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Ibn al-Hawwam al-Bagdadi. al-fawaid al-baha`iya fi-l qawaid al-hisabiya. Arabic manuscript on paper, Egypt or Syria, dated at middle of the month of Šaban of the year 735 AH (April AD 1335). 62 leaves, complete; leaf dimensions: mm. 175 x 125; text panel: mm. 130 x 75. 15 lines per page on single column in black nashi script. The titles and some words were marked in red ink, and there are copious marginal notes. Illuminated šamsah on the first leaf and illuminated unwan with the title at the beginning of the text. Soft morocco binding with gold tooled decorations. Very good conditions: only a handful of waterstains. 25.000,00 EUR
Abdullah b. Muhammad al-Hawwam al-Bagdadi received his education by Nasir ad-Din at-Tusi (597-672 AH/AD 1201-1274). His presence at the city of Isfahan was mentioned around the year 675 AH/AD 1277, as he was teaching there the sons of princes and ministers. He also taught fiqh at the Dar as-dahab in Bagdad, where he lived until his last days in the year 724 AH/AD 1324. This treatise deals with arithmetic, algebra, and geometry. In the first pages of this work we meet definitions and brief explanations of the simplest geometric elements, as are line, point, segment. Then the text goes on illustrating the different figures of the plane geometry, with relating illustrations. Triangles: starting from leaf 28 it is explained how to deal with the edges/sides of the triangles and its angles, in this case taking into account the right triangle. The square and rectangle - leaf 31v- are treated as constructions derivated from the triangle (idem for the rhombus and the parallelogram -leaf 32 ). Also the trapezium -which is given greater explanation- is always dependent on the triangle (s. leaves 33 and 34). From the leaf 35 onwards, the topic of circumference is treated exhaustively; then, on leaf 41, al-Hawwam gives us the rules for the volume of the sphere, as follows: `The sphere is a solid circumscribed by one surface inside which there is a point, and all the outgoing straight lines towards the circumscribed surface are equal. Its area is a cube of the diameter after subtracting its seventh and a half of its seventh, then subtracting the seventh and a half of its seventh from the resultant`. V = [d3 - (1/7 + 1/2.1/7)d3] - (1/7 + 1/2.1/7) [d3 - (1/7 + 1/2.1/7)d3]. In other words: V = (11/14)2.d3. Evidently, this is rule about the volume of the sphere is erroneous. In his commentary on the book of al-Hawwam, Kamal ad-Din al-Farisi reveals the error about this calculation of the sphere volume, explaining also the reason lying behind such error; then, he expresses its correct formula.
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