By Omar Al-khayam
Omar Al-Khayyam's well-known booklet on algebra and equations is taken into account to be possibly his most vital contribution to arithmetic - the cream of his paintings. students of arithmetic regard the publication 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 by utilizing geometrical techniques, occasionally regarding conic sections equivalent to parabolas and hyperbolas. The proofs provided are distinct and intensely deep. the writer made due acknowledgment and referral to the paintings and contributions of others who got here earlier 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 ebook either fascinating and informative.
Read or Download 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) PDF
Similar mathematics books
- Nonlinear Hybrid Continuous/Discrete-Time Models
- Harmonische Raume und ihre Potentialtheorie
- The Mathematical Foundation of Symbolic Trajectory Evaluation
- A note on the multiplicity of entire solutions in R2 for a class of almost periodic Allen-Cahn type equations
Additional info 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)
Some of its (this type) problems have no solution, and Abu-Aljood did not study them thoroughly. I mention all of this so that any person who has a chance to read both articles could compare my article with this honorable person’s article and see if what I was told about this honorable person is correct. I believe I did my best to study all problems thoroughly but with short proofs and without unnecessary details. I could have presented an example for each of the types and kinds (of problems) to prove validity.
Also, “a root plus two plus ten parts of the root equals twenty parts of a square” is equivalent to “a cube and two squares and ten roots equal twenty”. So we get the side of the cube using conic sections and it will be the required root. In summary, any four successive ranks of these seven ranks would fall in the same category of the mentioned twenty-five types. If it exceeds five, six or seven ranks, then there is no way to solve it. For example, the equation: a square plus two roots equals two plus two parts of the square, cannot be solved, because the square is the second rank and the part of the square is the sixth, and that exceeds five ranks.
So the location of this parabola is known. Now, we construct another (conic) section, the hyperbola hcz, with vertex at c, its axis along bc, and each of its two sides, the perpendicular and the oblique, equals bc. The location of this hyperbola is known, as was shown by Apollonius in proposition nh of article a. These two (conic) sections either meet or do not meet. If they do not meet, then there is no possible solution. If they meet tangentially at one point, or they intersect at two points, then the location of these point(s) is (are) known.
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