Nicomachus defined a “fifth proportion” to exist whenever among three terms

nicomachus defined a "fifth Proportion" to exist whenever among three terms the middle term is to the lesser as the diffrence is to the difference between the greater and the mean (2,4,5) plus give two otehr samples.....WRITE UP IS NOT PROPER SEE BELOW FOR CORRECT PROPOSITION ........

IN GENERAL LET THE NUMBERS BE [P,Q,R].....IN INCREASING ORDER

MIDDLE TERM = Q =4

LESSER TERM = P=2

RATIO OF MIDDLE TO LEAST = Q/P = 4 / 2 = 2 ...........................1. .................

DIFFERENCE BETWEEN MIDDLE AND LEAST = Q-P=4-2=2..............................................2...................

GREATER = R=5

DIFFERENCE NETWEEN GREATEST AND MIDDLE = R-Q=5-4=1.............................3......

RATIO OF THE ABOVE DIFFERENCES ......[Q-P] / [R-Q] = 2 /1 = 2 .......................4

THE 2 RATIOS 1 AND 4 SHALL BE EQUAL ..... THAT IS AS WE GOT ABOVE....

Q / P = [Q-P] / [ R-Q] = 2 = 2 ...OK......

SO TO GET OTHER NUMBERS NOW ........USING THE ABOVE FORMULA ....

[4,8,10]............................. ..[6,12,15].....[8,16,20]...ETC