# Johann Heinrich Lambert

Johann Heinrich Lambert (26 August 1728 – 25 September 1777) was a Swiss polymath who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.

## Quotes

* If in two ellipses having a common major axis we take two such arcs that their chords are equal, and that also the sums of the radii vectores, drawn respectively from the foci to the extremities of these arcs, are equal to each other, then the sectors formed in each ellipse by the arc and the two radii vectores are to each other as the square roots of the parameters of the ellipses.
** Sect. 4, Lemma 26, Insigniores orbitae cometarum proprietates (1761) [Notable properties of comets' orbits] translated by Florian Cajori, A History of Mathematics (1906) p. 259, from the German of Michel Chasles, Geschichte der Geometrie, haupsächlich mit Bezug auf die neuern Methoden (1839) p. 183.

### The System of the World (1800)

    Tr. James Jaque, source (1800)
* We would wish to discover the Plan of the Universe, and the means employed by the Eternal Architect in the execution of his magnificent design. We will first contemplate the System of which we make a part, and of which our Sun is the center. Thence we will ascend towards those Suns and those innumerable Worlds which are scattered through the immensity of space.
* But, are the faculties of our nature equal to this? and what are the principles which ought to guide us in these researches?
* We suppose the existence of a wise and beneficent Being who presided over the formation of the World, and who is pleased to display his infinite perfections on this illustrious theatre.
* We will found our hypothesis in the general laws of motion, whose effects are every where the same, and whose influence extends to the utmost limits of matter.
* We will next proceed by the lamp of experience, consulting with care the observations deposited in the records of astronomy.
* In order to supply the defects of experience, we will have recourse to the probable conjectures of analogy, conclusions which we will bequeath to our posterity to be ascertained by new observations, which, if we augur rightly, will serve to establish our theory and to carry it gradually nearer to absolute certainty.
* This is all to which weak and limited beings can pretend, beings who occupy a point, and last but a moment in this mighty edifice built for eternity.

## Quotes about Lambert

* The famous Lambert, another Leibnitz, because of the universality and thoroughness of his knowledge, deserves a place among those mathematicians who had preserved a knowledge and taste for geometry at a time when the wonders of analysis concerned all, and who made the most glorious applications of it.
** Michel Chasles, Geschichte der Geometrie, haupsächlich mit Bezug auf die neuern Methoden (1839) p. 182.
* Lambert was an 18th century Alsatian scholar, who is today regarded as a physicist, geometer, statistician, astronomer and philosopher and a representative of German rationalism. ...Among the achievements of Lambert... are the discovery of luminous intensity; the formulation of laws governing light absorption, and thereby the establishment of photometry; the formulation of a law of motion of comets or planets. He is among the first to appreciate the nature of the Milky Way; he established several theorems of non-Euclidean geometry, developed De Moivre's theorems on the trigonometry of complex variables and introduced the hyperbolic sine and cosine functions. He proved the irrationality of π and π$^2$, created a general theory of errors and finally, was the first to express Newton's second law of motion in the notation of the differential calculus.
** Maria Georgiadou, Constantin Carathéodory: Mathematics and Politics in Turbulent Times (2013)
* Mathematicians are usually regarded as clear and sober thinkers, but some of the men who have been gifted with the most marvelous power of mathematical analysis have not been free from the defects and vagaries of common mortals. Newton was extremely irritable, Laplace was inordinately vain, Monge, the inventor of descriptive geometry, was very forgetful and absent-minded. These men, however, were not fanciful dreamers, and few such are found among great mathematicians. One of these few was Johann Heinrich Lambert, the first man who endeavored to construct a system of the universe.
** Otto Hoffman, "The System of the Universe," (May 14, 1910) Scientific American: Supplement, Vol. 69, pp. 316-318.

