If in two ellipses having a common major axis we take two such arcs th — Johann Heinrich Lambert

"The tutor and his pupils repaired to Utretcht, and passed a year in Holland; where Mr. Lambert gave to a bookseller of 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..."

"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."

"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."

"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."

"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 ... 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..."

"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."