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abacus added advance Ages algebra already ancient angle appears applied Arabic Archimedes arithmetic astronomers beginning calculation called century circle classical common computing connected considered contributed curve developed Diophantus early elementary Elements equal equation essentially Euclid Europe evidence example expressed fact field figures five fractions gave geometry given Greece Greek hand hence higher idea important influence interest invention kind knowledge known late later Latin lead looked mathe mathematics means measure mentioned method Michigan nature original period Plato possibly present principles problem proportion propositions Pythagoras ratio recognized referred relating represented respect result Roman Rome root rule scholars schools seems side simple solved speak square symbols term Thales theory thought tion translated triangle trigonometry units University various writers
Side 45 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 156 - They have in view practice only, and are always speaking, in a narrow and ridiculous manner, of squaring and extending and applying and the like — they confuse the necessities of geometry with those of daily life; whereas knowledge is the real object of the whole science.
Side 159 - If Hippocrates comes to me he will not experience the sort of drudgery with which other Sophists are in the habit of insulting their pupils; who, when they have just escaped from the arts, are taken and driven back into them by these teachers, and made to learn calculation, and astronomy and geometry, and music...
Side ii - New York JOHN JAY CHAPMAN WILLARD V. KING THOMAS W. LAMONT DWIGHT W. MORROW MRS. DW MORROW ELIHU ROOT MORTIMER L.
Side i - EDITORS GEORGE DEPUE HADZSITS, PH.D. University of Pennsylvania DAVID MOORE ROBINSON, PH.D., LL.D The Johns Hopkins University CONTRIBUTORS TO THE "OUR DEBT TO GREECE AND ROME FUND," WHOSE GENEROSITY HAS MADE POSSIBLE THE LIBRARY 2D*bt to d&ttttt ana Home Philadelphia DR.
Side 58 - To be a Greek was to seek to know; to know the primordial substance of matter, to know the meaning of number, to know the world as a rational whole. In no spirit of paradox one may say that Euclid is the most typical Greek: he would fain know to the bottom, and know as a rational system, the laws of the measurement of the earth.
Side ii - WILLIAM C. SPROUL JOHN B. STETSON, JR. DR. J. WILLIAM WHITE (memorial) GEORGE D. WIDENER MRS. JAMES D. WINSOR OWEN WISTER The Philadelphia Society for the Promotion of Liberal Studies. Boston ORIC BATES (memorial) FREDERICK P.
Side ii - OWEN WISTER The Philadelphia Society for the Promotion of Liberal Studies. Boston ORIC BATES (memorial) FREDERICK P. FISH WILLIAM AMORY GARDNER JOSEPH CLARK HOPPIN Chicago HERBERT W. WOLFF Cincinnati CHARLES PHELPS TAFT Cleveland SAMUEL MATHER Detroit JOHN W.
Side 56 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 2 - It remains their everlasting glory that they discovered and made use of the serious scientific elements in the confused and complex mass of exact observations and superstitious ideas which constitutes the priestly wisdom of the East, and threw all the fantastic rubbish on one side.