Two of the texts hiding in the prayer book have not appeared in any other copy of Archimedes’s work, so no one but Heiberg had studied them until now. One of them, titled The Method, has special historical significance. It could be considered the earliest known work on calculus. [...]
The Greek philosopher Aristotle built defenses against infinity’s vexing qualities by distinguishing between the “potential infinite” and the “actual infinite.” An infinitely long line would be actually infinite, whereas a line that could always be extended would be potentially infinite. Aristotle argued that the actual infinite didn’t exist.
Archimedes developed rigorous methods of dealing with infinity—still used today—in which he followed Aristotle’s injunction. For example, Archimedes proved that the area of a section of a parabola is four-thirds the area of the triangle inside it (shown in red in the diagram below). To do so, he built a straight-lined figure that’s an approximation of the curvy one. Then he showed that he could make the approximation as close as anyone could ever demand to both the section of the parabola and to four-thirds the area of the triangle.
The writings had been hiding in plain sight, in a palimpsest underneath a book of prayer. One wonders about the monk who scraped the parchment clean. Did he have any idea? Could he have…?
The postulation of a lost age, where human beings had made great advances in science, medicine, and mathematics, has always made for wondrous fiction (especially when the ancients had steampunk spaceships.) This discovery leaves me despairing at the fragility of progress.