"(Legal) fiction." A presumption or assumption of a law.

Image Credit: Detail from "The School of Athens" by Raffaello Sanzio da Urbino (c. 1509–1511).

Euclid's common notions appear to be grounds for many of Marx's arguments in Ch. 1, but also throughout the book.

Near the beginning of Ch. 1 of the Elements Euclid lists them [PDF]:

• Things that are equal to the same thing are also equal to one another (the Transitive property of a Euclidean relation).
• If equals are added to equals, then the wholes are equal (Addition property of equality).
• If equals are subtracted from equals, then the differences are equal (Subtraction property of equality).
• Things that coincide with one another are equal to one another (Reflexive property).
• The whole is greater than the part.

Regarding the fifth, also see Aristotle, Metaphysics 8.6 [=1045a]; Topics 6.13 (=150a15-16);

On the concept of the "whole-before-the-parts" (along with the "whole of the parts" and the "whole in the part"), also see Proclus, El. Theol., prop. 67.

cf. SwiftOnSecurity. "Twitter / @SwiftOnSecurity: They started giving these at work today ..." January 24, 2020, 3:11 p.m.

https://twitter.com/SwiftOnSecurity/status/1220801208073494531

Marx refers to the thought experiment, common in economics, which is sometimes called Robinson Crusoe economics.

Doing "Robinson Crusoe economics" consists in imagining what can be learned, if anything, from a one agent economy that will provide insight into a real world economy with lots of agents.

Marx: "Yesterday I pawned a coat dating back to my Liverpool days in order to buy writing paper" (Karl Marx and Frederick Engels, Collected Works, vol. 38 [1852-55]: 221).

On the significance of Marx's coat, see Peter Stallybrass, “Marx’s Coat,” in Border Fetishisms: Material Objects in Unstable Spaces, ed. Patricia Spyer (New York: Routledge, 1998): 183–207. [PDF].

Diamonds were first discovered in Brazil in 1729 near the city of Belo Horizonte. This started a diamond rush and a period of feverish migration of workers.

Major diamond rushes also took place in the late 19th and early 20th centuries in South Africa and South-West Africa.

Diamond rushes, like gold rushes or other types of rushes, are for Marx economic bubbles or asset bubbles (sometimes referred to today as speculative bubbles, market bubbles, price bubbles, financial bubbles, speculative manias, or balloons).

Exchange value appears as the property of a commodity that is exchangeable for other commodities. It also presupposes societies who produce commodities and exchange them. While all societies have things with use values, exchange value is relative to a specific time and place.

Additionally, exchanging commodities must also presupposes a way to determine proportionality between different commodities, so that they can be exchanged in the first place.

Exchange therefore requires some other measure that stands above the two commodities meant to be exchanged. If there were no ways in which iron and corn were found similar to a society, for example, then we would not exchange them and they would have no exchange value.

Marx will contend that what each commodity must contain crystalized within it is value (formally) and that the substance of value is labor (viz. the common factor of both iron and corn is labor). Marx will call this kind of labor abstract labor.

See Simon Schaffer, "Ceremonies of Measurement: Rethinking the World History of Science," Annales HSS, 70, no. 2 (April-June 2015): 335-360. [PDF].

Schaffer: "No doubt all this explains why some historians have identified the advent of European modernity with the rise of the quantitative spirit, and, simultaneously, with the capacity of these Europeans to travel, loot, accumulate, and dominate beyond the limits of their own world and, in principle, everywhere."

Marx's analysis of a capitalist system begins by postulating that it's fundamentally composed of units called commodities.

In the capitalist system commodities have two features.

1. They are produced

2. They are produced by capitalists

Capitalists produce commodities by employing workers to produce them.

In this section, Marx begins his analysis of the first feature of the capitalist system (viz. that it is commodity producing). Workers and capitalists will not appear in Marx's analysis for several more chapters.

Calculating the Area of a Triangle

Decomposing rectilinear shapes to find an area.

What commodities are thought to be useful for or not is irrelevant to Marx at this very early stage of his analysis, even from a moral point of view. Diamonds satisfy a need in some societies at specific times and places the same as corn or iron.

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Victor follows the Creature along the windings of the Rhone, to the Black Sea, to Tartary and Russia, ever northward, ultimately into the ice.