Newton Writes Against the Trinity

In January 1697, John Bernoulli proposed to the most distinguished mathematicians of Europe 2 problems for solution.

Leibnitz admired the beauty of one of them. He requested the time for solving it to be extended to 12 months—twice the period originally named.

The delay was readily granted.

Newton, however, sent in, the day after he received the problems, a solution of them to the President of the Royal Society.

Bernouilli obtained solutions from Newton, Leibinitz and the Marquis De L’Hopital; but Newton’s though anonymous, he immediately recognised “tanquam ungue leonem” as the lion is known by his claw.

This was the famous problem of the trajectories proposed by Leibnitz, in 1716, for the purpose of “feeling the pulse of the English Analysts.”

Newton received the problem around 5pm as he was returning from the Mint. He solved it before he went to bed.

The Royal Academy of Sciences at Paris in 1699 was empowered by a new charter to admit a few foreign associates.

• Newton was elected a member of it that year.

In 1700, he communicated to Dr. Halley a description, published later in the Philosophical Transactions in 1742, of his reflecting instrument for observing the moon’s distance from the fixed stars.

The instrument was the same as that produced by Mr. Hadley, in 1731, and which, under the name of Hadley’s Quadrant, has been of so great use in navigation.

On the assembling of the new Parliament, in 1701, Newton was re-elected one of the members for the University of Cambridge.

In 1703, he was chosen President of the Royal Society of London, to which office he was annually re-elected till the period of his decease—about 25 years afterward.

Newton took a greater pride in his Optical discoveries.

But he did not publish a connected view of these labours till 1704, when they appeared as “A Treatise on the Reflexions, Refractions, Inflexions and Colours of Light”.

To this were added 2 Mathematical Treatises “Tractatus duo de speciebus et magnitudine figurarum curvilinearum”

1. Tractatus de quadratura curvarum
2. Enumeratio linearum tertii ordinis

He had to publish these because of plagiarisms from his manuscripts he loaned to his friends.

Dr. Samuel Clarke published a Latin translation of the Optics, in 1706; whereupon he was presented by Newton, as a mark of his grateful approbation, with five hundred pounds, or one hundred pounds for each of his children.

The work was afterward translated into French. It had a remarkably wide circulation, and appeared, in several successive editions, both in England and on the Continent.

There is displayed, particularly on this Optical Treatise, the author’s talent for simplifying and communicating the profoundest speculations.

It is a faculty rarely united to that of the highest invention. Newton possessed both; and thus that mental perfectness which enabled him to create, to combine, and to teach, and so render himself, not the “ornament” only, but inconceivably more, the pre-eminent benefactor of his species.

The honour of knighthood was conferred on Newton in 1705.

Soon afterwards, he was a candidate again for the Representation of the University, but was defeated by a large majority.

It is thought that a more pliant man was preferred by both ministers and electors. Newton was always remarkable for simplicity of dress, and his only known departure from it was on this occasion, when he is said to have appeared in a suit of laced clothes.

The Algebraical Lectures which he had, during nine years, delivered at Cambridge, were published by Whiston, in 1707, under the title of Arithmetica Universalis, sine de Compositione et Resolutions Arithmetica Liber. This publication is said to have been a breach of confidence on Whiston’s part.

Mr. Ralphson, not long afterward, translated the work into English; and a second edition of it, with improvements by the author, was issued at London, 1712, by Dr. Machin. Subsequent editions, both in English and Latin, with commentaries, have been published.

In June, 1709, Newton intrusted the superintendence of a second edition of the Principia to Roger Cotes, Plumian Professor of Astronomy at Cambridge. The first edition had been sold off for some time. Copies of the work had become very rare, and could only be obtained at several times their original cost.

A great number of letters passed between the author and Mr. Cotes during the preparation of the edition, which finally appeared in May, 1713. It had many alterations and improvements, and was accompanied by an admirable Preface from the pen of Cotes.

Newton’s early Treatise, entitled, Analysis per Equationes Numero Terminorum Infinitas, as well as a small Tract, bearing the title of Methodus Differentialis, was published, with his consent, in 1711. The former of these, and the Treatise De Quadratura Curvarum, translated into English, with a large commentary, appeared in 1745.

His work, entitled, Artis Analyticæ Specimina, vel Geometria Analytica, was first given to the world in the edition of Dr. Horsley, 1779.