O Nārada, listen as I recount the sacred methods by which the proper use of words is determined concisely. This is accomplished through the interplay of base, suffix, substitution, elision, and addition. Yet, because of the infinite and all-encompassing nature of these combinations, no one is able to express them all, not even the wisest among men. By mere knowledge of these methods, people are able to accomplish dharma. Consider, O Brāhmaṇa, the fields of calculation, the casting of horoscopes, and the collections known as Skandha. These encompass inquiries into the timing of lunar and solar eclipses, and the phenomenon called Udāsya. Within the study of horoscopes, one learns the divisions of the zodiac signs, the origins of the planets, and matters related to birth. One must also understand actions, the span of life, the eight groups, royal yogas, and celestial combinations. The results of planetary positions and the mixed yogas that provide support are to be examined. There is the determination of a lost birth and the characteristics of the Dreṣkāṇa. One must consider the conjunctions of lunar days, weekdays, stars, and the so-called half-tithis. The waxing and waning of the moon, as well as the seasons associated with all the lunar mansions, are also to be observed. In the course of life, there are auspicious rites such as the first cutting of hair, the piercing of ears, the tonsure, and the ritual tying of the knife. One must also consider the beginning of journeys, entering new places, sudden rain, and actions of a special kind. In calculations, numbers such as one, ten, a hundred, a thousand, ten thousand, and a hundred thousand are employed. Terms like niravara, mahāpadma, shaṅku, and even the ocean itself are used to express vast quantities. Whether in their natural order or otherwise, combinations are made according to the result that is sought. When the divisor is pure, O sage, the quotient is multiplied by the last remainder to yield the result. But if the last number is odd, that odd part is set aside, and the root is determined separately. That product, O Brāhmaṇa, is then abandoned and divided again by the root. This is the operation known as samatra, and the rule for the solid is applied in its proper place. Wealth, too, must be purified by the odd number from the last; this is called the root. With that product, one purifies what has been struck down, as well as the nighnī. In the process of mutual taking and striking down, shares are to be exactly apportioned. The proportion of shares must be understood by those who reflect on the meaning of this science. By subtracting the shares from the total, one assigns to each their own increased share. When the shares are equal, the combination is made at the end, O sage. The result is obtained by operations of subtracting, cutting, striking, and multiplying the differing shares. The remainder is taken during the division of shares, and the rule of multiplication is applied. To accomplish each step, one should produce a sound at every stage and also a sound everywhere, ensuring clarity. One should make both one’s own debt and the debt to oneself visible, for this reveals the sign in the zodiac. The portion here remains unchanged; in the reverse process, the remainder is as previously stated. By multiplying the desired with the observed, the quotient of the zodiac is obtained—never the unassigned. The difference between the zodiac signs is the surplus of the group; it is given to the one who is born, to those two. One group of this is divided, thus one zodiac sign is considered superior. In another union of groups, the single entities are the zodiac signs, and the groups are made of these two. Both seekers are manifest, and in calculation, only the manifest is considered. Half of the product of the observed is not added; instead, the product, once grouped, becomes the multiplier. In the same way, the root multiplier divided by those two is achieved, just as with the manifest. Finally, the desired multiplied by the first taken remainder is the result, separated by the reverse. Thus, O sage, the subtle science of calculation and the mysteries of the zodiac are revealed.