Great Moments in Mathematics (before 1650)Mathematical Association of America, 1980 - 270 pages |
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Page 99
... Ptolemy's theorem : In a cyclic quadri- lateral the product of the diagonals is equal to the sum of the prod- ucts of the two pairs of opposite sides . Certainly practical trigonometry cannot progress very far without the use of so ...
... Ptolemy's theorem : In a cyclic quadri- lateral the product of the diagonals is equal to the sum of the prod- ucts of the two pairs of opposite sides . Certainly practical trigonometry cannot progress very far without the use of so ...
Page 108
... Ptolemy's second theorem . In the above quadrilateral n = ad + bc m ab + cď For those interested we here state an extension of Ptolemy's theorem and a singularly beautiful generalization of the theorem . Extension of Ptolemy's theorem ...
... Ptolemy's second theorem . In the above quadrilateral n = ad + bc m ab + cď For those interested we here state an extension of Ptolemy's theorem and a singularly beautiful generalization of the theorem . Extension of Ptolemy's theorem ...
Page 270
... Ptolemy's , 99 , 106 , 107 Ptolemy's ( extension of ) , 108 Ptolemy's ( generalization of ) , 108 Ptolemy's second , 108 Pythagorean ( see Pythagorean theorem ) Theory of sets , 197 Theudias of Magnesia , 71 Thymaridas , 132 bloom of ...
... Ptolemy's , 99 , 106 , 107 Ptolemy's ( extension of ) , 108 Ptolemy's ( generalization of ) , 108 Ptolemy's second , 108 Pythagorean ( see Pythagorean theorem ) Theory of sets , 197 Theudias of Magnesia , 71 Thymaridas , 132 bloom of ...
Contents
LECTURE TWO The greatest Egyptian pyramid | 8 |
LECTURE FOUR The first great theorem | 26 |
LECTURE FIVE Precipitation of the first crisis | 43 |
Copyright | |
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abacus algebra algorithm altitude analytic geometry ancient angle Archimedes arithmetic Arithmetica base Book Cavalieri century chord circle compasses computing congruent construction counters cube cubic equation curve cylinder denote Descartes digit Diophantus divides divisor ellipse equal Euclid's Elements Euclidean Eudoxian Fermat Fibonacci Figure formula Further Reading given golden ratio Greek Hindu Hindu-Arabic numeral system hypotenuse integers irrational number Kepler known later lecture legs length Liber abaci line segment logarithms mathematician method MOMENTS IN MATHEMATICS multiplication Napier obtain pair parallel perfect numbers plane polygon positive integers problem proof proposition Prove Ptolemy's Ptolemy's theorem pyramid Pythagorean theorem Pythagorean triple quadratic quadrilateral quartic equation radius rational number relatively prime right triangle roots sequence Show side solid solution solve sphere spherical square straightedge symbols tangent tetrahedron tion triangle ABC trisection vertex volume whence