पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/२८४

86 GANITASĀRASANGRAHA. CHAPTER V RULE-OF-THREE The fourth subject of treatment. 1. Salutation to that blessed Vardhamana, who is like a (helpful) relation to (all) the three worlds, and is (resplendent) like the sun in the matter of absolute knowledge, and has cast off (the taint of) all the karmas Next we shall expound the fourth subject of treatment, viz., rule-of-three The rule of operation in respect thereof is as follows:- 2 Here, in the rule-of-three, Phala multiplied by Iccha and divided by Pramana, becomes the (required) answer, when the Iccha and the Pramana are similar, (ie, in direct proportion); aud in the case of this (proportion) being inverse, this operation (involving multiplication and division) is reversed, (so as to have division in the place of multiplication and multiplication in the place of division) Examples relating to the former half of the above rule, 1.e, on the direct rule-of-three. 3. The man who in 3 days goes over 5 yojanas-give out what (distance) he (goes over) in a year and a day 4. A lame man walks over of a hrose together with (there- of) in 7 days. Say what (distance) he (goes over) in 3 years (at this rate). 5. A worm goes in of a day over of an angulu In how many days will it reach the top of the Mēru mountain from its bottom? 6. The man who in 3 days uses up 14 karsapanas-in what time (will) he (use up) 100 puranas along with 1 pana ? 2. Pramana and Phala together give the rate, in which Phala is a quantity of the same kind as the required answer and Pramana is of the same kind as Iccha. This Iccha is the quantity about which something is required to be found out at the given rate. For instance in the problem in stanza 3 here, 3 days is the Pramana, 5 yojanas is the Phala, and 1 year and 1 day is the Iccha. 5. The height of the mountain is supposed to be 99,000 yojanas or 76,032,000,000 angulas,