The intellectual legacy of the brilliant polymath Ibn Sinna (aka Avicenna)

by Guest Mon Oct 23, 2017 7:56 pm

Ibn Sina is often known by his Latin name of Avicenna, although most references to him today have reverted to using the correct version of ibn Sina...

Ibn Sina's two most important works are The Book of Healing and The Canon of Medicine. The first is a scientific encyclopaedia covering logic, natural sciences, psychology, geometry, astronomy, arithmetic and music. The second is the most famous single book in the history of medicine...

Ibn Sina's wrote about 450 works, of which around 240 have survived. Of the surviving works, 150 are on philosophy while 40 are devoted to medicine, the two fields in which he contributed most. He also wrote on psychology, geology, mathematics, astronomy, and logic. His most important work as far as mathematics is concerned, however, is his immense encyclopaedic work, the Kitab al-Shifa'Ⓣ. One of the four parts of this work is devoted to mathematics and ibn Sina includes astronomy and music as branches of mathematics within the encyclopaedia. In fact he divided mathematics into four branches, geometry, astronomy, arithmetic, and music, and he then subdivided each of these topics. Geometry he subdivided into geodesy, statics, kinematics, hydrostatics, and optics; astronomy he subdivided into astronomical and geographical tables, and the calendar; arithmetic he subdivided into algebra, and Indian addition and subtraction; music he subdivided into musical instruments.

The geometric section of the encyclopaedia is, not surprisingly, based on Euclid's Elements. Ibn Sina gives proofs but the presentation lacks the rigour adopted by Euclid. In fact ibn Sina does not present geometry as a deductive system from axioms in this work. We should note, however, that this was the way that ibn Sina chose to present the topic in the encyclopaedia. In other writings on geometry he, like many Muslim scientists, attempted to give a proof of Euclid's fifth postulate. The topics dealt with in the geometry section of the encyclopaedia are: lines, angles, and planes; parallels; triangles; constructions with ruler and compass; areas of parallelograms and triangles; geometric algebra; properties of circles; proportions without mentioning irrational numbers; proportions relating to areas of polygons; areas of circles; regular polygons; and volumes of polyhedra and the sphere. Full details are given in [17].

Ibn Sina made astronomical observations and we know that some were made at Isfahan and some at Hamadan. He made several correct deductions from his observations. For example he observed Venus as a spot against the surface of the Sun and correctly deduced that Venus must be closer to the Earth than the Sun. This observation, and other related work by ibn Sina, is discussed in [53]. Ibn Sina invented an instrument for observing the coordinates of a star. The instrument had two legs pivoted at one end; the lower leg rotated about a horizontal protractor, thus showing the azimuth, while the upper leg marked with a scale and having observing sights, was raised in the plane vertical to the lower leg to give the star's altitude. Another of ibn Sina's contributions to astronomy was his attempt to calculate the difference in longitude between Baghdad and Gurgan by observing a meridian transit of the moon at Gurgan. He also correctly stated, with what justification it is hard to see, that the velocity of light is finite.

As ibn Sina considered music as one of the branches of mathematics it is fitting to give a brief indication of his work on this topic which was mainly on tonic intervals, rhythmic patterns, and musical instruments. Some experts claim that ibn Sina's promotion of the consonance of the major third led to the use of just intonation rather than the intonation associated with Pythagoras. More information is contained in T S Vyzgo's paper "On Ibn Sina's contribution to musicology" in [5].

Mechanics was a topic which ibn Sina classified under mathematics. In his work Mi'yar al-'aqul ibn Sina defines simple machines and combinations of them which involve rollers, levers, windlasses, pulleys, and many others. Although the material was well-known and certainly not original, nevertheless ibn Sina's classification of mechanisms, which goes beyond that of Heron, is highly original....

Ibn Sina is known to have corresponded with al-Biruni. In [10], eighteen letters which ibn Sina sent to al-Biruni in answer to questions that he had posed are given. These letters cover topics such as philosophy, astronomy and physics. There is other correspondence from ibn Sina which has been preserved which has been surveyed in the article [31]. The topics of these letters include arguments against theologians and those professing magical powers, and refutation of the opinions those who having a superficial interest in a branch of knowledge. Ibn Sina writes on certain topics in philosophy, and writes letters to students who must have asked him to explain difficulties they have encountered in some classic text. The authors of [31] see ibn Sina as promoting natural science and arguing against religious men who attempt to obscure the truth.

http://www-groups.dcs.st-and.ac.uk/history/Biographies/Avicenna.html