A History of Mathematics |
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Page 1
... proved to be useless . The chemist smiles at the childish efforts of alchemists , but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of to - day . He is ...
... proved to be useless . The chemist smiles at the childish efforts of alchemists , but the mathematician finds the geometry of the Greeks and the arithmetic of the Hindoos as useful and admirable as any research of to - day . He is ...
Page 2
... proved in 1761 that the ratio of the circumference of a circle to its diameter is incom- mensurable . Some years ago , Lindemann demonstrated that this ratio is also transcendental and that the quadrature of the circle , by means of the ...
... proved in 1761 that the ratio of the circumference of a circle to its diameter is incom- mensurable . Some years ago , Lindemann demonstrated that this ratio is also transcendental and that the quadrature of the circle , by means of the ...
Page 12
... proved at all , but were known to be true merely from observation or as matters of fact . The second great defect was their inability to bring the numerous special cases under a more general view , and thereby to arrive at broader and ...
... proved at all , but were known to be true merely from observation or as matters of fact . The second great defect was their inability to bring the numerous special cases under a more general view , and thereby to arrive at broader and ...
Page 21
... proved by the Pythagoreans after the manner of Euclid . They demonstrated also that the plane about a point is completely filled by six equilateral triangles , four squares , or three regular hexagons , so that it is possible to divide ...
... proved by the Pythagoreans after the manner of Euclid . They demonstrated also that the plane about a point is completely filled by six equilateral triangles , four squares , or three regular hexagons , so that it is possible to divide ...
Page 27
... proving that if magnitudes are infinitely divisible , motion is impossible . Zeno argues that Achilles could not overtake a tortoise ; for while he hastened to the place where the tortoise had been when he started , the tortoise crept ...
... proving that if magnitudes are infinitely divisible , motion is impossible . Zeno argues that Achilles could not overtake a tortoise ; for while he hastened to the place where the tortoise had been when he started , the tortoise crept ...
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Popular passages
Page 292 - THEOREM. If a straight line, falling on two other straight lines, make the alternate angles equal to each other ; these two straight lines shall be parallel.
Page 13 - 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 90 - In an inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Page 419 - FERRERS.— AN ELEMENTARY TREATISE on TRILINEAR CO-ORDINATES, the Method of Reciprocal Polars, and the Theory of Projections. By the Rev. NM FERRERS, MA, Fellow and Tutor of Gonville and Caius College, Cambridge.