A history of elementary mathematics |
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... taken , with only slight alteration , from my History of Mathematics , Macmillan & Co. , 1895. Some parts of the present work are , therefore , not independent of the earlier one . It has been my privilege to have my manuscript read by ...
... taken , with only slight alteration , from my History of Mathematics , Macmillan & Co. , 1895. Some parts of the present work are , therefore , not independent of the earlier one . It has been my privilege to have my manuscript read by ...
Page 7
... three antique letters , 5 , 9 , 1 , and the 1 CANTOR , Vol . I. , pp . 44 and 45. The hieratic numerals are taken from Cantor's table at the end of the volume . ! ,, η , symbol M , were used for NUMBER - SYSTEMS AND NUMERALS 7.
... three antique letters , 5 , 9 , 1 , and the 1 CANTOR , Vol . I. , pp . 44 and 45. The hieratic numerals are taken from Cantor's table at the end of the volume . ! ,, η , symbol M , were used for NUMBER - SYSTEMS AND NUMERALS 7.
Page 16
... taken from FRIEDRICH UNGER , Die Methodik der Praktischen Arithmetik in Historischer Entwickelung vom Ausgange des Mittelalters bis auf die Gegenwart , Leipzig , 1888 , p . 39. ( Hereafter this work will be cited as UNGER . ) The double ...
... taken from FRIEDRICH UNGER , Die Methodik der Praktischen Arithmetik in Historischer Entwickelung vom Ausgange des Mittelalters bis auf die Gegenwart , Leipzig , 1888 , p . 39. ( Hereafter this work will be cited as UNGER . ) The double ...
Page 22
... taken appears to be 45 , for the numbers are stated as 111 , 51 1 , 41 , 11 , 1. The sum of these is 23 forty - fifths . Add to this , and the sum is . Add } , and we have 1. Hence the quantity to be added to the given fraction is their ...
... taken appears to be 45 , for the numbers are stated as 111 , 51 1 , 41 , 11 , 1. The sum of these is 23 forty - fifths . Add to this , and the sum is . Add } , and we have 1. Hence the quantity to be added to the given fraction is their ...
Page 23
... taken of 2 . This process is seen again in Ahmes's calculations to verify the identities in the table of unit - fractions . Ahmes then proceeds to eleven problems leading to simple equations with one unknown quantity . The unknown is ...
... taken of 2 . This process is seen again in Ahmes's calculations to verify the identities in the table of unit - fractions . Ahmes then proceeds to eleven problems leading to simple equations with one unknown quantity . The unknown is ...
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A History of Elementary Mathematics, with Hints on Methods of Teaching Florian Cajori No preview available - 2019 |
Common terms and phrases
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.