“Among all the studies of natural causes and reasons Light chiefly delights the beholder; and among the great features of Mathematics the certainty of its demonstrations is what preeminently (tends to) elevate the mind of the investigator. Perspective, therefore, must be preferred to all the discourses and systems of human learning. In this branch [of science] the beam of light is explained on those methods of demonstration which form the glory not so much of Mathematics as of Physics and are graced with the flowers of both.”

— Leonardo Da Vinci

The Notebooks of Leonardo da Vinci (1883), I Prolegomena and General Introduction to the Book on Painting

Adopted from Wikiquote. Last update Sept. 27, 2023. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Among all the studies of natural causes and reasons Light chiefly delights the beholder; and among the great features o…" by Leonardo Da Vinci?

Leonardo Da Vinci 363

Italian Renaissance polymath 1452–1519

Related quotes

“Among all the studies of natural causes and reasons, light most delights the contemplators”

John Peckham (1227–1292) Archbishop of Canterbury

Perspectiva communis, translated by, and appearing in the notebooks (C.A.<sub>543r</sub>) of Leonardo da Vinci, as quoted by Martin Kemp, Leonardo Da Vinci: The Marvellous Works of Nature and Man (2006) p. 112.
Context: Among all the studies of natural causes and reasons, light most delights the contemplators; among the great things of mathematics, the certainty of its demonstrations most illustriously elevates the minds of its investigators; perspective must therefore be preferred to all human discourses and disciplines, in the study in which radiant lines are expounded by means of demonstrations and in which the glory is found not only of mathematics, but also physics: it is adorned with the flowers of one and the other.

“1. We are the contemporaries of a third epoch of science after the Greek and Galilean. The caesura which opens this third epoch is not (a with the Greek) an invention - that of demonstrative mathematics - nor is it (like the Galilean) a break - that which mathematized the discourse of physics. It is a split, through, which the very nature of the base of mathematical rationality reveals itself, as does the character of hte dision of thought which establishes it.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

“The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics.”

Benjamin Peirce Linear Associative Algebra

§ 2.
Linear Associative Algebra (1882)
Context: The branches of mathematics are as various as the sciences to which they belong, and each subject of physical enquiry has its appropriate mathematics. In every form of material manifestation, there is a corresponding form of human thought, so that the human mind is as wide in its range of thought as the physical universe in which it thinks.

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

“In this branch of study exactness is an essential feature; and mathematical difficulties must not be shrunk from when the nature of the subject leads to them.”

William John Macquorn Rankine (1820–1872) civil engineer

p, 125
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)

“A finished or even a competent reasoner is not the work of nature alone… education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided that it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history may be chosen for this purpose. Now, of all these, it is desirable to choose the one… in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not.
.. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:—
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except the self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is attained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if… reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded.
…These are the principal grounds on which… the utility of mathematical studies may be shewn to rest, as a discipline for the reasoning powers. But the habits of mind which these studies have a tendency to form are valuable in the highest degree. The most important of all is the power of concentrating the ideas which a successful study of them increases where it did exist, and creates where it did not. A difficult position or a new method of passing from one proposition to another, arrests all the attention, and forces the united faculties to use their utmost exertions. The habit of mind thus formed soon extends itself to other pursuits, and is beneficially felt in all the business of life.”

Augustus De Morgan (1806–1871) British mathematician, philosopher and university teacher (1806-1871)

Source: On the Study and Difficulties of Mathematics (1831), Ch. I.

“Laplace created a number of new mathematical methods that were subsequently expanded into branches of mathematics, but he never cared for mathematics except as it helped him to study nature.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p. 495

“The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference.”

George Pólya (1887–1985) Hungarian mathematician

Induction and Analogy in Mathematics (1954)

“Our design, not respecting arts, but philosophy, and our subject, not manual, but natural powers, we consider chiefly those things which relate to gravity, levity, elastic force, the resistance of fluids, and the like forces, whether attractive or impulsive; and therefore we offer this work as mathematical principles of philosophy; for all the difficulty of philosophy seems to consist in this — from the phenomena of motions to investigate the forces of nature, and then from these forces to demonstrate the other phenomena…”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface
Philosophiae Naturalis Principia Mathematica (1687)

“Mathematics, from the earliest times to which the history of human reason can reach, has followed, among that wonderful people of the Greeks, the safe way of science. But it must not be supposed that it was as easy for mathematics as for logic, in which reason is concerned with itself alone, to find, or rather to make for itself that royal road. I believe, on the contrary, that there was a long period of tentative work (chiefly still among the Egyptians), and that the change is to be ascribed to a revolution, produced by the happy thought of a single man, whose experiments pointed unmistakably to the path that had to be followed, and opened and traced out for the most distant times the safe way of a science. The history of that intellectual revolution, which was far more important than the passage round the celebrated Cape of Good Hope, and the name of its fortunate author, have not been preserved to us. … A new light flashed on the first man who demonstrated the properties of the isosceles triangle (whether his name was Thales or any other name), for he found that he had not to investigate what he saw hi the figure, or the mere concepts of that figure, and thus to learn its properties; but that he had to produce (by construction) what he had himself, according to concepts a priori, placed into that figure and represented in it, so that, in order to know anything with certainty a priori, he must not attribute to that figure anything beyond what necessarily follows from what he has himself placed into it, in accordance with the concept.”

Immanuel Kant book Critique of Pure Reason

Preface to the Second Edition [Tr. F. Max Müller], (New York, 1900), p. 690; as cited in: Robert Edouard Moritz, Memorabilia mathematica or, The philomath's quotation-book https://openlibrary.org/books/OL14022383M/Memorabilia_mathematica, Published 1914. p. 10
Critique of Pure Reason (1781; 1787)

Help us to complete the source, original and additional information

Leonardo Da Vinci 363

Related quotes

Related topics