# How did Saint Vincent prove the logarithmic property of areas under hyperbolas?

How did Saint Vincent prove that if $\frac{a}{b} = \frac{c}{d}$, then the area of a hyperbola $y = \frac{1}{x}$ from $a$ to $b$ equals the area from $c$ to $d$? What references (pdfs, links, books) are there on this specific subject (ideally are there any english translations of the relevant work of Saint Vincent)?