An ambitious synthesis of all the mathematical knowledge he could find,Pacioli’s Summa de arithmetica, geometria, proportioni et proportionalitais a baggy monster of a book. Six hundred and fifteen pages long, nearlyhalf a million words, full folio in size, closely printed on fine paper, itcomprehensively sums up the state of European mathematical knowledge,and was intended for a wide audience – Fra Luca wrote informally, inTuscan, not Latin, making it accessible to anyone with a basic education.The book combines a general treatise on theoretical and practical arithmetic– including the Liber Abaci of the then little-known Fibonacci, whichPacioli had discovered on a monastery bookshelf – with an introduction toalgebra, currency conversions, multiplication tables, weights and measuresof the Italian states, a summary of Euclidean geometry, and accounts ofArchimedes, Euclid and Piero della Francesca.
5 Matching Annotations
- Jul 2025
-
Local file Local file
-
- Feb 2020
-
marxdown.github.io marxdown.github.io
-
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
-
- Feb 2019
-
Local file Local file
-
Euclid
The Free Masons seem attracted to him.
Some Euclid Background
-