A history of elementary mathematics |
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Page 3
... units , but a quinary system thus carried out was never in actual use : whenever it was extended to higher numbers it invariably ran either into the decimal or into the vigesimal system . " The home par excellence of the quinary , or ...
... units , but a quinary system thus carried out was never in actual use : whenever it was extended to higher numbers it invariably ran either into the decimal or into the vigesimal system . " The home par excellence of the quinary , or ...
Page 4
... unit or a stop- ping - place , to the total number of fingers and toes as an upper unit or resting - point . The vigesimal system is less common than the quinary , but , like it , is never found entirely pure . In this the first four units ...
... unit or a stop- ping - place , to the total number of fingers and toes as an upper unit or resting - point . The vigesimal system is less common than the quinary , but , like it , is never found entirely pure . In this the first four units ...
Page 5
... unit . Any number between 10 and 100 was pronounced according to the plan b ( 10 ) + a ( 1 ) , a and b being ... unit 10 being here treated in a manner similar to the treatment of the lower unit 1 in expressing numbers below 100. Any num ...
... unit . Any number between 10 and 100 was pronounced according to the plan b ( 10 ) + a ( 1 ) , a and b being ... unit 10 being here treated in a manner similar to the treatment of the lower unit 1 in expressing numbers below 100. Any num ...
Page 6
... unit , << > was interpreted , not as 20 x 100 , but as 10 x 1000. In this notation no numbers have been found as large as a million . The principles applied in this notation are the additive and the multiplicative . Besides this the ...
... unit , << > was interpreted , not as 20 x 100 , but as 10 x 1000. In this notation no numbers have been found as large as a million . The principles applied in this notation are the additive and the multiplicative . Besides this the ...
Page 8
... unit - fraction , thus 8 ' . The Greeks applied to their numerals the additive and , in cases like M for 50,000 , also the multiplicative principle . = In the Roman notation we have , besides the additive , the principle of subtraction ...
... unit - fraction , thus 8 ' . The Greeks applied to their numerals the additive and , in cases like M for 50,000 , also the multiplicative principle . = In the Roman notation we have , besides the additive , the principle of subtraction ...
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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.