Theorem on Equal Ratios
Nihar Mahajan
contributed
If \(\dfrac{a_1}{b_1}=\dfrac{a_2}{b_2}=\dfrac{a_3}{b_3}=\dots =\dfrac{a_n}{b_n}\) then, each ratio equals \(\dfrac{m_1a_1+m_2a_2+m_3a_3+\dots + m_na_n}{m_1b_1+m_2b_2+m_3b_3+\dots + m_nb_n}\) for some constants \(m_i\) .
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Theorem on Equal Ratios.
Brilliant.org.
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