- Feb 2020
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.
the area of the triangle itself is expressed by something totally different from its visible figure, namely, by half the product of the base multiplied by the altitude
In order to calculate and compare the areas of rectilinear figures, we decompose them into triangles
- Khan Academy
- Transitive Property
- Common Notions
- Reflexive Property
- Parts and Wholes
- Common Terms
- Feb 2019