A History of Mathematics |
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Page 3
... tion of an angle . When they know how to construct a square whose area is double the area of a given square , tell them about the duplication of the cube - how the wrath of Apollo could be appeased only by the construction of a cubical ...
... tion of an angle . When they know how to construct a square whose area is double the area of a given square , tell them about the duplication of the cube - how the wrath of Apollo could be appeased only by the construction of a cubical ...
Page 7
... tion of integers the " principle of position " was employed . Thus , in 1.4 ( = 64 ) , the 1 is made to stand for 60 , the unit of the second order , by virtue of its position with respect to the 4. The introduction of this principle at ...
... tion of integers the " principle of position " was employed . Thus , in 1.4 ( = 64 ) , the 1 is made to stand for 60 , the unit of the second order , by virtue of its position with respect to the 4. The introduction of this principle at ...
Page 14
... tion of this table , a fraction whose numerator exceeds two can be expressed in the desired form , provided that there is a fraction in the table having the same denominator that it has . Take , for example , the problem , to divide 5 ...
... tion of this table , a fraction whose numerator exceeds two can be expressed in the desired form , provided that there is a fraction in the table having the same denominator that it has . Take , for example , the problem , to divide 5 ...
Page 17
... of vertical angles , the equality of the angles at the base of an isosceles triangle , the bisec- tion of a circle by any diameter , and the congruence of two triangles having a side and the two adjacent angles equal THE GREEKS . 17.
... of vertical angles , the equality of the angles at the base of an isosceles triangle , the bisec- tion of a circle by any diameter , and the congruence of two triangles having a side and the two adjacent angles equal THE GREEKS . 17.
Page 23
... tion of cones and cylinders . This problem reduces itself to finding two mean proportionals between two given lines . These mean proportionals were obtained by Archytas from the section of a half - cylinder . The doctrine of proportion ...
... tion of cones and cylinders . This problem reduces itself to finding two mean proportionals between two given lines . These mean proportionals were obtained by Archytas from the section of a half - cylinder . The doctrine of proportion ...
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60 cents abacus Abelian functions algebra Almagest analysis analytical angles Apollonius applied Arabic Archimedes arithmetic astronomical Berlin Bernoulli Boethius calculus called Cambridge Cauchy Cayley century circle Clebsch coefficients College conic sections contains Crelle's Journal cubic curve degree Descartes determine differential calculus differential equations Diophantus discovery Edition Egyptian elasticity Elementary Treatise elliptic functions equal Euclid Euler expressed Fermat fluxions fractions Gauss gave geometry given gives Greek Hindoo infinite integral invention investigations Jacobi John Bernoulli known Lagrange Laplace Legendre Leibniz linear logarithms mathe mathematicians mathematics matical mechanics memoir method motion Newton notation paper Pappus Paris plane polygon principle problem professor progress proof published pupil Pythagoreans quadratic quadrature quantities ratio researches Riemann roots sexagesimal solids solution solved spherical square surface symbol synthetic geometry tangents theorem theory of numbers theta-functions Thomson tion translated triangle trigonometry variable Vieta Wallis writings wrote
Popular passages
Page 202 - I was so persecuted with discussions arising out of my theory of light, that I blamed my own imprudence for parting with so substantial a blessing as my quiet, to run after a shadow.
Page 298 - THEOREM If a straight line falling on two other straight lines, make the alternate angles equal to one another, the two straight lines shall be parallel to one another.
Page 21 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.