Mañjula and the Laghumānasa — Finding the True Moon
From The Laghumānasa of Mañjula — the Dawn of Calculus, taught by Acharya T Krishnatrey. This lesson is free to read.
Around **932 CE**, the astronomer **Mañjula** (also called **Muñjāla**) composed the **Laghumānasa** — a short, brilliant handbook (karaṇa) of planetary computation. In solving a very practical problem — where exactly is the Moon RIGHT NOW? — Mañjula wrote down one of the earliest known Indian statements of what amounts to the **derivative of the sine**: his rule that the Moon's motion-correction (gatiphala) is the **koṭijyā (Rcosine) times the daily motion** — in effect **sin w′ − sin w = (w′ − w) · cos w**. Hidden in a lunar correction lies a seed of the CALCULUS. <pre data-block="quote">The Moon never stands still — so to find its true place one must reckon its motion at the very instant. In answering that, Mañjula touched the infinitesimal.</pre>