"The lasting importance of Horologium Oscillatorium stemmed more from its applied mathematics than from its pure mathematics. The next generation of mathematicians spent a great deal of time trying to find curves that satisfied specific physical properties. What other curve, if any, is a tautochrone? What curve does a hanging chain delineate? What shape does a sail take? What is the curve of fastest descent? These were the test cases for the new mathematical technique Leibniz called 'calculus.'"

"Foremost, Huygens gave us precise time. His clocks were the first timekeepers to be accurate enough to be reliable in scientific experiments."

"This [Horologium Oscillatorium] is the first modern treatise in which a physical problem is idealized by a set of parameters then analyzed mathematically. It is one of the seminal works of applied mathematics."

"One of the masterpieces of seventeenth-century scientific literature was... published in 1673 under the title Horologium Oscillatorium (The Pendulum Clock). Much more than a mere description of a clock... it was in fact a treatise on the accelerated motion of a falling body, as exemplified by the bob of a pendulum clock. ...The culminating proposition is Huygen's proof that a body falling along an inverted cycloid reaches the bottom in a fixed amount of time. In other words, the cycloid is isochronous. The third section... introduces his theory of evolutes... that, among other applications, allows one to find the length of a curve. Using evolutes... he proves mathematically that the cycloidal-shaped plates will force the bob of the pendulum to move along the isochronous cycloidal path. The fourth... section... presents his theory of the compound pendulum, in which the motion of a pendulum with mass distributed along its length is compared with that of an ideal simple pendulum... The last part of the book introduces... a variant of a conical clock in which the pendulum, instead of swinging, rotates about a vertical axis... kept on an isochronous path... by the theory of evolutes."

"Huygens stated everything verbally when he was in his "geometric mode" and used [mathematical] symbols... only when he switched to his "algebraic mode." Facile mathematician that he was, he switched back and forth between the two modes as his needs changed within the same problem..."

"Mons. Huygens found out a Method whereby the Ball of a Pendulum may be always carried along the Arch of a Cycloid."