can they all do it together?3—Answer, 2 days.
In what time would a cistern be filled by cocks which would separately fill it in 12, 11, 10, and 9 hours?—Answer, (2⁴⁵⁴/₇₆₃) hours.
- The principal results of this section may be exhibited algebraically as follows; let a, b, c, &c. stand for any whole numbers. Then
| (107) | a | = | 1 | × | a |
|---|---|---|---|---|---|
| b | a | ||||
| (108) | a | = | ma | ||
| b | ma |
| (111) | a | and | c | are the same as | ad | and | bc |
|---|---|---|---|---|---|---|---|
| b | d | bd | bd |
| (112) | a | + | b | = | a + b |
|---|---|---|---|---|---|
| c | c | c | |||
| a | - | b | = | a - b | |
| c | c | c | |||
| (113) | a | + | c | = | ad + bc |
| b | d | bd | |||
| a | - | c | = | ad - bc | |
| b | d | bd | |||
| (118) | a | × | c | = | ac |
| b | d | bd |