A History of Mathematics |
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Page 2
... method was tried by the best heads , and answered at last , by that method , after thou- sands of complete failures . " But progress was made on this problem by approaching it from a different direction and by newly discovered paths ...
... method was tried by the best heads , and answered at last , by that method , after thou- sands of complete failures . " But progress was made on this problem by approaching it from a different direction and by newly discovered paths ...
Page 13
... methods of numeration was ob- tained through the ingenious deciphering of the hieroglyphics by Champollion , Young ... method of figuring so extensively used by peoples of antiquity . The Egyptians used the decimal scale . Since , in ...
... methods of numeration was ob- tained through the ingenious deciphering of the hieroglyphics by Champollion , Young ... method of figuring so extensively used by peoples of antiquity . The Egyptians used the decimal scale . Since , in ...
Page 28
... method of reductio ad absurdum the falsity of the supposition that c > c . Since c ' can be neither larger nor smaller than c , it must be equal to it , Q.E.D. Hankel refers this Method of Exhaustion back to Hippo- crates of Chios , but ...
... method of reductio ad absurdum the falsity of the supposition that c > c . Since c ' can be neither larger nor smaller than c , it must be equal to it , Q.E.D. Hankel refers this Method of Exhaustion back to Hippo- crates of Chios , but ...
Page 30
... method of proof . To be sure , this method had been used unconsciously by Hippocrates and others ; but Plato , like a true philosopher , turned the instinc- tive logic into a conscious , legitimate method . The terms synthesis and ...
... method of proof . To be sure , this method had been used unconsciously by Hippocrates and others ; but Plato , like a true philosopher , turned the instinc- tive logic into a conscious , legitimate method . The terms synthesis and ...
Page 33
... method . " By this ' section ' is meant , no doubt , the " golden section " ( sectio aurea ) , which cuts a line in extreme and mean ratio . The first five propositions in Euclid XIII . relate to lines cut by this section , and are ...
... method . " By this ' section ' is meant , no doubt , the " golden section " ( sectio aurea ) , which cuts a line in extreme and mean ratio . The first five propositions in Euclid XIII . relate to lines cut by this section , and are ...
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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.