The Principia Mathematica is a three-volume work on the foundations of mathematics, written with the goal of deriving all mathematical truths from a well-defined set of axioms and inference rules in symbolic logic. The authors aim to show that mathematics is a development of logic and avoid any hidden assumptions. The work covers topics like class theory, relation theory, and quantity theory, and it is known for its rigorous and meticulous approach.

This book is a comprehensive collection of definitions, postulates, propositions, and mathematical proofs written by an ancient Greek mathematician. It is considered one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics, especially geometry, from the time of its publication until the late 19th or early 20th century. The book covers topics such as plane geometry, proportion in general, the properties of numbers, incommensurable magnitudes, and solid geometry.

"The Foundations of Arithmetic" is a philosophical treatise that explores the concept of number and the philosophical foundations of mathematics. The work critically examines previous theories of number and develops a new approach, arguing that arithmetic is a branch of logic rather than being empirical or purely mathematical. The author introduces a rigorous system to define numbers and arithmetic operations through logical propositions, aiming to demonstrate that arithmetic truths can be derived from logical axioms and definitions. This groundbreaking perspective laid the groundwork for modern mathematical logic and had profound implications for the philosophy of mathematics and logic.

The book in question is a comprehensive exploration of the nature, origin, and historical development of mathematics. It delves into the philosophical and logical foundations of mathematical concepts, examining how they arise from natural phenomena and human activities. The work discusses the structure and function of mathematical language and its relation to logic and set theory, while also considering the role of mathematics in the physical sciences, and its application to problems in the real world. The author presents a unified view of mathematics as a coherent whole, emphasizing the interplay between its abstract form and practical function.

"La Géométrie" introduces a revolutionary approach to mathematics by merging algebra and geometry into a single discipline. The work outlines the method of using equations to describe geometric shapes and using algebraic formulas to solve geometric problems, thereby laying the groundwork for what is now known as analytic geometry. This treatise fundamentally changed the course of mathematics by providing a systematic framework that allowed for the graphical representation of algebraic equations, and vice versa, thus enabling the precise analysis of geometric spaces using algebra.