Isaac Newton in the context of "Old Style and New Style dates"

The Age of Enlightenment (also the Age of Reason) was a period in the history of Europe and Western civilization during which the Enlightenment, an intellectual and cultural movement, flourished, emerging in the late 17th century in Western Europe and reaching its peak in the 18th century, as its ideas spread more widely across Europe and into the European colonies, in the Americas and Oceania. Characterized by an emphasis on reason, empirical evidence, and scientific method, the Enlightenment promoted ideals of individual liberty, religious tolerance, progress, and natural rights. Its thinkers advocated for constitutional government, the separation of church and state, and the application of rational principles to social and political reform.

The Enlightenment emerged from and built upon the Scientific Revolution of the 16th and 17th centuries, which had established new methods of empirical inquiry through the work of figures such as Galileo Galilei, Johannes Kepler, Francis Bacon, Pierre Gassendi, Christiaan Huygens and Isaac Newton. Philosophical foundations were laid by thinkers including René Descartes, Thomas Hobbes, Baruch Spinoza, and John Locke, whose ideas about reason, natural rights, and empirical knowledge became central to Enlightenment thought. The dating of the period of the beginning of the Enlightenment can be attributed to the publication of Descartes' Discourse on the Method in 1637, with his method of systematically disbelieving everything unless there was a well-founded reason for accepting it, and featuring his dictum, Cogito, ergo sum ('I think, therefore I am'). Others cite the publication of Newton's Principia Mathematica (1687) as the culmination of the Scientific Revolution and the beginning of the Enlightenment. European historians traditionally dated its beginning with the death of Louis XIV of France in 1715 and its end with the outbreak of the French Revolution in 1789. Many historians now date the end of the Enlightenment as the start of the 19th century, with the latest proposed year being the death of Immanuel Kant in 1804.

Natural philosophy or philosophy of nature (from Latin philosophia naturalis) is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the development of modern science.

From the ancient world (at least since Aristotle) until the 19th century, natural philosophy was the common term for the study of physics (nature), a broad term that included botany, zoology, anthropology, and chemistry as well as what is now called physics. It was in the 19th century that the concept of science received its modern shape, with different subjects within science emerging, such as astronomy, biology, and physics. Institutions and communities devoted to science were founded. Isaac Newton's book Philosophiæ Naturalis Principia Mathematica (1687) (English: Mathematical Principles of Natural Philosophy) reflects the use of the term natural philosophy in the 17th century. Even in the 19th century, the work that helped define much of modern physics bore the title Treatise on Natural Philosophy (1867).

Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. The earliest documented mention of the concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers. In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference. This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages, displacing earlier beliefs in a flat Earth. A practical demonstration of Earth's sphericity was achieved by Ferdinand Magellan and Juan Sebastián Elcano's circumnavigation (1519–1522).

The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia. In the early 19th century, the flattening of the earth ellipsoid was determined to be of the order of 1/300 (Delambre, Everest). The modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25. The scientific study of the shape of the Earth is known as geodesy.

Latin literature includes the essays, histories, poems, plays, and other writings written in the Latin language. The beginning of formal Latin literature dates to 240 BC, when the first stage play in Latin was performed in Rome. Latin literature flourished for the next six centuries. The classical era of Latin literature can be roughly divided into several periods: early Latin literature, the golden age, the imperial period and Late Antiquity.

Latin was the language of the ancient Romans as well as being the lingua franca of Western and Central Europe throughout the Middle Ages. Latin literature features the work of Roman authors, such as Cicero, Virgil, Ovid and Horace, but also includes the work of European writers after the fall of the Empire, from religious writers like Aquinas (1225–1274) to secular writers like Francis Bacon (1561–1626), Baruch Spinoza (1632–1677), and Isaac Newton (1642–1727).

Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz, US also /ˈhɔɪɡənz/ HOY-gənz; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.

Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.

In physics, motion is when an object changes its position with respect to a reference point in a given time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed, and frame of reference to an observer, measuring the change in position of the body relative to that frame with a change in time. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics.

If an object is not in motion relative to a given frame of reference, it is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there is no absolute frame of reference, Isaac Newton's concept of absolute motion cannot be determined. Everything in the universe can be considered to be in motion.

Gottfried Wilhelm Leibniz (or Leibnitz; 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labour. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.

Leibniz contributed to the field of library science, developing a cataloguing system (at the Herzog August Library in Wolfenbüttel, Germany) that came to serve as a model for many of Europe's largest libraries. His contributions to a wide range of subjects were scattered in various learned journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.

A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning into Moral Subjects (1739–40) is a book by Scottish philosopher David Hume, considered by many to be Hume's most important work and one of the most influential works in the history of philosophy. The book has appeared in many editions since the death of the author in 1776.

The Treatise is a classic statement of philosophical empiricism, scepticism, and naturalism. In the introduction Hume presents the idea of placing all science and philosophy on a novel foundation: namely, an empirical investigation into human nature. Impressed by Isaac Newton's achievements in the physical sciences, Hume sought to introduce the same experimental method of reasoning into the study of human psychology, with the aim of discovering the "extent and force of human understanding". Against the philosophical rationalists, Hume argues that the passions, rather than reason, cause human behaviour. He introduces the famous problem of induction, arguing that inductive reasoning and our beliefs regarding cause and effect cannot be justified by reason; instead, our faith in induction and causation is caused by mental habit and custom. Hume defends a sentimentalist account of morality, arguing that ethics is based on sentiment and the passions rather than reason, and famously declaring that "reason is, and ought only to be the slave to the passions." Hume also offers a sceptical theory of personal identity and a compatibilist account of free will.

A treatise is a formal and systematic written discourse on some subjects concerned with investigating or exposing the main principles of the subject and its conclusions. A monograph is a treatise on a specialized topic.