I believe I have fulfilled the duties you required; for first, I have arranged everything in the order most suitable for teaching, and in explaining these matters I have constantly employed the analytical method The analytical method starts from the unknown and works back to known principles, whereas the synthetic method starts from axioms to prove a result., which is rightly preferred by far over synthesis in instruction. Furthermore, I have added not a few entirely new things throughout, by which I have increased and enriched this science of motion original: "de motu scientiam" to the best of my ability. Therefore, I earnestly ask and beseech you to deign to receive this labor of mine—which I trust will be not useless to both teachers and students—with kindness, and I humbly commend myself to your favor and benevolence.

ILLUSTRIOUS

AND

MOST EXCELLENT SIR

Given at St. Petersburg original: "Petropoli"
on the 1st day of August, in the year 1736.

Your most devoted servant,

Leonhard Euler.