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''Yuktibhāṣā'' ((マラヤーラム語:യുക്തിഭാഷ); "Rationale in the Malayalam/Sanskrit language"〔) also known as ''Gaṇitanyāyasaṅgraha'' ("Compendium of astronomical rationale"),〔 is a major treatise on mathematics and astronomy, written by Indian astronomer Jyesthadeva of the Kerala school of mathematics in about AD 1530.〔 〕 The treatise is a consolidation of the discoveries by Madhava of Sangamagrama, Nilakantha Somayaji, Parameshvara, Jyeshtadeva, Achyuta Pisharati and other astronomer-mathematicians of the Kerala school. ''Yuktibhasa'' is mainly based on Nilakantha's ''Tantra Samgraha''.〔 〕 It is considered an early text on some of the foundations of calculus and predates those of European mathematicians such as James Gregory by over a century. However, the treatise was largely unnoticed beyond Kerala, as the book was written in the local language of Malayalam. However, some have argued that mathematics from Kerala were transmitted to Europe. The work was unique for its time, since it contained proofs and derivations of the theorems that it presented; something that was not usually done by any Indian mathematicians of that era.〔 〕 Some of its important developments in analysis include: the infinite series expansion of a function, the power series, the Taylor series, the trigonometric series for sine, cosine, tangent and arctangent, the second and third order Taylor series approximations of sine and cosine, the power series of π, π/4, θ, the radius, diameter and circumference, and tests of convergence. ==Contents== ''Yuktibhasa'' contains most of the developments of earlier Kerala School mathematicians, particularly Madhava and Nilakantha. The text is divided into two parts — the former deals with mathematical analysis of arithmetic, algebra, trigonometry and geometry, logistics, algebraic problems, fractions, Rule of three, ''Kuttakaram'', circle and disquisition on R-Sine; and the latter about astronomy.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Yuktibhāṣā」の詳細全文を読む スポンサード リンク
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