Trigonometry in Two Sixteenth Century Works; The de Revolutionibus Orbium Coelestium and the Sidra Al-Muntahā

Extract

In Greece, Autolycos (4th cent. B.C.), Aristarchos of Samos (3rd cent.B.C.), Hipparchos (2nd cent.B.C.), Menelaos (1st cent. A.D.), and Ptolemaos (2nd cent. A.D.) are the forerunners of trigonometry. The Greeks used chords and prepared a table of chords.

Later, the Hindus produced Siddhāntas (4th cent.A.D.). The most important feature of these works is the use of jyā instead of chords, and utkramajyā (versed sine).

In Islam, al-Battānī al-Ṣābī (858-929) used the sine, cosine, tangent, and cotangent with clear consciousness of their individual characteristics.

As is known, trigonometry developed as a branch of astronomy. Although in the thirteenth century Naṣīr al-Dīn al-Ṭūsī (in the Islamic world) and in the fifteenth century Regiomontanus (in the West) established trigonometry as a science independent of astronomy, the essential situation did not change, and the subject went on developing as before.