Antonio Hugo de Omerique

Analysis Geometrica1698.

Antonio Hugo de Omerique (Sanlúcar de Barrameda, present-day province of Cádiz, January 6, 1634 - Cádiz, February 27, 1705) was a married Spanish mathematician of the 17th century.

Biography

First page of Omerique's will, released in 2016.

The son of a merchant family originally from the Spanish Netherlands (Hugo Antonio and María David), he studied at the Colegio de la Compañía de Jesús in Cádiz, in such a way that he mastered Latin and mathematics. He married twice, the first time with Ana Caro and, after being widowed, with Magdalena de Lasarraga, from whose marriage three children were born: Máximo Antonio, Xavier Esteban and Ignacio Próspero.

He dedicated himself to commerce, but in 1672 it went bankrupt because a ship he had chartered was seized by Barbary pirates at Cape San Vicente.

In 1689, two problems proposed and solved by Omerique on reciprocal lines and squares appeared in a Spanish translation of Euclid's Elements published by the Austrian Jacobo Kresa, a Jesuit mathematician, then a professor at the Imperial College of Madrid. Kresa praised in the text his friend Omerique, who he said would give geometry "its greatest polish"; and that “his works would soon see the light.” Two years later he published a pamphlet in which he applied knowledge of logarithms to simplify business operations.

Omerique is known to have written a treatise on arithmetic and two on trigonometry, all of which have been lost. In 1698 he published a treatise on geometric analysis: Analysis geometrica, sive nova et vera methodus resolvendi tam problemanda geometrica quam arithmeticas quaestiones ("Geometric Analysis or Method of Solving New and True Problems, as well as of arithmetic questions", 1698), a work that earned praise from Isaac Newton, not at all inclined to them, in a letter the following year:

I have look into De Omerique ́s Analysis Geometrica & fint it a judicious & valuable answering to ye Title. For therin is laid a foundation for restoring the Analysis of the Anciens...

I have studied the Geometric Analysis of De Omerique and I find it a judicious and valuable work that responds to its title, because it exposes the method of restoring the analysis of the ancients, which is easier and more on purpose for a geómetra than the algebra of the modern. Thus, your method leads you easier and directly to troubleshooting. It usually comes to simpler and more elegant resolutions than those obtained with algebra

In this work, Omerique describes and applies a general method that combines algebraic and geometric analysis. In a second part, which was never published and whose manuscript has been lost, Omerique appears to have applied three-dimensional coordinates to the description of curved surfaces, thus anticipating Clairaut's 1731 work by some 30 years.

In Madrid, he had the opportunity to meet Prince Roger de Vintimille again and collect some of his problems. Certain historians, for example Albert Dou, consider Hugo de Omerique as a successor to François Viète.

He died on the night of February 26-27, 1705, according to a notation in the margin of the will that he dictated a few hours before he died. He was equally appreciated by Johann Wilhelm Von Camerer (1763-1847) in his De tractionibus (1795), by Montucla in his History of mathematics (volume II), by Lucio del Valle and José Echegaray and also later by Michel Chasles, in his historical review of mathematics.

Works

Analysis Geometrica, 1698.

• An arithmetic treatise, unpublished, lost.
• Two treatises of trigonometry, unpublished, lost.
• Two problems included in Jacobo Kresa, Elements of EuclidesBrussels, by Francisco Frappens, 1689. (on Commons)
• Trade the silver bars. Artificial boards to adjust short, easy, and punctually the value of a bar according to the styles of Spain and the IndiasCadiz, Society of Jesus, 1691. Contrary to what appears to be asserting Navarro-Loidi that no copy is retained, José Ramón Barroso and Santiago Saborido say they have found a copy at the Biblioteca Menéndez Pelayo de Santander.
• Analysis Geometrica Cadiz (440 pages) by Cristóbal de Reque, 1698. First part of the work and only one that came to be published. (on Commons)
• Part two Analysis Geometrica, unpublished, lost.