II. 1) The Ratio between

the Numbers

 
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by dr. fazli arslan
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start: 09 january 2007, up-date: 09 january 2007
According to Safi al-Dîn there is always a ratio between two numbers. He arranged them as 12 parts. Firstly, two numbers are equal to each other. (The position of equality) If there is no equality between the numbers, there is one of the ratios below.
 
Mithl and cuz': First level 1+1/2 (3/2), then going on forever like 1+1/3 (4/3), 1+1/4 (5/4).. This super particular is the ratio of (1+1/N).
Mithl and aczâ: the first level of this goes on like 1+2/3 (5/3), 1+3/4 (7/4), 1+4/5 (9/5)…
Di'f and cuz': starts with 2+1/2 (5/2) and goes on like 2+1/3 (7/3), 2+1/4 (9/4) …
Di'f and aczâ: starts with 2+2/3 (8/3) and goes on like 2+3/4 (11/4), 2+4/5 (14/5) …
Amthal: First level is 3 and then goes on like 5, 6, 7, 9 …
Amthal and cuz': First level goes on like 3+1/2 (7/2), 3+1/3 (10/3), 3+1/4 (13/4) …
Amthal and aczâ: First level goes on like 3+2/3 (11/3). 3+3/4 (15/4) ….
Ada'f : First level is 4, then goes on like 8, 16. In order to keep the word short Safi al-Dîn says "cuz' and aczâ are added like this and goes on forever". That is to say, ada'f and cuz' starts with 4+1/2 (9/2), 4+1/3 (13/3), and ada'f and aczâ with 4+2/3 (14/3) then goes on like 4+3/4 (19/4) ….
Then he showed all the ratios between the two numbers on a thread divided into 12 equal parts in order to make us see all the ratios practically.
 
img0000000626

Let us have a loo k at the ratios between numbers on this figure.

 
YB/Y=6/5, YB/T=4/3, YB/H=3/2, YB/Z=12/7, YB/V=2, YB/h=12/5, YB/D=3, YB/C=4, YB/B=6, Then, YA/Y=11/10, YA/T=11/9, YA/H=11/8, YA/Z=11/7, YA/V=11/6, YA/h=11/5, YA/D=11/4, YA/C=11/3, YA/B=11/2, Then, Y/T=10/9, Y/H=5/4, Y/Z=10/7, Y/V=5/3, Y/h=2, Y/D=5/2, Y/C=10/3, Y/B=5, Then, T/H=9/8, T/Z=9/7, T/V=3/2, T/h=9/5, T/D=9/4, T/C=3, T/B=9/2, Then, H/Z=8/7, H/V=4/3, H/h=8/5, H/D=2, H/C=8/3, H/B=4, Then, Z/V=7/6, Z/h=7/5, Z/D=7/4, Z/C=7/3, Z/B=7/2, Then, V/h=6/5, V/D=3/2, V/C=2, V/B=3, Then, h/D=5/4, h/C=5/3, h/B=5/2, Then, D/C=4/3, D/B=2, D/A=4, Then, C/B=3/2, C/A=3, Then, B/A=2 (3)