Deshbhushanji Aacharya Abhinandan Granth

SR No.: 012045
Original Sutra Author: N/A
Author: R C Gupta
Publisher: Deshbhushanji Maharaj Trust
Publication Year: 1987
Total Pages: 1766
Language: Hindi, English
Classification: Smruti_Granth & Articles
File Size: 56 MB

Page 903

1. Parikarma (“fundamental operations") 2. Vyavahara ("subjects of treatment") 3. Rajju
("rope" meaning "geometry") 4. Rasi
("heap" meaning "mensuration of solid bodies") 5. Kala Savarnama ("fraction") 6. Yavat-tavat ("as many as" meaning "simple equations") 7. Varga
("square" meaning "quadratic equations") 8. Ghana
("cube" meaning "cubic equations”) 9. Varga-varga (biquadratic equations”) 10. Vikalpa or bhong (permutations and combinations")
The exact meaning of some of the above terms is not known and this has been a subject matter of controversy for the mathematicians. However, in the light of the available text and the usage of the above terms in later Hindu mathematics, we can define the above terms as below:
Parikarma means the four fundamental operations of arithmetic viz. addition, subtraction, multiplication and division. Vyavahara means applied arithmetic. It is the application of arithmetic to concrete problems. Kalasavarnama refers to operations with fractions. Mahavira (850 A. D.) has used these three terms in exactly this sense in his GSS. The first two terms appear indeed in the works of all the Hindu mathematicians from Brahmagupta (7th Cent. A. D.) onwards.
Rajju is the ancient Hindu name for geometry. It was called Sulva in the vedic period. Rassi means a heap in general and it may refer to the section on the treatment of the mensuration of solid bodies.
Yavat-tawat is the symbol for an unknown quantity in Hindu algebra. According to Abhayadeva Suri (11th cent. A. D.), the commentator of the Sthananga Sutra (before 300 B. C.) this term refers to multiplication or to the summation of series (samkalita). But obviously multiplication is included in the fundamental operations.
Varga means both square and square-root, and it refers to quadratic equations. Ghana means both cube and cube-root, and it refers to cubic equations. Varga-varga refers to biquadratic equations. It may be noted here that Abhayadeva Suri (11th cent. A.D.) thought that varga, ghana, varga-varga refer respectively to the rules for finding out the square, cube and fourth power of a number. But in Hindu mathematics from earliest times, these operations were regarded as fundamental operations and hence they are coverd under the first term viz. Parikarma. Thus the inference of Abhayadeva Suri is not correct.
Vikalpa or bhong is the Jaina name for permutations and combinations. This topic has been accorded a separate mention on account of its importance in mathematics.
6. MULTIPLICATION AND DIVISION BY FACTORS
In the Tattvartha dhigama-sutra-Bhashyal of Umaswati (150 B.C.), a reference has been made of two methods of multiplication and division. In one method, the respective operations are carried on with the two numbers considered as a whole. In the second method, the operations are carried on in successive stages by the factors, one after another, of the multiplier and the divisor. The former method is our ordinary method, and the later is a shorter and a simpler one. The method of multiplication by factors has been mentioned by
1. See Chap. 11, p. 52.
जैन प्राच्य विद्याएँ