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algebra analysis analytical angles appeared applied Arabic arithmetic astronomical attention became Berlin calculus called century circle complete considered construction contains continued curve definition Descartes determine developed differential equations discovery early equal equations Euler existence expressed extended figures formula four fractions functions Gauss gave geometry given gives Greek groups Hindu idea important infinite integral interest introduced invention Italy John known Lagrange later Leibniz letter limit linear logarithms London Math mathematicians mathematics means method motion nature Newton notation obtained original Paris plane positive principle probability problem professor progress proof proved published quantities question received recent relation remarkable represented researches roots rule says showed sides solution solved square surface symbols tables theorem theory third tion triangle University variables writings wrote
Page 105 - 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 262 - M. Laplace, they tell me you have written this large book on the system of the universe, and have never even mentioned its Creator.
Page 18 - 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.
Page 286 - Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Page 30 - Give him threepence, since he must make gain out of what he learns.
Page 197 - I consider mathematical quantities in this place not as consisting of very small parts, but as described by a continued motion. Lines are described, and thereby generated, not by the apposition of parts, but by the continued motion of points...
Page 390 - One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours.
Page 18 - Conspicuous is the absence of theorems on the circle. The Pythagoreans demonstrated also that the plane about a point is completely filled by six equilateral triangles, four squares, or three regular hexagons, so that a plane can be divided into figures of either kind.
Page 150 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.