...great difficulties are felt at first and these cannot be overcome except by starting from experiments .. and then be conceiving certain hypotheses ... But even so, very much hard work remains to be done and one needs not only great perspicacity but often a degree of good fortune.

How vast those Orbs must be, and how inconsiderable this Earth, the Theatre upon which all our mighty Designs, all our Navigations, and all our Wars are transacted, is when compared to them. A very fit consideration, and matter of Reflection, for those Kings and Princes who sacrifice the Lives of so many People, only to flatter their Ambition in being Masters of some pitiful corner of this small Spot.

I believe that we do not know anything for certain, but everything probably.

I esteem his understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of his work, where the author studies things of little use or when he builds on the improbable principle of attraction.
Writing about Newton's Principia. Huygens had some time earlier indicated he did not believe the theory of universal gravitation, saying it 'appears to me absurd.'

Mariotte took everything from me, … as can attest those of the Academy, M. du Hamel, M. Gallois, and the registers. [He took] the machine, the experiment on the rebound of glass balls, the experiment of one or more balls pushed together against of line of equal balls, the theorems that I had published. He should have mentioned me. I told him that one day, and he could not respond.

One may conceive light to spread successively, by spherical waves.

The World is my Country, Science my Religion.

We can see that there is only one substance in the universe and that man is the most perfect one. He is to the ape and the cleverest animals what Huygens's planetary clock is to one of Julien Leroy's watches. If it took more instruments, more cogs, more springs to show or tell the time, if it took Vaucanson more artistry to make his flautist than his duck, he would have needed even more to make a speaking machine, which can no longer be considered impossible, particularly at the hands of a new Prometheus. Thus, in the same way, nature needed more artistry and machinery to construct and maintain a machine which could continue for a whole century to tell all the beats of the heart and the mind; for we cannot tell the time from the pulse, it is at least the barometer of heat and liveliness, from which we can judge the nature of the soul.

The Commonwealth of Learning is not at this time without Master-Builders, whose mighty Designs, in advancing the Sciences, will leave lasting Monuments to the Admiration of Posterity; But every one must not hope to be a Boyle, or a Sydenham; and in an Age that produces such Masters, as the Great-Huygenius, and the incomparable Mr. Newton, with some other of that Strain; 'tis Ambition enough to be employed as an Under-Labourer in clearing Ground a little, and removing some of the Rubbish, that lies in the way to Knowledge.

Wij zien daar den wereldburger Christiaan Huygens, den man, die als devies had kunnen voeren “the World is my country, to promote Science my religion.”
We see there the cosmopolitan Christiaan Huygens, the man whose motto could have been “the World is my country, to promote Science my religion."

Most, if not all, of the great ideas of modern mathematics have had their origin in observation. Take, for instance, the arithmetical theory of forms, of which the foundation was laid in the diophantine theorems of Fermat, left without proof by their author, which resisted all efforts of the myriad-minded Euler to reduce to demonstration, and only yielded up their cause of being when turned over in the blow-pipe flame of Gauss’s transcendent genius; or the doctrine of double periodicity, which resulted from the observation of Jacobi of a purely analytical fact of transformation; or Legendre’s law of reciprocity; or Sturm’s theorem about the roots of equations, which, as he informed me with his own lips, stared him in the face in the midst of some mechanical investigations connected (if my memory serves me right) with the motion of compound pendulums; or Huyghen’s method of continued fractions, characterized by Lagrange as one of the principal discoveries of that great mathematician, and to which he appears to have been led by the construction of his Planetary Automaton; or the new algebra, speaking of which one of my predecessors (Mr. Spottiswoode) has said, not without just reason and authority, from this chair, “that it reaches out and indissolubly connects itself each year with fresh branches of mathematics, that the theory of equations has become almost new through it, algebraic geometry transfigured in its light, that the calculus of variations, molecular physics, and mechanics” (he might, if speaking at the present moment, go on to add the theory of elasticity and the development of the integral calculus) “have all felt its influence”.