गणितसारसंग्रह (महावीराचार्य - प्रो. लक्ष्मीचन्द्र जैन सविस्तार हिन्दी अनुवाद सटीक)

xi

Here is a brief survey of the contents of the book :
Chapter I opens with the salutation to Lord Mahāvīra, the
twentyfourth Tīrthaṅkara of the Jainas, who by his knowledge of the
science of the numbers illuminates the three worlds. This is follwed
by a warm and handsome tribute of gratitude paid to his royal patron,
Amoghavarsha. After this, comes the most enthusiastic and unique
panegyric ever bestowed on the science of Mathematics. Then we have
measures used, names of operations and numerals. Rules governing
the use of negative numbers are correctly stated; those regarding the
use of zero may be stated in modern notation thus :
a ± 0 = a; a × 0 = 0; a ÷ 0 = a.
The last part is obviously wrong. As regards the square root
of a negative number, the author observes that since squares of
positive and negative numbers are positive, square root of a negative
number cannot exist. Considering the limitations of his time,
Mahāvīrāchārya could not have reached a more sensible conclusion.
We may note, in this context, that the necessary extension of the
concept of number which assimilates square roots of negative
numbers into the number system, was achieved as late as in 1797
by C. Wessel a Norwegian surveyor ( Bell's 'The Development
of Mathematics' page 177 ).
Chapter II deals, in respect of integers, with operations of
multiplication, division, squaring and its inverse, cubing and its
inverse, arithmetic and geometric series.
Problem II 17. In this problem, put down in order (from the
unit's place upwards ) 1, 1, 0, 1, 1, 0, 1 and 1, which ( figures so
placed ) give the measure of a number and (then) if this number is
multiplied by 91, there results that necklace which is worthy of a
prince. The 'Necklace' referred to, may be displayed thus :
11011011 × 91 — 1002002001.
Two more 'garlands worthy of a prince' are : ( II 11, 15 ) :
333333666667 × 33 = 11000011000011;
and 752207 × 73 = 11, 111, 111.