hence the name " Arabic notation . ” No blame attaches to the Arabs for this pseudo - name ; they always acknowledged the notation as an inheritance from India . During ...
... century . It was transmitted to the Occi- dent through the Arabs , hence the name " Arabic notation . ” No blame attaches to the Arabs for this pseudo - name ; they always acknowledged the notation as an inheritance from India . During ...
Page 14
... century . 3. The East and the West Arabs both assigned to the num- erals a Hindu origin . “ Gubar - numerals " are " dust - numerals , ” in memory of the Brahmin practice of reckoning on tablets strewn with dust or sand . 4. Not less ...
... century . 3. The East and the West Arabs both assigned to the num- erals a Hindu origin . “ Gubar - numerals " are " dust - numerals , ” in memory of the Brahmin practice of reckoning on tablets strewn with dust or sand . 4. Not less ...
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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.