**Monteiro da Rocha** was a Portuguese mathematician who made important contributions to applied mathematics and astronomy.

- Monteiro was born in Canaveses, a small town in the Vila Real district about 100 km east of Porto.
- The modern boundaries of Brazil were essentially set by the Treaty of Madrid, but the Jesuits with many missions in that part of the world resisted giving these up.
- With this background, it is not too surprising that, on joining the Jesuits in 1752, da Rocha was sent to the Jesuit College of the Bay of All Saints in the city of São Salvador da Bahia in Brazil.
- It was at this College that da Rocha obtained a solid foundation to his education.
- Although we have only a little specific information about the topics studied by da Rocha at the College, we know that the standard education provided there was in three areas, Letters, Philosophy and Theology.
- Da Rocha was taught science by the German Johannes Josephus Breuer (1718-1789).
- Returning to the secular life, da Rocha remained in São Salvador where he applied for positions teaching Latin Grammar and Rhetoric.
- Francisco de Lemos, who, along with Melo, was in charge of reforming the University of Coimbra, was well aware of Monteiro da Rocha's talents and invited him to participate in the process of drawing up the Statutes.
- On 16 August 1771, da Rocha travelled to Lisbon where, along with seven other members of the Board, he began the process of deciding on the reforms and drawing up the Statutes.
- Before teaching began, Monteiro da Rocha, who had drawn up the mathematics syllabus as part of the new Statutes, was appointed as a professor in the chair of Physics and Mathematics of the new Faculty of Mathematics at Coimbra.
- Since one of the requirements was that professors should have doctorates, the University held a ceremony on Friday 9 October 1772 at which da Rocha, and other newly appointed staff, were awarded doctorates.
- He was given the honour of delivering the inaugural address to the new Faculty of Mathematics on the following day, Saturday 10 October 1772.
- Our description of da Rocha's career to this point seems a little strange.
- In 1772 he is appointed as a professor of mathematics and physics (probably applied mathematics would be most accurate in today's terminology) yet he seems not to have studied much mathematics up to that point.
- Da Rocha held the Chair of Applied Mathematics at the University of Coimbra from 1772 until 1783 when he was appointed to the Chair of Astronomy.
- For example he drew up regulations for the Astronomical Observatory which required those working at the Observatory to make scientific foreign trips to update their knowledge.
- In 1779 da Rocha was appointed as Principal of the Royal College of Nobles of the three Provinces of the North.
- On 21 March 1800, da Rocha had been appointed as Councillor to the Prince Regent and, in recognition of his services, he received the Commendation of the Order of Christ of Portalegre.
- From that time on Da Rocha lived on his estate at São José de Ribamar, near Lisbon.
- Our description of da Rocha's life has shown his importance in the progress of science in Portugal through his administrative skills.
- Da Rocha was responsible too for the translations into Portuguese (carried out between 1773 and 1775) of a set of fundamental French textbooks (Bézout, Marie and Bossut) to be used at lessons.
- However Monteiro da Rocha's main scientific work was in the field of astronomy.
- This work spans from theoretical to practical astronomy, the most significant elements being the following: a work on the determination of comets' orbits; several papers on the calculation of eclipses; a work on longitudes; astronomical tables of the Sun, Moon, and planets and charts of Jupiter's satellites; a work on the use of the small rhomboidal net; and a work on the use and calibration of the transit instrument.
- Da Rocha was very unlucky with his work on orbits of comets.
- They did get round to producing a journal and, in the first two volumes, published papers which had been presented to the Academy since its foundation in 1780.
- Da Rocha's paper Determinação das órbitas dos Cometas Ⓣ(Determination of the orbits of comets) was only published in 1799, two years after Wilhelm Olbers published essentially the same method.
- The following four astronomy papers by da Rocha, Cálculo dos Eclipses Ⓣ(Calculation of eclipses) (1803), Uso do retículo Rhomboidal Ⓣ(Using the rhomboidal reticle) (1805), Uso do Instrumento de Passagens Ⓣ(Use of the transit instrument) (1805), and Exposição dos methodos particulares de que se faz uso no calculo destas Ephemerides Ⓣ(Exposition of the particular methods used in the calculation of ephemerides) (1807) were translated into French and appeared as Mémoires sur l'Astronomie Pratique Ⓣ(Memoirs on practical astronomy) by M J Monteiro da Rocha (Paris, 1808).
- The French titles are: Mémoire sur l'usage du Réticule Rhomboïdal Ⓣ(Memoir on the use of the rhomboidal reticle) (pages 1-16); Mémoire sur l'usage de l'Instrument des Passages Ⓣ(Instructions on the use of the transit instrument) (pages 17-29); Nouvelle méthode sur le calcul des Éclipses sujettes aux effets des parallaxes Ⓣ(New method on the calculation of eclipses subject to the effects of parallaxes) (pages 30-120); and Exposition des méthodes particulières employées dans les calculs des Éphémérides de Coimbra Ⓣ(Exposition of the particular methods used in the calculations of the ephemerides of Coimbra) (pages 121-164).
- The contributions we have just mentioned are in the area of astronomy but da Rocha also made contributions to mathematics.
- Interesting works on mathematics by da Rocha include Additamentos à regra de M Fontaine para resolver por approximação os Problemas que se reduzem às Quadraturas Ⓣ(Corrections to the rule of M Fontaine to solve by approximation problems that are reduced to quadraturas) (1797) and Solução Geral do problema de Kepler sobre a medição das Pipas e Tonéis Ⓣ(General solution of Kepler's problem on the measurement of pipes and barrels) (1797).

Born 25 June 1734, Canaveses, Portugal. Died 11 December 1819, São José de Ribamar, near Lisbon, Portugal.

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Astronomy, Origin Portugal

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive