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To get the ratio p : q (for p is not equal to q) one has to add a number to each term of the ratio x : y, then the number is: |
\(\frac{px+qy}{p-q}\) \(\frac{qx-py}{p-q}\) \(\frac{px-qy}{p-q}\) \(\frac{px+qx}{p-q}\) |
\(\frac{qx-py}{p-q}\) |
\(\frac{x + r}{y + r}\) = \(\frac{p}{q}\) ⇒ q(x + r) = p(y +r) ⇒ qx + qr = py + pr ⇒ qr - pr = py - qx ⇒ r(q - p) = py - qx ⇒ r = \(\frac{py - qx}{q - p}\) |