### Encomium of Mr. Lambert (1800)

    James Jaque, in The System of the World by Johann Heinrich Lambert (1800) Tr. James Jaque
* His mother, in order to prevent his reading when he ought to be asleep, denied him the use of a light. Young Lambert had been at much pains in learning to write a fine hand, which was afterwards of great use to him: he wrote and drew extremely well; he made little designs or drawings, which he sold to his companions for a farthing or a halfpenny according as they contained more or fewer figures; and from this money he supplied himself with candles, which he lighted the moment all those of the family were put out.
* The pupils of Mr. Lambert were the grandsons of the Count and sons of the Podestate of Coire. It was now in instructing his charge, that Mr. Lambert found all those means of instructing himself of which he had hitherto been so much in want. Becoming more and more conscious of the strength of his natural powers, he embraced, without hesitation, physics, astronomy, mathematics, mechanics, nor did he deem himself unequal to the studies of theology, metaphisics, eloquence, and poetry. He composed verses in all the languages he understood, German, French, Latin, Italian; but he would not dare to attempt the versification of the Greeks.
* Having one day read that Paschal invented a certain arithmetical machine, by a mere effort of his own genius, he could take no rest till he invented one of the same description. He likewise constructed with his own hand a mercurial watch or pendulum, which kept going 27 minutes, and served to ascertain precise portions of time in his physical experiments. His arithmetical scales and a machine for facilitating the art of drawing in perspective are no less worthy of our notice.
* The tutor and his pupils repaired to Utretcht, and passed a year in Holland; where Mr. Lambert gave to a bookseller of the Hague his treatise on the Passage of Light. But in the over ardent pursuit of this object, he found himself in the situation of the astrologer, who fell into a well... In consequence of a habit equally whimsical and invariable in him, he never presented himself but sideways, changed his position as often as the person with him sought to place himself in front, and he retreated in proportion as the other advanced. It was in a situation of this kind, that, making some steps backwards without attending to a stair case which was directly behind him, he fell at once from top to bottom, heels over head. The fall was dreadful; he lay long in a state of absolute insensibility, nor did he return to his senses till the end of twenty-four hours, when he opened his eyes totally black with extravasated blood...
* In the month of Sept. 1759, Mr. Lambert was at Ausburg... for the purpose of giving the last touch to his Photometry, and to have it printed under his own eye. At the same period was instituted the Electoral Academy of Sciences at Munich... they... expressed their desire to have him more particularly attached to them by engaging him to furnish them literary papers, and to assist them with his advice. As a remuneration of his services, he received the title of Honorary Professor, and a pension of 800 florins. ...This connection, however, was of short duration. They accused him of not having the interest of the learned academy sufficiently at heart; and he complained... that they neglected his advice, and were at no pains to reform the abuses which he pointed out to them. They withdrew his pension, and he would not condescend to take any step for its recovery. Mr. Lambert was too much occupied with the abstract principles of science to give his thoughts to things so material; and yet, he was by no means in easy circumstances. He was satisfied if the profit of his works would enable him to lead the life of a philosopher from one publication to another...
* The works of Mr. Lambert... have been duly appreciated by competent judges, who, by bestowing on them a distinguished reputation, have unalterably fixed the high rank the author has... held in the republic of letters. In the year 1760, he collected the different pieces, still in a fugitive state, of his Novum Organum [Neues Organon]; but which was not published till the year 1764. In the year 1761, he published his Treatise on the Properties of the Orbits of Comets, printed at Ausburg.
* The torrent of his ideas, which flowed incessantly and rapidly from his brain, ever brought along with it useful materials for the construction of the system of the world. In these consisted his wealth; and no man could say, with more truth than himself, that all he was worth he carried about with him.
* The reputation of his works is established, and posterity will confirm the decision of the present age.
* The history of Mr. Lambert's intellect during the space of 25 years, the progress of his genius, his rapid advancement in knowledge, and the series of his operations... he noted with equal truth and simplicity, in a sort of journal which is continued from the month of January, 1752, to the month of May, 1777. Such are those fugitive leaves more precious than the leaves of the Sybil. Never were there any which better merited to be preserved; and I request of the academy that they may be printed and annexed to my Eloge, on which they will bestow life and value.
* Mr. Lambert was a man with whom the eye and the ear found it extremely difficult to become familiar.
