492 agathe keller
and equilateral triangles have sides ( aśra , for all sides), fl anks ( pārśva , a
synonym) and sometimes earths ( bhū , for the base), right-angled triangles
have a ‘base’ ( bhujā ), an ‘upright side’ ( kot. i ) and a ‘hypotenuse’ ( karn. a ),
as shown in Figure 14.1. In the fi rst half of Ab.2.17, Bhāskara states the
Pythagorean Th eorem:
Th at which precisely is the square of the base and the square of the upright side is
the square of the hypotenuse. 14
Th erefore, in order to indicate that a situation involves a right-angled
triangle, Bhāskara gives the names of the sides of a right-angled triangle
to the segments concerned by his reasoning. Two examples of Bhāskara’s
‘reinterpretation’ will demonstrate how he employed this theorem.2.3 ‘Reinterpretation’ with gnomons
Th e section devoted to gnomons ( śa ̇nku ) contains two illuminating cases.2.3.1 A gnomon and a source of light
Th e standard situation is as follows: a gnomon ( śa ̇nku , DE) casts a shadow
(EC), produced by a source of light (A), as illustrated in Figure 14.2.
First, consider the procedure given in Ab.2.15:
Th e distance between the gnomon and the base, with <the height of> the gnomon
for multiplier, divided by the diff erence of the <heights of the> gnomon and the
base.|14 yaś caiva bhujāvargah. kot. īvargaś ca karn. avargah. sah. (Shukla 1976 : 96).Figure 14.1 Names of the sides of a right-angled triangle.bhuja ̄karn·a
kot·i