“As a Line, I say, is looked upon to be the Trace of a Point moving forward, being in some sort divisible by a Point, and may be divided by Motion one Way, viz. as to Length; so Time may be conceiv'd as the Trace of a Moment continually flowing, having some Kind of Divisibility from an Instant, and from a successive Flux, inasmuch as it can be divided some how or other. And like as the Quantity of a Line consists of but one Length following the Motion; so the Quantity of Time pursues but one Succession stretched out as it were in Length, which the Length of the Space moved over shews and determines. We therefore shall always express Time by a right Line; first, indeed, taken or laid down at Pleasure, but whose Parts will exactly answer to the proportionable Parts of Time, as its Points do to the respective Instants of Time, and will aptly serve to represent them. Thus much for Time.”

p, 125
Geometrical Lectures (1735)

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 "As a Line, I say, is looked upon to be the Trace of a Point moving forward, being in some sort divisible by a Point, an…" by Isaac Barrow?

Isaac Barrow20

English Christian theologian, and mathematician 1630–1677

Proclus (412–485) Greek philosopher

Book III. Concerning Petitions and Axioms.
The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements Vol. 2 (1789)

“Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. There-fore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section III On The Principles Of The Form Of The Sensible World

“As Magnitudes themselves are absolute Quantums Independent on all Kinds of Measure, tho' indeed we cannot tell what their Quantify is, unless we measure them; so Time is likewise a Quantum in itself, tho' in Order to find the Quantity of it, we are obliged to call in Motion to our Assistance as a Measure… and thus Time as measurable signifies Motion; for if all Things were to continue at Rest, it would be impossible to find out by any Method whatsoever how much Time has elaps'd; and the several Ages wou'd roll on imperceptibly and undistinguish'd. Do I say we shou'd not perceive how Time flows? No indeed, nor any Thing else, but remain like Stocks or Stones in a continual Insensibility. We perceive nothing, unless so far as we may be instigated by some Change affecting the Senses, or that our Souls are mov'd and excited by the internal Operation of the Mind. We esteem the Quantities and different Degrees of Things according to the Extension or Intension of Motions striking upon us either interiorly or exteriorly. So that the Quantity of Time so far as we can observe; depends upon the Extension of Motion.”

Isaac Barrow (1630–1677) English Christian theologian, and mathematician

p, 125
Geometrical Lectures (1735)

“Momentum may be roughly described as quantity motion. A body moving at a speed of say twenty an hour, has a certain quantity of motion. If the body goes forty miles an hour there is twice as motion; or if twice as much matter goes twenty miles hour, there is also twice as much motion. Momentum is measured by the quantity of matter moving at a rate mass \times velocity.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

"Energy and Force" (Mar 28, 1873)

“Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought.”

Isaac Newton book Arithmetica Universalis

Arithmetica Universalis (1707)
Context: Whereas in Arithmetick Questions are only resolv'd by proceeding from given Quantities to the Quantities sought, Algebra proceeds in a retrograde Order, from the Quantities sought as if they were given, to the Quantities given as if they were sought, to the End that we may some Way or other come to a Conclusion or Æquation, from which one may bring out the Quantity sought. And after this Way the most difficult problems are resolv'd, the Resolutions whereof would be sought in vain from only common Arithmetick. Yet Arithmetick in all its Operations is so subservient to Algebra, as that they seem both but to make one perfect Science of Computing; and therefore I will explain them both together.<!--pp.1-2

“These formulae [in (1) and (2) above] may be shown to be valid for a circle or a triangle in the hyperbolic plane… for which K < 0. Accordingly here the perimeter and area of a circle are greater, and the sum of the three angles of a triangle are less, than the corresponding quantities in the Euclidean plane. It can also be shown that each full line is of infinite length, that through a given point outside a given line an infinity of full lines may be drawn which do not meet the given line (the two lines bounding the family are said to be "parallel" to the given line), and that two full lines which meet do so in but one point.”

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)