George Rusby Kaye

“ What four numbers are such that their product is equal to twenty times their sum, say, learned mathematician who art conversant with the topic of the product of unknown quantities?
Answer—5, 4, 2, 11. V. 210.
Bhāskara puts arbitrary values for three of the quantities and gets 11 for the fourth.
68. If you are conversant with operations of algebra tell the number of which the fourth power less double the sum of the square and of two hundred times the simple number is ten thousand less one?
Answer—11. V. 138.
This may be expressed by . It is the only case in which the fourth power occurs. ”

“ The principal multiplied by its time and divided by the interest, and the quotient being multiplied by the factor less one is the time. The sum of principal and interest divided by unity added to the interest on unity is the principal. ”

“ Of a quadrilateral figure whose base is the square of four and the face two hastas and altitude twelve, the flanks thirteen and fifteen, what is the area?
Answer—108. S. 77.
46. In the figure of the form of a young moon the middle length is sixteen and the middle breadth is three hastas. By splitting it up into two triangles tell me, quickly, its area?
Answer—24. S. 83.
47. The sides of a quadrilateral with unequal sides are , and the top side is the cube of 5 and the bottom side is 300. What are all the values here beginning with that of the diagonals? ”

“ Draw one of the sides across the oblong so that it touches the other side. Where it touches there cut off. By this line which has been cut off the small square is deducted from the large one.
*⁠*⁠*⁠*⁠* 58. If you wish to turn a square into a circle draw half of the cord stretched in the diagonal from the centre towards the prāchī line. Describe the circle together with the third part of that piece of the cord which stands over.
Āryabhata's gaņita— (Circa. A.D. 520) .
6. The area of a triangle is the product of the perpendicular common to the two halves and half the base. ”

“ What is there unknown to the intelligent? Therefore for the dull alone it is set forth.
V. 225. To augment wisdom and strengthen confidence, read, read, mathematician, this abridgement elegant in style, easily understood by youth, comprising the whole essence of calculation and containing the demonstration of its principles—full of excellence and free from defect.
APPENDIX II.
Examples. [2]
1. One-half, one-sixth, and one-twelfth parts of a pole are immersed respectively under water, clay, and sand. Two hastas are visible. Find the height of the pole?
Answer—8 hastas. S. 23. ”

“ A white-ant advances 8 yavas less one-fifth in a day and returns the twentieth part of an añgula in 3 days. In what space of time will one, whose progress is governed by these rates of advancing and receding proceed 100 yojanas? ”

“ Two elephants, which are ten in length, nine in breadth, thirty-six in girth and seven in height, consume one droņa of grain. How much will be the rations of ten other elephants which are a quarter more in height and other dimensions? ”

“ A snake's hole is at the foot of a pillar 9 hastas high and a peacock is perched on the summit. Seeing a snake, at a distance of thrice the pillar, gliding towards his hole, he pounces obliquely on him. Say quickly at how many hastas from the snake's hole do they meet, both proceeding an equal distance? ”

“ One purchases seven for two and sells six for three. Eighteen is the profit. What is the capital?
Answer—. Bakhshāli Ms. 54.
17. If a pala of best camphor may be had for two nishkas, and a pala of sandal wood for the eighth part of a dramma and half a pala of aloe wood also for the eighth of a dramma, good merchant, give me the value of one nishka in the proportions of 1, 16 and 8; for I wish to prepare a perfume? ”

“ C. 283.
(8 yavas=1 añgula, 768000 añgulas=1 yojana) .
8. Twenty men have to carry a palanquin two yojanas and 720 dīnāras for their wages. Two men stop after going two krośas, after two more krośas three others give up, and after going half the remaining distance five men leave. What wages do they earn?
Answers—18, 57, 155, 490. M. vi, 231.
(4 krośas=1 yojana) .
9. It is well known that the horses belonging to the sun's chariot are seven. Four horses drag it along being harnessed to the yoke. They have to do a journey of 70 yojanas. ”