It was an England, too, that throbbed with a virile intellectual activity.

throbbed with = full of.

If you describe a man as virile, you mean that he has the qualities that a man is traditionally expected to have, such as strength and sexual power.

Hobbes (1588–1679) had carried out the skeptical spirit of the Renaissance, and the practical spirit of his master, into so complete and outspoken a materialism as would have won him in France the honor of martyrdom for a fallacy.

Hobbes worked for some time as a secretary to Francis Bacon.

If someone suffers martyrdom, they are killed or made to suffer greatly because of their religious or political beliefs.

Collins, Tyndal and other deists were re-affirming their faith in God while calling into question every other doctrine of the established church.

Deism is the belief that there is a God who made the world but does not influence human lives.

“Not long ago,” he writes, “a distinguished company were discussing the trite and frivolous question, who was the greatest man,—Cæsar, Alexander, Tamerlane, or Cromwell? Some one answered that without doubt it was Isaac Newton. And rightly: for it is to him who masters our minds by the force of truth, and not to those who enslave them by violence, that we owe our reverence.”

If you say that something such as an idea, remark, or story is trite, you mean that it is dull and boring because it has been said or told too many times.

If you describe someone as frivolous, you mean they behave in a silly or light-hearted way, rather than being serious and sensible.

… he did not dare to print them, for they praised “perfidious Albion” too highly to suit the taste of the royal censor.  They contrasted English political liberty and intellectual independence with French tyranny and bondage, they condemned the idle aristocracy and the tithe-absorbing clergy of France, with their perpetual recourse to the Bastille as the answer to every question and every doubt; they urged the middle classes to rise to their proper place in the state, as these classes had in England. Without quite knowing or intending it, these letters were the first cock’s crow of the Revolution.

Bondage is the condition of being someone’s property and having to work for them.

A tithe is a fixed amount of money or goods that is given regularly in order to support a church, a priest, or a charity.

For five years Voltaire enjoyed again that Parisian life whose wine flowed in his veins and whose spirit flowed from his pen.

王孝伯言:名士不必须奇才,但使常得无事,痛饮酒,熟读《离骚》,便可称名士。——世说新语·任诞

闻一多先生一边抽烟,一边讲课,常吟曰“痛饮酒,熟读离骚,方为真名士”!

And then some miscreant of a publisher, getting hold of the Letters on the English, turned them without the author’s permission into print, …

A miscreant is someone who has done something illegal or behaved badly.

Like a good philosopher, he took to his heels—merely utilizing the occasion to elope with another man’s wife.

If you take to your heels, you run away.

When two people elope, they go away secretly together to get married.

The Marquise du Chatelet was twenty-eight; Voltaire, alas, was already forty. She was a remarkable woman: she had studied mathematics with the redoubtable Maupertuis, and then with Clairaut; she had written a learnedly annotated translation of Newton’s Principia; she was soon to receive higher rating than Voltaire in a contest for a prize offered by the French Academy for an essay on the physics of fire; in short she was precisely the kind of woman who never elopes.

Émilie du Châtelet

In classical mechanics, Maupertuis’ principle (named after Pierre Louis Maupertuis), is that the path followed by a physical system is the one of least length (with a suitable interpretation of path and length).

Clairaut’s theorem is a general mathematical law giving the surface gravity on a viscous rotating ellipsoid in equilibrium under the action of its gravitational field and centrifugal force.

In the frontispiece to Voltaire’s book on Newton’s philosophy, du Châtelet appears as Voltaire’s muse, reflecting Newton’s heavenly insights down to Voltaire.

and decided that her chateau at Cirey was an admirable refuge from the inclement political weather of Paris.

A château is a large country house or castle in France.

Cirey is a commune in the Haute-Saône department in the region of Bourgogne-Franche-Comté in eastern France.

In France and some other countries, a commune is a town, village, or area which has its own council.

Inclement weather is unpleasantly cold or stormy.

Because of the mariages de convenance which forced rich old men on young women who had little taste for senility but much hunger for romance, the morals of the day permitted a lady to add a lover to her ménage, …

If old people become senile, they become confused, can no longer remember things, and are unable to look after themselves.

In the chateau at Cirey they did not spend their time billing and cooing.

If you bill and coo with someone you love, you talk quietly to them and kiss them.

He was happy to be the centre of this corrupt and brilliant world; he took nothing too seriously, and for a while made “Rire et faire rire” his motto. Catherine of Russia called him “the divinity of gayety.” “If Nature had not made us a little frivolous,” he said, “we should be most wretched. It is because one can be frivolous that the majority do not hang themselves.”   There was nothing of the dyspeptic Carlyle about him. “Dulce est desipere in loco. Woe to philosophers who cannot laugh away their wrinkles. I look upon solemnity as a disease.”

Rire et faire rire (French): Laugh and make laugh.

Dulce est desipere in loco (Latin): Sweet, sometime in place.

Dyspepsia is the same as indigestion.

If you say woe betide/to anyone who does a particular thing, you mean that something unpleasant will happen to them if they do it.

Thomas Carlyle

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