Page:A History Of Mathematical Notations Vol I (1928).djvu/36

16 24. Explanation: The algebraic equations is $x⁄2$+ $x⁄4$+x=10 i.e., (1+½+¼)x=10

The solution answers the question, By what must (1 ½ ¼) be multiplied to yield the product 10? The four lines 2–5 contain on the right the following computation:

Twice (1 ½ ¼) yields 3½. Four times (1 ½ ¼) yields 7. One-seventh of (1 ½ ¼) is ¼.

[i,ei, taking (1 12 1) once, then fourtimes, togetherwith 10f it,yields only 9; there is lacking 1. The remaining computation is on the four lines 275, on the left. Since Eof (1 5 1,) yields (‘7 1‘, 2‘“) or 9‘, 0r]

(3 2‘3) 0f (1 -‘2 3% yields 32 And the double of this, namely, (g,‘,) of (1 12 1) yields 1, Adding together 1, 4, # and (7,1;71‘4), we Obtain Heap=5ug

% 1‘4 or 5‘13, the answer.