Sketch 9

```Laura Farnam
 Techniques developed
wherever math was studied
 Rhind Papyrus
 A quantity; its half and its
third are added to it. It
becomes 10.
 x + (1/2)x + (1/3)x = 10
 False Position
 Double False Position
 Guessing method
 Expect wrong answer
 Make computations easy
 Example 1: A quantity; its fourth is added to it. It
becomes 15.
 Example 1: A quantity; its fourth is added to it. It
becomes 15.
 x + (1/4)x = 15
 4 + (1/4)(4) = 4+1 = 5
 15/5 = 3
 4 x 3 = 12
 Example 2: A quantity; its third and its fifth are added
to it. It becomes 46.
 Example 2: A quantity; its third and its fifth are added
to it. It becomes 46.
 x + (1/3)x + (1/5)x = 46
 15 + 5 + 3 = 23
 46/23 = 2
 15 x 2 = 30
Why Does it Work?
 Ax = B
 Multiply x by a factor
 A(kx) = k(Ax) = kB
 Used in textbooks until
19th century
 Daboll’s Schoolmaster’s
Assistant (early 1800s)
 Guessing method
 Example 3:
A purse of 100 dollars is to be divided among four men
A, B, C, and D, so that B may have four dollars more
than A, and C eight dollars more than B, and D twice
as many as C; what is each one’s share of the money?
Steps
 Guess
 Find error
 Repeat
 Cross-multiply guesses and errors
 Take the difference (if similar) or the sum (if different)
 Divide by the difference/sum of the errors
 y = mx +b
 Plot the line using two
points
 “Rise over Run”
 100 – 70 = 100 – 80
x–6
x-8
 False Position (Ax = B)
 Double False Position (Ax + C = B)
 Linear
 A constant ratio
 “the change in the output is proportional to the change
in the input”
```