[Chapter on the Three Problems] Laghumanasa

The multiplier original: "guna" increased by the difference between the unit-radiant and the multiplier; if the unit is greater, it is added, if smaller, it is subtracted. This results in the desired corrected value. || 6 ||

From the sum of those, multiplied by the square of the gnomon, and adding the square of the product of the midday shadow and the multiplier; the square root of that sum, divided by the divisor, is the desired shadow. || 7 ||

From the sum of those: Place the multiplier and the divisor separately. Add one to the other and multiply by the square of the gnomon A vertical pillar used to cast a shadow, usually 12 digits high (the square of twelve). Then, add the square of the multiplier which has been multiplied by the digits of the midday shadow, and take the square root. One should then divide that root by the divisor. The result obtained there is the shadow-digits of a twelve-digit gnomon. By multiplying the remainder by eight and dividing by the divisor, the result is in fractional digits original: "vyangula". Desired shadow—this means the shadow of a twelve-digit gnomon at the desired time. In the absence of a midday shadow, the desired shadow is the square root of the sum of the multiplier and divisor multiplied by the square of the gnomon, divided by the divisor. In that case, at midday, the hypotenuse is exactly twelve. Furthermore, multiply that shadow-digit by thirteen and divide by twenty-four. The result is the shadow-length in terms of a "man's pace" original: "purusha-pada". The remainder multiplied by twenty-four gives the digits. || 7 ||

The square root of the sum of the squares of the shadow and the sun (gnomon) is the hypotenuse; from that, the shadow is also found. The desired hypotenuse is the multiplier multiplied by the difference of its own midday hypotenuse. || 8 ||

Now, he describes the calculation of the hypotenuse The diagonal line from the top of the gnomon to the tip of the shadow in order to calculate the time (in ghatikas) from the desired shadow: Shadow-sun... Multiply the shadow-paces of a man at the desired time by twenty-four and divide by thirteen. The result is the shadow-digits of a twelve-digit gnomon. By this method, or by setting up the gnomon, one should calculate the shadow-digits of a twelve-digit gnomon with its fractions. Square that, add the square of the "suns" (twelve), and take the square root. That root is the desired hypotenuse. The square root of the sum of the squares of the midday shadow 1. Or "the sum" and the gnomon is the midday hypotenuse. Thus, one should calculate the desired hypotenuse and the midday hypotenuse with their fractions. From that also the shadow having first calculated the hypotenuse, from that the shadow is to be brought forth from the hypotenuse as well. This means the shadow is the square root of the remainder after subtracting the square of the gnomon from the square of the hypotenuse. The hypotenuse is:

The midday hypotenuse is the divisor; the desired hypotenuse is that plus itself. The square root of the difference between the squares of the hypotenuse and the sun (gnomon) shall be the shadow of the gnomon.

This is the observation. However, at the equator original: "niraksha-desha", the place with no latitude, one should assign the values 20, 16, and 7 respectively as the ascensional difference factors original: "charaguna". Having multiplied the half-ascensional difference by itself and dividing by twenty, one brings out the midday shadow, and then brings out the desired shadow without the ascensional difference.