/sci/ - Science & Math

>>15621040
[math] \frac{a}{e} = \frac{b}{f} [/math] implies [math] \frac{a}{e} = \frac{b}{f} = \frac{c}{g} [/math]
let [math] k = \frac{a}{e} = \frac{b}{f}[/math]
[math] \displaystyle
k(e \alpha + f \beta + g) = a \alpha + b \beta + kc = 0 = a \alpha + b \beta + g \\
g = kc \\
\frac{g}{c} = k = \frac{a}{e} = \frac{b}{f}
[/math]