By Agathe Keller
In the fifth century the Indian mathematician Aryabhata (476-499) wrote a small yet well-known paintings on astronomy, the Aryabhatiya. This treatise, written in 118 verses, provides in its moment bankruptcy a precis of Hindu arithmetic as much as that point. 2 hundred years later, an Indian astronomer known as Bhaskara glossed this mathematial bankruptcy of the Aryabhatiya.
An english translation of Bhaskara’s remark and a mathematical complement are awarded in volumes.
Subjects taken care of in Bhaskara’s remark variety from computing the amount of an equilateral tetrahedron to the curiosity on a loaned capital, from computations on sequence to an complex technique to unravel a Diophantine equation.
This quantity includes causes for every verse remark translated in quantity 1. those supplementations speak about the linguistic and mathematical issues uncovered by way of the commentator. relatively precious for readers are an appendix on Indian astronomy, problematic glossaries, and an intensive bibliography.
Read Online or Download Expounding the Mathematical Seed Volume 2: The Supplements: A Translation of Bhāskara I on the Mathematical Chapter of the Āryabhatīya PDF
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Additional resources for Expounding the Mathematical Seed Volume 2: The Supplements: A Translation of Bhāskara I on the Mathematical Chapter of the Āryabhatīya
The cube-root extracted is 12. 1 Area of a triangle ¯ Aryabhat askara’s interpretation14 concerns a general case: . ab. The bulk of the area of a trilateral is the product of half the base and the perpendicular| This can be understood as follows: 14 Because Aryabhat ¯ . ¯ı or “halving upright”, probably this rule was intended originally only for equilaterals and isosceles. C. 6 23 Figure 7: Equilateral and isoceles triangles E F K E F G K G As illustrated in Figure 8, let M N O be a triangle. 1 NO × M D.
6 25 Figure 8: Any triangle M D N O In other words: Let M N O be any triangle such as is illustrated in Figure 8, let M D be a height. The sections of the base are the two segments N D and DO for the sides M N and M O. The ﬁrst sentence of this paragraph may be translated in our algebraical language as M N 2 − M O2 = (M N + M O)(M N − M O) = (N D + DO)(N D − DO) The last equality, which may also be stated as M N 2 − M O2 = N D2 − DO2 , is easily derived from the “Pythagoras Theorem”. ay¯ a vibhajya labdham um¯ av eva .
1 R¯a´sis A r¯ a´si, as can be seen in Figure 19, is 1/12th of a circle, or 30 degrees. Bh¯askara seems to consider the arc made of two r¯ a´sis as a ﬁeld of its own. 168 sqq] 46 Supplements Figure 19: The chord of a sixth part of the circumference, which is the chord subtending two r¯ a´sis, is equal to the radius Two råßis or a two råßi field is the 6th part of the circumference a jyå R ardha-jyå half-chord of one råßi this is the idea of Prabh¯ akara – then as the couple formed by a diameter and a circumference.