xy

And is not this Medium the same with that Medium by which Light is refracted and reflected and by whose Vibrations Light communicates Heat to Bodies, and is put into Fits of easy Reflexion and easy Transmission? ...And do not hot Bodies communicate their Heat to contiguous cold ones, by the Vibrations of this Medium propagated from them into the cold ones? And is not this Medium exceedingly more rare and subtile than the Air, and exceedingly more elastick and active? And doth it not readily pervade all Bodies? And is it not (by its elastick force) expanded through all the Heavens?
Query 18
Opticks (1704)

“The Ellipse is the most simple of the Conic Sections, most known, and nearest of Kin to a Circle, and easiest describ'd by the Hand in plano.”

Isaac Newton book Arithmetica Universalis

Though many prefer the Parabola before it, for the Simplicity of the Æquation by which it is express'd. But by this Reason the Parabola ought to be preferr'd before the Circle it self, which it never is. Therefore the reasoning from the Simplicity of the Æquation will not hold. The modern Geometers are too fond of the Speculation of Æquations.
Arithmetica Universalis (1707)

“I frame no hypotheses.”
Hypotheses non fingo.

Isaac Newton book Philosophiae Naturalis Principia Mathematica

A famous statement in the "General Scholium" of the third edition, indicating his belief that the law of universal gravitation was a fundamental empirical law, and that he proposed no hypotheses on how gravity could propagate.

Variant: I feign no hypotheses. / As translated by Alexandre Koyré (1956)
Source: Philosophiæ Naturalis Principia Mathematica (1687)
Context: I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.

As translated by I. Bernard Cohen and Anne Whitman (1999)

“Who is a liar, saith John, but he that denyeth that Jesus is the Christ? He is Antichrist that denyeth the Father & the Son. And we are authorized also to call him God: for the name of God is in him.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

Exod. 23.21. And we must believe also that by his incarnation of the Virgin he came in the flesh not in appearance only but really & truly , being in all things made like unto his brethren (Heb. 2 17) for which reason he is called also the son of man. <br class="br">Drafts on the history of the Church (Section 3). Yahuda Ms. 15.3, National Library of Israel, Jerusalem, Israel. 2006 Online Version at Newton Project http://www.newtonproject.sussex.ac.uk/view/texts/normalized/THEM00220

“Abel was righteous & Noah was a preacher of righteousness & by his righteousness he was saved from the flood. Christ is called the righteous & by his righteousness we are saved & except our righteousness exceed the righteousness of the Scribes and Pharisees we shall not enter into the kingdome of heaven. Righteousness is the religion of the kingdom of heaven & even the property of God himself towards man. Righteousness & Love are inseparable for he that loveth another hath fulfilled the law.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

A short Schem of the true Religion

“The Prophecies of Daniel are all of them related to one another, as if they were but several parts of one general Prophecy, given at several times. The first is the easiest to be understood, and every following Prophecy adds something new to the former.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

Vol. I, Ch. 3: Of the vision of the Image composed of four Metals
Observations upon the Prophecies of Daniel, and the Apocalypse of St. John (1733)

“The Vision of the Image composed of four Metals was given first to Nebuchadnezzar, and then to Daniel in a dream: and Daniel began then to be celebrated for revealing of secrets, Ezek. xxviii. 3. The Vision of the four Beasts, and of the Son of man coming in the clouds of heaven, was also given to Daniel in a dream. That of the Ram and the He-Goat appeared to him in the day time, when he was by the bank of the river Ulay; and was explained to him by the prophetic Angel Gabriel. It concerns the Prince of the host, and the Prince of Princes: and now in the first year of Darius the Mede over Babylon, the same prophetic Angel appears to Daniel again, and explains to him what is meant by the Son of man, by the Prince of the host, and the Prince of Princes.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

The Prophecy of the Son of man coming in the clouds of heaven relates to the second coming of Christ; that of the Prince of the host relates to his first coming: and this Prophecy of the Messiah, in explaining them, relates to both comings, and assigns the times thereof.
Vol. I, Ch. 10: Of the Prophecy of the Seventy Weeks
Observations upon the Prophecies of Daniel, and the Apocalypse of St. John (1733)

“The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiæ Naturalis Principia Mathematica (1687)

“I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Definitions - Scholium
Philosophiæ Naturalis Principia Mathematica (1687)

“To every action there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Laws of Motion, III
Philosophiæ Naturalis Principia Mathematica (1687)

“Hypotheses non fingo.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

I frame no hypotheses.

A famous statement in the "General Scholium" of the third edition, indicating his belief that the law of universal gravitation was a fundamental empirical law, and that he proposed no hypotheses on how gravity could propagate.

Variant translation: I feign no hypotheses.

As translated by Alexandre Koyré (1956)

I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.

As translated by I. Bernard Cohen and Anne Whitman (1999)
Philosophiae Naturalis Principia Mathematica (1687)

“The alternation of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Laws of Motion, II
Philosophiae Naturalis Principia Mathematica (1687)

“Through algebra you easily arrive at equations, but always to pass therefrom to the elegant constructions and demonstrations which usually result by means of the method of porisms is not so easy, nor is one's ingenuity and power of invention so greatly exercised and refined in this analysis.”

Isaac Newton (1643–1727) British physicist and mathematician and founder of modern classical physics

The Mathematical Papers of Isaac Newton (edited by Whiteside), Volume 7; Volumes 1691-1695 / pg. 261. http://books.google.com.br/books?id=YDEP1XgmknEC&printsec=frontcover <br class="br">Geometriae (Treatise on Geometry)

“It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses. Yet the thing is not altogether desperate; for we have some arguments to guide us, partly from the apparent motions, which are the differences of the true motions; partly from the forces, which are the causes and effects of the true motions.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Definitions - Scholium
Philosophiae Naturalis Principia Mathematica (1687)