* Mean and singular in his dress, he presented himself in a very awkward manner; a stranger to the received usages of society, or careless of conforming to them, he seemed to be occupied with nothing but himself; his philosophic volubility of tongue was unceasing till be found himself alone; and, even then I have seen him, after broaching a subject with some person who was called away, go on and finish it as if he had been speaking all the while to an attentive hearer. Add to this that flashes of self-love, and expressions of the high idea he entertained of his own merit...
* Giving himself no manner of uneasiness as to what others might think of him, nor caring either to please or displease, he was uniformly without disguise; and, as he shewed himself on all occasions in the same colours, he at last subdued the prejudice, and forced the admiration of others to identify itself with his own.
* We came finally to regard him... as an ingot of pure gold, whose value could not be enhanced by the fashion of the artist.
* Frederick, let into the singularity of the man... would not deprive his Academy of a member from whom so much was to be expected. He was therefore admitted with a pension, and pronounced his inaugural oration in the month of January, 1765. Since that period, his Majesty honoured him with frequent and distinguished marks of his esteem; placed him in the financial commission of the Academy, and the architectural department, with the title of Superior Counsellor, at the same time making a considerable addition to his appointment. During these twelve years... Mr. Lambert, in his proper element, devoted his incessant labours to the improvement of science and the public good. He published some excellent performances, and furnished tracks without number, which have been inserted in the Memoires of the Academy, the Astronomical Tables of Berlin, and other collections. All his writings are highly expressive of a universal and original genius.
* He possessed great powers of invention... Not possessing himself, and being in no condition to obtain the instruments necessary for making observations, or a single machine for the purposes of experimental philosophy, he contrived to supply that deficiency by making them of the most common materials that fell in his way; and the dexterity he came to employ in the management of them made amends for the imperfection of their construction.
* Mr. Lambert was a stranger to the three kingdoms of nature (He was however tolerably conversant in chemistry; he made various experiments on salts... the subject of different papers... in the academy.): he had never given his attention to individuals, nor to facts in that arrangement. All his points of view centered in the starry vault, in a straight line before him, and in the chamber of his brain, where he was continually immured, even when you thought you were with him, and fixed, or at least divided his attention. No divergency in him either to the right or to the left, always in the region of abstractions, objects in the order, of what are called concretes scarcely grazed his sphere.
* He was almost destitute of taste... in spite of his partiality for the muses, he was ever ready to ask as to subjects of taste, What does it prove? ...I was no stranger to his pretensions to wit ...Great men would drive their inferiors to despair if they paid no tribute to humanity.
* Mr. Lambert was upright in every sense of the word. Rectitude of views, rectitude of intentions, rectitude of action. I will not be accused of attributing to him impeccability, more than infallibility. But... Optimism was unquestionably a proper attribute of the deceased.
* Fontenelle, as he concludes his Eloge of Ozanam, informs us, that it used to be a saying of this academician, that it is the prerogative of the mathematician to go to Paradise in a perpendicular line. This, I have no doubt, was Mr. Lambert's route upon quitting the earth; nor had he occasion for a chariot of fire to carry him to heaven, a single ray of light would afford him a vehicle.
* In proportion as his intellectual pursuits were various and complex... the plan of his life was simple and uniform.
* Until late in life he had no access to what is called the great or fine world; but feeling in himself more real beauty and grandeur than he found in those whom he met usually in fashionable circles, he assigned a place to himself, from which it would not have been an easy matter to dislodge him. Such is the effect of the most precious of prerogatives mens conscia recti (A mind conscious of its own rectitude).
* He had religion, and even devotion... he was still more a Christian than a philosopher, and... all the erroneous flights of a certain false philosophy were utterly unknown to him. He was too great a man to condescend to its acquaintance. His journal takes notice in the month of January 1755, of a composition intituled Oratio de characteribus Christian, ejusque præstantia Præ Philosopho [Prayer of Christian character, and his excellence prior to the Philosopher]. His whole life has been a commentary on this text, and an incontestible proof of it.
* Lambert is dead, and ye live ignorant mortals; ye live enemies of knowledge; ye live an useless burden on the earth, born to consume its good things without the capacity to produce one.
* When I turn my eyes to the place where we were accustomed to see our illustrious colleague, and where we saw him with so much pleasure, and where we used to hear him speak as if he had been inspired, I say to myself, certainly without the smallest intention to detract from the merit of any man: that place, is it filled? or, rather, shall it ever be filled again?

## See also

* History of mathematics
* History of science

## External links

* Johann Heinrich Lambert (1728-1777): Collected Works - Sämtliche Werke Online
* "Johann Heinrich Lambert", at the MacTutor History of Mathematics archive