“Grégoire de Saint-Vincent… was a Jesuit, taught mathematics in Rome and Prag (1629-1631), and was afterwards called to Spain by Phillip IV as tutor to his son… He wrote two works on geometry [Principia Matheseos Univerales (1651); Exercitationum Mathematicarum Libri quinque (1657)], giving in one of them the quadrature of the hyperbola referred to its asymptotes, and showing that as the area increased in arithmetic series the abscissas increased in geometric series.”

— David Eugene Smith

p, 125
History of Mathematics (1923) Vol.1

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Grégoire de Saint-Vincent… was a Jesuit, taught mathematics in Rome and Prag (1629-1631), and was afterwards called to …" by David Eugene Smith?

David Eugene Smith 33

American mathematician 1860–1944

Related quotes

“Population, when unchecked, increases in a geometrical ratio, Subsistence, increases only in an arithmetical ratio.”

Thomas Robert Malthus (1766–1834) British political economist

Source: An Essay on The Principle of Population (First Edition 1798, unrevised), Chapter I, paragraph 18, lines 1-2

“No superior can supervise directly the work of more than five or, at the most, six subordinates whose work interlocks. The reason for this is simple. What is supervised is not only the individuals, but the permutations and combinations of the relationships between them. And while the former increase in arithmetical progression with the addition of each fresh subordinate, the latter increase by geometrical progression. If a superior adds a sixth to five immediate subordinates he Increases his opportunity of delegation by 20 per cent, but he adds over 100 per cent to the number of relationships he has to take into account. Because ultimately it is based on the limitations imposed by the human span of attention, this principle is called The Span of Control.”

Lyndall Urwick (1891–1983) British management consultant

Source: 1940s, The Elements of Business Administration, 1943, p. 53

“Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially. Adding a few more members can dramatically increase the value of the network.”

Kevin Kelly (1952) American author and editor

Out of Control: The New Biology of Machines, Social Systems and the Economic World (1995), New Rules for the New Economy: 10 Radical Strategies for a Connected World (1999)

“Of the contemporaries of Newton one of the most prominent was John Wallis. …Wallis was a voluminous writer, and not only are his writings erudite, but they show a genius in mathematics… He was one of the first to recognize the significance of the generalization of exponents to include negative and fractional as well as positive and integral numbers. He recognized also the importance of Cavalieri's method of indivisibles, and employed it in the quadrature of such curves as y=xn, y=x1/n, and y=x0 + x1 + x2 +… He failed in his attempts at the approximate quadrature of the circle by means of series because he was not in possession of the general form of the binomial theorem. He reached the result, however, by another method. He also obtained the equivalent of ds = \! dx \sqrt{1+(\frac{dy}{dx})^2} for the length of an element of a curve, thus connecting the problem of rectification with that of quadrature.”

David Eugene Smith (1860–1944) American mathematician

History of Mathematics (1923) Vol.1

“The term `geometry'...refers to a pattern of processing within our brains related to our spatial and visual senses, more than it refers to a separate content area of mathematics.”

William Thurston (1946–2012) mathematician

Foreword to Teichmüller Theory

“When… we have a series of values of a quantity which continually diminish, and in such a way, that name any quantity we may, however small, all the values, after a certain value, are severally less than that quantity, then the symbol by which the values are denoted is said to diminish without limit. And if the series of values increase in succession, so that name any quantity we may, however great, all after a certain point will be greater, then the series is said to increase without limit. It is also frequently said, when a quantity diminishes without limit, that it has nothing, zero or 0, for its limit: and that when it increases without limit it has infinity or ∞ or 1⁄0 for its limit.”

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

Introductory Chapter, pp.9-10
The Differential and Integral Calculus (1836)

“After Pythagoras, Anaxagoras the Clazomenian succeeded, who undertook many things pertaining to geometry. And Oenopides the Chian, was somewhat junior to Anaxagoras, and whom Plato mentions in his Rivals, as one who obtained mathematical glory. To these succeeded Hippocrates, the Chian, who invented the quadrature of the lunula, and Theodorus the Cyrenean, both of them eminent in geometrical knowledge. For the first of these, Hippocrates composed geometrical elements: but Plato, who was posterior to these, caused as well geometry itself, as the other mathematical disciplines, to receive a remarkable addition, on account of the great study he bestowed in their investigation. This he himself manifests, and his books, replete with mathematical discourses, evince: to which we may add, that he every where excites whatever in them is wonderful, and extends to philosophy. But in his time also lived Leodamas the Thasian, Architas the Tarentine, and Theætetus the Athenian; by whom theorems were increased, and advanced to a more skilful constitution. But Neoclides was junior to Leodamas, and his disciple was Leon; who added many things to those thought of by former geometricians. So that Leon also constructed elements more accurate, both on account of their multitude, and on account of the use which they exhibit: and besides this, he discovered a method of determining when a problem, whose investigation is sought for, is possible, and when it is impossible.”

Proclus (412–485) Greek philosopher

Source: The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 1 (1788), Ch. IV.

“The ancients considered mechanics in a twofold respect; as rational, which proceeds accurately by demonstration, and practical. To practical mechanics all the manual arts belong, from which mechanics took its name. But as artificers do not work with perfect accuracy, it comes to pass that mechanics is so distinguished from geometry, that what is perfectly accurate is called geometrical; what is less so is called mechanical. But the errors are not in the art, but in the artificers. He that works with less accuracy is an imperfect mechanic: and if any could work with perfect accuracy, he would be the most perfect mechanic of all; for the description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn; for it requires that the learner should first be taught to describe these accurately, before he enters upon geometry; then it shows how by these operations problems may be solved.”

Isaac Newton book Philosophiae Naturalis Principia Mathematica

Preface (8 May 1686)
Philosophiæ Naturalis Principia Mathematica (1687)

“In 1673 he wrote his great work De Algebra Tractatus; Historicus & Practicus, of which an English edition appeared in 1685. In this there is seen the first serious attempt in England to write on the history of mathematics, and the result shows a wide range of reading of classical literature of the science.”

David Eugene Smith (1860–1944) American mathematician

This work is also noteworthy because it contains the first of an effort to represent the imaginary number graphically by the method now used. The effort stopped short of success but was an ingenious beginning.
History of Mathematics (1923) Vol.1

“[my goal is] to photograph not a factory but the work itself from the most effective point of view.... in order to show the grandness of a machine, one should photograph not all of it but give a series of snapshots.”

Alexander Rodchenko (1891–1956) Russian artist and photographer

Quote, 1930: from Rodchenko lecture at the October group's meeting; as quoted by Margarita Tupitsyn in Chapter 'Fragmentation versus Totality: The Politics of (De)framing', in The great Utopia - The Russian and Soviet Avant-Garde, 1915-1932; Guggenheim Museum, New York, 1992, p. 486
the issue was not to take 'photo pictures' of the entire object but to make 'photo stills' of characteristic parts of an object

Help us to complete the source, original and additional information

David Eugene Smith 33

Related quotes

Related topics