William Trail on Pappus of Alexandria

“Snellius, Vieta, Marinus, Ghetaldus, and Fermat, attempted, from the description of the τόωος άναλυομἐνος in the seventh book, to restore several of the lost books of Apollonius, which made a principal part of that collection. Afterwards Schooten, Dr. Wallis, and subsequently Dr. Halley, pursued the same track; and thus a number of these ancient treatises were restored, with various success indeed, and with different characters of elegance and accuracy...”

“From the defective mode of notation among the Greeks... though there be much ingenuity in some of their methods, we need not be surprised at the great inferiority of their system. Dr. Wallis remarks, that the business of the second book of Pappus appears to be nearly equivalent to what is now considered as a very simple proposition, viz. that the multiplication of any numbers... The first book he with much probability conjectures to have been employed about the simple operations of the addition and subtraction of numbers.”

“The superior lines treated of by Pappus, and other ancient writers, were the conchoid, the cissoid, the spiral, and the quadratrix; and a few others are slightly alluded to.”