A History of Mathematics |
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Page 2
... means : Euclid's postulates and nothing more . We cannot remember an instance in which a question to be solved by a definite method was tried by the best heads , and answered at last , by that method , after thou- sands of complete ...
... means : Euclid's postulates and nothing more . We cannot remember an instance in which a question to be solved by a definite method was tried by the best heads , and answered at last , by that method , after thou- sands of complete ...
Page 11
... harpedonaptæ , applied to Egyptian geometers , means " rope - stretchers , " would point to the conclusion that the Egyptian , like the Indian and Chinese 3 geometers , constructed a right triangle upon a given THE EGYPTIANS . 11.
... harpedonaptæ , applied to Egyptian geometers , means " rope - stretchers , " would point to the conclusion that the Egyptian , like the Indian and Chinese 3 geometers , constructed a right triangle upon a given THE EGYPTIANS . 11.
Page 22
... mean progress in geometry . Of the theorems generally ascribed to the Italian school , some cannot be attributed to Pythagoras himself , nor to his earliest successors . The progress from empirical to reasoned solutions must , of ...
... mean progress in geometry . Of the theorems generally ascribed to the Italian school , some cannot be attributed to Pythagoras himself , nor to his earliest successors . The progress from empirical to reasoned solutions must , of ...
Page 23
... mean proportionals between two given lines . These mean proportionals were obtained by Archytas from the section of a half - cylinder . The doctrine of proportion was advanced through him . There is every reason to believe that the ...
... mean proportionals between two given lines . These mean proportionals were obtained by Archytas from the section of a half - cylinder . The doctrine of proportion was advanced through him . There is every reason to believe that the ...
Page 25
... means of a ruler and compass only . Proclus mentions a man , Hippias , presum- ably Hippias of Elis , as the ... mean proportionals between a given line and another twice as long . For , in the proportion a : x = x : y = y : 2a , since ...
... means of a ruler and compass only . Proclus mentions a man , Hippias , presum- ably Hippias of Elis , as the ... mean proportionals between a given line and another twice as long . For , in the proportion a : x = x : y = y : 2a , since ...
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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.