# المهاني

هذه صفحة مكتوبة بالعربية البسيطة، انظر الصفحة الأصلية

أبو عبد الله محمد بن عيسى الماهاني (ازدهر حوالي عام 860 وتوفي حوالي عام 880)، كان عالم رياضيات وفلك فارسي مسلم[1] وُلِد في ماهان، (في ما هو اليوم كرمان، بلاد فارس) ونشط في بغداد، الدولة العباسية. أعماله الرياضية المعروفة تضم تعليقاته على كتاب إقليدس العناصر، وكتاب أرخميدس' في الكرة والأسطوانة وكتاب منلاوس Sphaerica, as well as two independent treatises. He unsuccessfully tried to solve a problem posed by Archimedes of cutting a sphere into two volumes of a given ratio, which was later solved by 10th century mathematician أبو جعفر الخازن. His only known surviving work on astronomy was on the calculation of azimuths. He was also known to make astronomical observations, and claimed his estimates of the start times of three consecutive lunar eclipses were accurate to within half an hour.

## فهرست

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

## سيرته

يعرف المؤرخون القليل عن حياة الماهاني لقلة المصادر.[2] وقد وُلِد في ماهان، ببلاد فارس (ولذا نسبه الماهاني).[2] وقد نشط في القرن التاسع الميلادي أي القرن الثالث الهجري، وعاش في بغداد حوالي 860 وتوفي حوالي 880.[2][3] من إشارة في كتاب ابن يونس الزيج الحاكمي، وقد عُرف بقيامه بأرصاد فلكية بين 853 و 866، مما سمح للمؤرخين بتقدير زمن حياته وأنشطته.[2][4]

## أعماله

### الرياضيات

غطت أعماله في الرياضيات مواضيع الهندسة والحساب والجبر. بعض أعماله الرياضية ربما كانت بسبب مشاكل قابلها في علم الفلك. كتالوج القرن العاشر كتاب الفهرست يذكر إسهامات الماهاني في الرياضيات وليس في الفلك.[4]

He also worked on current mathematical problems at his time.[2] He wrote commentaries on Greek mathematical works: Euclid's Elements, Archimedes' On the Sphere and Cylinder and Menelaus' Sphaerica.[2] In his commentaries he added explanations, updated the language to use "modern" terms of his time, and reworked some of the proofs.[2][5] He also wrote a standalone treatise Fi al-Nisba ("On Relationship") and another on the squaring of parabola.[5]

His commentaries on the Elements covered Books I, V, X and XII; only those on Book V and parts of those on book X and XII survived today. In the Book V commentary, he worked on ratio, proposing a theory on the definition of ratio based on continued fractions that was later discovered independently by Al-Nayrizi.[6][7]

In the Book X commentary, he worked on irrational numbers, including quadratic irrational numbers and cubic ones. He expanded Euclid's definition of magnitudes—which included only geometrical lines—by adding integers and fractions as rational magnitudes as well as square and cubic roots as irrational magnitudes. He called square roots "plane irrationalities" and cubic roots "solid irrationalities", and classified the sums or differences of these roots, as well as the results of the roots' additions or substractions from rational magnitudes, also as irrational magnitudes. He then explained Book X using those rational and irrational magnitudes instead of geometric magnitudes like in the original.[6][7][8]

His commentaries of the Sphaerica covered book I and parts of book II, none of which survived today. His edition was later updated by Ahmad ibn Abi Said al-Harawi (10th century). Later, Nasir al-Din al-Tusi (1201 – 1274) dismissed Al-Mahani and Al-Harawi's edition and wrote his own treatment of the Sphaerica, based on the works on Abu Nasr Mansur. Al-Tusi's edition became the most widely known edition of the Sphaerica in the Arabic-speaking world.[2][7]

Al-Mahani also attempted to solve a problem posed by Archimedes in On the Sphere and Cylinder, book II, chapter 4: how to divide a sphere by a plane into two volumes of a given ratio. His work led him to an equation, known as "Al-Mahani's equation" in the Muslim world: ${\displaystyle x^{3}+c^{2}b=cx^{2}}$. However, as documented later by Omar Khayyam, "after giving it lengthy meditation" he eventually failed to solve the problem. The problem was then considered unsolvable until 10th century Persian mathematician Abu Ja'far al-Khazin solved it using conic sections.[4][6][9]

### الفلك

His astronomical observations of conjunctions as well as solar and lunar eclipses was cited in the zij (astronomical tables) of Ibn Yunus (c. 950 – 1009). Ibn Yunus quoted Al-Mahani as saying that he calculated their timings with an astrolabe. He claimed his estimates of the start times of three consecutive lunar eclipses were accurate to within half an hour.[2][7]

He also wrote a treatise, Maqala fi ma'rifat as-samt li-aiy sa'a aradta wa fi aiy maudi aradta ("On the Determination of the Azimuth for an Arbitrary Time and an Arbitrary Place"), his only known surviving work on astronomy. In it, he provided two graphical methods and an arithmetic one of calculating the azimuth—the angular measurement of a heavenly object's attitude. The arithmetric method corresponds to the cosine rule in spherical trigonometry, and was later used by Al-Battani (c. 858 – 929).[2][5]

He wrote another treatise, whose title, On the Latitude of the Stars, is known but its content is entirely lost. According to later astronomer Ibrahim ibn Sinan (908 – 946), Al-Mahani also wrote a treatise on calculating the ascendant using a solar clock.[5]

## انظر أيضاً

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

## الهامش

### مراجع

1. ^ On science and the construction of identities : remembering Ibn al-Haytham (965-1039) page 99 : "He neatly resolved the problem of al-Mahanī, a Persian mathematician of the 9th century"
2. ^ أ ب ت ث ج ح خ د ذ ر Dold-Samplonius 2008, p. 141.
3. ^ Sesiano 1993, p. 141.
4. ^ أ ب ت
5. ^ أ ب ت ث Sesiano 1993, p. 405.
6. ^ أ ب ت Dold-Samplonius 2008, p. 142.
7. ^ أ ب ت ث
8. ^ Matvievskaya 1987, p. 259.
9. ^ Sarton 1927, p. 598.

الكلمات الدالة: