﻿APPENDIX. 495 



method, said he had found some indications of the 

 Binomial Theorem in much older authors. The me- 

 thod however by which that great man investigated 

 the powers independent of each other, is exactly the 

 same as that in the following translation from the 

 Sanscrit. 



<( A Raja's palace had eight doors ; now these doors 

 " mav either be opened by one at a time, or by two 

 i( at a time, or by three at a time, and so on through 

 ** the whole, till at last all are opened together. It is 

 *' required to tell the numbers of times that this can 

 " be done ? 



u Set down the number of the doors, and proceed 

 " in order, gradually decreasing by one to unity, 

 •* and then in a contrary order, as follows : 



8 7 6 5 4 3 2 * 

 12345678 



<c Divide the first number eight by the unit beneath 

 " it, and the quotient eio;ht shews the number of 

 " times that the doors can be opened by one at a 

 il time. Multiply this last eight by the next term seven j 

 <c ar.d divide the product by the two beneath it, and 

 " the result twenty eight is the number of times that 

 " two different doors may be opened ; multiply the 

 '* last found twenty-eight by the next figure six, and 

 " divide the product by the three beneath it, and the 

 «' quotient fifty-six shews the number of times that 

 " three different doors may be opened. Again, this 

 " nfty-six multiplied by the next five, and divided by 

 " the four beneath it, is seventy, the number of 

 " times that four different doors may be opened. In 

 " the same manner fifty-six is the number of fives that 

 " can be opened : twenty-eight the numjber of times 

 " that six can be opened : eight the number of times 



