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 904

all the Indian mathematicians from Brahmgupta1 (7th cent. A.D.) onwards. The division by factors is found in Trisatika of Sridhara (8th cent. A.D.). This method reached Italy in the middle ages through the Arabs and was called the "Modo per rekiego".
7. CERTAIN MENSURATION FORMULE
The following formulae for the mensuration of a circle were stated by Umaswati (150 B.C.) in his Tattvartha Dhigama-Sutra-Bhashya3:
(i) Circumference of a circle=√10 (diameter of the circle)
(ii) Area of a circle= (circumference) × (diameter)
If a denotes the arc of a segment of a circle less than a semi circle, c its chord, h its height or arrow, and d the diameter of the circle, then
All the above formulae, except the formula (v) for finding the arrow, are restated in the Jambudvipa samasa of Umaswati. In this work, the formula corresponding to (v) is
h=√√√(022),
which is the same as (v) in another form.
(iii) c=4h (d-h) (iv) h=(d-d2-c2)
(v) a= √6h2+c2
(vi) d--(+4)
As stated earlier, the above mensuration formulae given in the work of Umaswati were not discovered by him. In fact most of these formulae were known in India, centuries before him. In the Surya Prajnapti (500 B.C.) and other early Jaina works, are stated the length of the diameter and the circumference of certain circular bodies. These texts have used some of the above formulae for the computation of the circumference of the Jambudvipa (the earth) from its given diameter. According to the Jain cosmography," the Jambudvipa is a circle of diameter 100,000 yojana and is divided into seven parts by a system of six mountain ranges running parallel, east to west, at regular intervals. The sacred books of the Jainas (of about 500 B.C.) give the dimensions of the Jambudvipa as:
1. See Brahma-Sphuta-Siddhanta (B. S. S.) Chap. XII, p. 55.
Brahmagupta calls it Bheda method, while others call it Vibhaga-gunana. Compare H. T. Colebrooke. "Algebra with arithmetic and mensuration from the Sanskrit of Brahmagupta and Bhashkara." London 1817, p. 61.
2. See Rule 9.
3. Tattvärtha-Dhigama-Sutra-Bhashya with the commentary of Umaswati and notes of Siddhasena Gani (c. 56 B. C.) Part I.
Edited by H. R. Kapadia. Bombay 1926, p. 258-260.
4. Surya Prajnapti. See Sutra 20.
5. Datta "Geometry in the Jaina Cosmography".
Quellen Und Studien Zur Ges. D. Maths. Ab. B. Ed.-1 (1931) p, 245-254.
Also See Tattvärtha Dhigama-Sutra-Bhāṣhya.
6.
३८
See. 1. Jambudvipa Prajnapti. Sutra 3.
Ed. A. N. Upadhaya and Hira Lal Jain.
Jain Sanskrit Sansksha Sangha. Solapur 1958.
आचार्य रत्न श्री देशभूषण जी महाराज अभिनन्दन ग्रन्थ