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\(a:b=c:d=e:f \)
ধরি, \(\cfrac{a}{b}=\cfrac{c}{d}=\cfrac{e}{f}=k\) (যেখানে, \(k≠0\))
\(∴a=bk,c=dk\) এবং \(e=fk\)

\(∴ \cfrac{5a-7c-13e}{5b-7d-13f}= \cfrac{5bk-7dk-13fk}{5b-7d-13f}= \cfrac{k(5b-7d-13f)}{(5b-7d-13f)}=k\)

\(∴\cfrac{a}{b}=\cfrac{c}{d}=\cfrac{e}{f}=\cfrac{5a-7c-13e}{5b-7d-13f} \) [প্রমানিত]