proportion is always proportion al

Moon

   

link

Each of the six unit fractions

 is attributed to one of six fractions

Of the image of the eye as drawn

This measure is used for volume 

In units of two

1/2   2/2   3/2/ interior angle/arc

1/4   2/4   3/4  4/4 iris/pupil

1/8   2/8.  3/8  4/8  5/8  6/8 βrow

1/16 2/16 exterior angle/arc

1/32 ocular muscle/wire to power

1/64 tear duct/ground

 line-by-line translation

Example of calculating [the surface area of] a basket [hemisphere].

You are given a hemisphere with 

a mouth representing a radius 

of 4 + 1/2 [in diameter].

What is its surface?

Take 1/9 of of 9 [since]

the basket is half an egg [hemisphere]. You get 1.

Calculate the remainder [when subtracted from 9] which is 8.

Calculate 1/9 of 8.

You get 2/3 + 1/6 + 1/18.

Find the remainder of this 8

After subtracting 2/3 + 1/6 + 1/18. You get 7 + 1/9.

Multiply 7 + 1/9 by 4 + 1/2.

You get 32. Behold this is its surface [area]!

You have found it correctly.

In our notation and method here is what occurred.

Let d be the diameter and S be the surface area.

S = 2d(8/9)(8/9)d =

The problem and its solution can be interpreted as follows: Find the area of a hemisphere (a basket of half an egg] of diameter 4 + 1/2. The surface area of a hemisphere is

 = 256/81 = 3 + 1/9 + 1/27 + 1/81