The Science of the Shulba: A Study in Early Hindu Geometry c18.43

c18.43

It should be noted that the relevant portions of the existing manuscripts of the *Kātyāyana Śulba* might be considered to be quite correct and his results extremely accurate if we follow a certain interpretation of the text. Let us suppose that (1) the term *ekaśata-vidha* means "the construction (of a Fire-altar having an area) of 101 (square puruṣas)," and (2) that the area of 101 square puruṣas comprises only the complete puruṣas in the altar, not including the two aratnis and the prādeśa. Then the algebraic representation of the second method of enlargement of the primitive falcon-shaped Fire-altar will be $7x² = 7+m.$ Therefore $x² = 1+m/7.$