Get An Essay by the Uniquely Wise 'Abel Fath Omar Bin Al-khayam PDF

By Omar Al-khayam

ISBN-10: 1435634772

ISBN-13: 9781435634770

ISBN-10: 1859641806

ISBN-13: 9781859641804

Omar Al-Khayyam's well-known ebook on algebra and equations is taken into account to be maybe his most vital contribution to arithmetic - the cream of his paintings. students of arithmetic regard the booklet as an important merchandise in either their own libraries and institutional collections. This ebook offers with the answer of quadratic and cubic equations. Al-Khayyam solved all attainable instances of such equations through the use of geometrical methods, occasionally concerning conic sections akin to parabolas and hyperbolas. The proofs awarded are exact and intensely deep. the writer made due acknowledgment and referral to the paintings and contributions of others who got here sooner than him. a contemporary reader could be astonished via the top of the range of the paintings, linguistically in addition to mathematically. Historians of technology, lecturers of arithmetic and mathematicians themselves will locate the e-book either fascinating and informative.

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Additional resources for An Essay by the Uniquely Wise 'Abel Fath Omar Bin Al-khayam on Algebra And Equations: Algebra Wa Al-Muqabala (Great Books of Islamic Civilization)

Example text

Assume, if possible, it meets t, so its square equals the product of at and tb (which equals bc). But this perpendicular equals the perpendicular on dt, so the square of td equals the product of at and tb (which is also equal to the product of bt with itself), and that is impossible. Also it does not meet the line at a point on the extension through t, because in such a case, that perpendicular must be shorter than td, which again is impossible. So the perpendicular must pass through a point between a and t, say z, and let the perpendicular be hz.

The four lines are proportional: the ratio of zc to cb is as the ratio of cb to zt and as the ratio of zt to za. So the ratio of the square of zc (the first) to the square of bc (the second) is the same as the ratio of bc (the second) to za (the fourth). Hence the cube of bc (which is equal to the given number) equals the parallelepiped whose base is the square zc and height za. We make the cube zc common. So the cube zc plus the given number equals the parallelepiped whose base is the square zc and height ac, which equals the number of squares.

Equations that contain the inverse of the unknown We have studied the twenty-five types of the introductory algebra and equations and covered them completely. We discussed the different kinds of each type. We also presented rules of how to distinguish the ones with possible solutions from those which are impossible to solve. We showed that most of them have solutions. Let us now study their parts (inverses). 01 Book of Algebra 24/11/07 1:54 PM Page 38 ALGEBRA WA AL-MUQABALA 38 The part of a number (its reciprocal) is a number whose ratio to one is the same as the ratio of one to the number.

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An Essay by the Uniquely Wise 'Abel Fath Omar Bin Al-khayam on Algebra And Equations: Algebra Wa Al-Muqabala (Great Books of Islamic Civilization) by Omar Al-khayam


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