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104 THEORY OF THE PULVERISER is called a pulveriser (ku!akara). The pulveriser of the type (1) is called a non-residual pulveriser (miragra-ku!!akara), and that of the type 2) is called a residual pulveriser (ठagra ku!!akara) The difference between the two types will become clearer by the follow ing examples, of which the first relates to the non-residual pulveriser and the second to the residual pulveriser: Ex. 1. “8 is multiplied by some number and the product is increased by 6 and then the sum is divided by 13. If the division be exact, what is the (unknown) multiplier and what the resulting guotient ?” Bx. 2. *What is that number, O mathematician, which yields 5 as re mainder when divided by 12, and 7 when divided by 31 ?” The rules given in the following starm2as relate to the non-residual pulve riser, which is of the type (1). It may be mentioned that in equation (1), ८ is called the “dividend', b the *divisor', and ८ the *interpolator'. When the interpolator is negative, it is technically called gata ; and when the inter polator is positive, it is called guntarya 2:3. Preliminary operation : गुणकारभागहारौ विभजेदन्योन्यभक्तशेषेण । तौ तत्र भाज्यहारौ दृढ़ावाप्तौ विनिर्दिष्टौ ।। ३ ।। अन्योन्यशेषभक्तं गतगन्तव्यं यदा निरवशेषम तत्रेष्टाभ्यां कार्य कुट्टनमन्यत्र दृढ़ाभ्याम् ।। ४ ।। .८., “Divide out the dividend (1it. multiplier) and the divisor by the (non-Zero) remainder of their mutual division. The re resulting dividend and divisor are then said to be prime to each other When the gata (i.e., negative interpolator) or garntaya (i.८ positive interpolator) is found to be exactly divisible by the (non-Zero) remainder of the mutual division, (it should be understood that the given interpolator corresponds to the true non-abraded values of the dividend and divisor, and 50) onc should proceed with the actual (non-abraded) values of the