Some Proofs of Desargues' Triangle Theorem

Author

Arthur Cleo Moseley, Prairie View A&M College

Date of Award

8-1968

Document Type

Thesis

Degree Name

Master of Science

Degree Discipline

Mathematics

Abstract

It is the French mathematician Gerard Desargues' triangle theorem that I will be concerned with in this paper. It states, IF TWO TRIANGLES ARE CENTRALLY PERSPECTIVE, THEY ARE AXIALLY PERSPECTIVE. Desargue theorized this theorem in 1639. He was born in Lyons on March 2, 1591. The importance of his theorem was not fully realized until after his death in 1661 which was the case of many mathematicians during that time.

It will be my objective in this paper to try to make the reader realize how one problem in geometry can bring out such a diversified amount of accummulated facts and apply it to one problem. This is true in all branches of mathematics but I think geometry gives a person a chance to express his mathematical creativity more than any of the other areas. After reading this paper the reader should see some of this variety.

In this paper I have investigated, originated and developed in details eight different proofs to the one theorem. The proofs involve both Euclidean and non-Euclidean geometry by using the following methods: parallelism; Menelaus' Theorem; analytic geometry; ideal point and plane intersection. A brief discussion of some of the ideal element concepts are written in this first chapter.

Committee Chair/Advisor

Samuel Good

Committee Member

A. D. Stewart

Publisher

Prairie View A&M College

Rights

Date of Digitization

3-11-2022

Contributing Institution

John B Coleman Library

City of Publication

Prairie View

MIME Type

Application/PDF

Recommended Citation

Moseley, A. C. (1968). Some Proofs of Desargues' Triangle Theorem. Retrieved from https://digitalcommons.pvamu.edu/pvamu-theses/1301