Formula for Volume of a Pyramid or Pyramid Section

To find the volume of a pyramid or pyramid section, the Egyptians used the following algorithm. This method is not perfectly accurate, but it does provide a very good estimate.
1. square top edge
2. square bottom edge
3. multiply top edge by bottom edge
4. add results of 1, 2 and 3
5. find 1/3 of Height
6. multiply results of 4 and 5 together

Formula for area of a circle

The Egyptian method for finding the area of a circle is similar to the one for the volume of a pyramid in the fact that it is not entirly accurate but quite close. The Egyptians applied "close enough" in these two formulas as well as with their fractions. The algorithm is,
1. take 1/9 of diamiter
2. subtract result of 1 from diamiter
3. square the answer

Formula for Multiplication

To Multiply numbers, the Egyptians used the following method,
1. make three columns A, B, and C
2. place one number being multiplied at bottom of A
3. place the other at the top of C
4. put 1 at the top of B
5. double the value of B, repeat this step until B is as large as possible without being greater than A
6. put the new B values in the B column in descending order 7. double the value of C once for every time B is doubled
8. put in the new values in the C column in descending order
9. subtract the largest availible B value from the A value, if this would make A less than zero, cross out the row and move to the next. repeat this step untill all B values have been tested. 10. add up all the C values that have not been crossed out. This is the answer
A B C
cross out 1 5
0 2 10
2 4 20
6 8 40
14 16 80
30

When the remaining C values added the result comes to 150, which is correct.

Formula for Division

The Egyptians used a similar formula for division as they did for multiplication The difference is that the B and C columns are switched as in this example of 30/5, in all other respects the formula is the same.
A B C
cross out 5 1
0 10 2
10 20 4
cross out 40 8
cross out 80 16
30

When the remaining C values added the result comes to 6, which is correct.

Egyptian and modern formulas for slope

The modern formula for slope is rise over run or deltaY/DeltaX. To find slope by the modern method, you take two points, find their x and y values and plug them into the deltaY/deltaX equation as in this example.

point 1 = (1,1) point 2 = (3,2)
3-1 2
--- = -
2-1 1

This gives the answer, the slope is 2.
The Egyptian method is slightly different, they calculated slope as run over rise. Furthermore, they had the run in palms over the rise in cubits. 1 cubit is equal to 7 palms. To convert from modern to egyptian slope you take the reciprical of the modern slope and multiply the numerator by 7 if both numbers are in cubits. This works because the reciprical of rise/run is run/rise which is the egyptian slope. Multiplying the numerator by 7 converts it into palms from cubits.
Example,

2 1 * 7 7
- changes to - = -
1 2 2




This gives you the Egyptian slope from the modern slope, in this case 7 palms over 2 cubits. To turn the Egyptian slope into a modern slope you take the inverse, and devide the denominator by 7. As you can see, this is the reverse of what you do to convert to an Egyptian fraction and so it undoes the conversion turning the Egyptian slope into a modern one.
On to Babylon