
The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.
As quoted in Carl Friedrich Gauss: Titan of Science (1955) by Guy Waldo Dunnington. p. 306
The Notebooks of Leonardo da Vinci (1883), XIX Philosophical Maxims. Morals. Polemics and Speculations.
Source: 19th century, Popular Scientific Lectures [McCormack] (Chicago, 1898), p. 197; On mathematics and counting.
Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)
Richard Courant, What is Mathematics?, (1941) p. xix
General System Theory (1968), 4. Advances in General Systems Theory
“For the things of this world cannot be made known without a knowledge of mathematics.”
Cited in: Opus majus: A translation by Robert Belle Burke. Vol 1 (1962). p. 128
Opus Majus, c. 1267
Context: For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first … gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, … It likewise treats of the size and shape of the habitable earth … All this information is secured by means of instruments suitable for these purposes, and by tables and by canons.. For everything works through innate forces shown by lines, angles and figures.
In the 1661 translation by Thomas Salusbury: … such are the pure Mathematical sciences, to wit, Geometry and Arithmetick: in which Divine Wisdom knows infinite more propositions, because it knows them all; but I believe that the knowledge of those few comprehended by humane understanding, equalleth the divine, as to the certainty objectivè, for that it arriveth to comprehend the necessity thereof, than which there can be no greater certainty." p. 92 (from the Archimedes Project http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?page=92;dir=galil_syste_065_en_1661;step=textonly)
In the original Italian: … tali sono le scienze matematiche pure, cioè la geometria e l’aritmetica, delle quali l’intelletto divino ne sa bene infinite proposizioni di piú, perché le sa tutte, ma di quelle poche intese dall’intelletto umano credo che la cognizione agguagli la divina nella certezza obiettiva, poiché arriva a comprenderne la necessità, sopra la quale non par che possa esser sicurezza maggiore." (from the copy at the Italian Wikisource).
Dialogue Concerning the Two Chief World Systems (1632)
Source: The Reconstruction of Religious Thought in Islam https://www.google.com/books/edition/The_Reconstruction_of_Religious_Thought/uCh14nl09jkC?hl=en (1930), p. 14
“... a sober evaluation of the data suggests the phenomena warrants further scrutiny.”
In reference to UFOs on Young's autobiography on his website, "About This Website" http://kenny.anomalyresponse.org/about.html.