Mathematical Institutions (Veracruz, 1794)

An Electronic Edition · Miguel Vendrell y Puig (C-18)

Original Source: Don Miguel Vendrell y Puig, Ynstituciones Mathematicas/Mathematical Institutions (Veracruz 1794) (pp. 53-53v)

Full Colophon Information

Translated and annotated by Claire Gillespie (William & Mary), using the manuscript copy held in Swem Library, Special Collections Resource Center

In plainest discourse, the manner of the conduction of water from the Jamapa River[1] to the new city of Veracruz, for the new Project that I, Don Miguel Vendrell y Puig, present to Your Lordships[2] in this Mathematic Dissertation which the Council celebrated on September 4, 1794. They ordered it put aside to have it available at the appropriate time.

My Illustrious Mathematical Dissertation

In gratitude for the esteem that Your Lordships deigned to give to the New Project proposed in my Mathematic Dissertation, and that the gentleman Attorney General Don Domingo Lagoa de Miranda’s powerful recommendation[3] made me finally able to collect some useful thoughts for the conduction of water to this city, which foundational institutions they obligated me to now present to Your Lordships, that I hope to present after it was viewed by the gentleman Don Gorostisa,[4] may he rest in peace, that will explicate the advantages to which I refer in summary: and having raised the necessary water for conduction to the convenient height of my hydraulic machine without more assistance than that of the water itself, not exposed to frequent, and expensive construction as some have proposed, but the contrary, that I will prove with examples. Water can be conducted with the greatest possible ease. With this, the public will gain a benefit, justly forthcoming on its own merits, and worthy of the attention of Your Lordships with the best advantages you can provide. [end p. 53]

So many public and scientific works have been achieved by the past mathematicians that in their concept and in those matters that much more remains to be discovered from them than what has been discovered, as Andrés says.[5] In the past, the breath of Nature inspired the men of antiquity to great effect, and we have yet to reach their heights, and we even ignore them in the present, as can be inferred from the forty machines that the Great Archimedes invented, as Father Tosca says,[6] and of those machines, we have scant notice of any, save for the one single hydraulic, which is known as Archimedes’ Point. It is known that more than the top of the tower will be set on fire. The wood’s angle reflects the rays of the sun, and their firey bristles augment that virtuous heat. It is known that a grand tower that did not lean or fall was built inside the walls of Syracuse,[7] and they came to say that if given a lever and a fulcrum, one could move the entire world. Also it is known according to Bocant,[8] Mallet,[9] Kircher,[10] and other historians that a pyramidal stone of 130 feet tall and 25 feet wide was brought from Armenia to Babylon, which the Queen Semiramis[11] ordered to be built into a circuit wall,[12] that crossed below Euphrates from her Real Palace to her storehouse[13] whose side was some gardens and grounds fifty raised cubits[14] whose height has carried abundant hydraulic machines for fountains, waterfalls, and other watery impasses, one thousand works of art and nature: In view of this and much more that I could refer to, what difficultly it is, given our Nature, for any other man to produce some new discourse for the culture of knowledge in the Enlightened age in which so much applause has been acquired in the natural sciences among the most cultured nations. [end p. 53v]

[1] Located about nine miles south of Veracruz in the southwestern corner of the Gulf of Mexico.

[2] Abbreviated “VSS,” which I interpret as an abbreviation for “Vuestras Señorías” See A. Roberta Carlin, A paleographic guide to Spanish abbreviations, 1500-1700/Una guía paleográfica de abbreviaturas españolas, 1500-1700 (Reno: Universal Publishers, 1999), 168.

[3] A document from the Archivos Notariales de la Universidad Veracruzana refers to Don Domingo Lagoa de Miranda as a citizen of New Veracruz. See Protocolo 74, 1810-05-04, pp. 124v-126v.

[4] Don Pedro Fernández de Gorostiza y Lorea, was the governor of Vera Cruz until his death in 1794. His son, military commander-cum-playwright Manuel Eduardo de Gorostiza, played an important role in Mexico’s wars of independence against Spain, France, and the United States. See Eduardo González Pedrero, País de un solo hombre: La sociedad del fuego cruzado (México: Fondo de Cultura Económica, 1993). For digital copies of primary sources, see Correspondencia que ha mediado entre le Legacion extraordinaria de Mexico y el Departamento de estado de los Estados-Unidos: sobre el paso del Sabina por las tropas que mandaba el general Gaines (México: J.F.M. de Lara, 1837), available on googlebooks. English-language edition: House Documents, Otherwise Publ[ished] as Executive Documents: 13th Congress, 2d Session-49th Congress, 1st Session (Washington: Blair and Rives, 1836).

[5] Possibly a reference to Andrés Puig, Aritmetica especulativa y practiva: y arte del algebra: en la cual se contiene todo lo que pertenece al arte menor ò mercantil y à las dos algebras, racional è irracional, con la explicacion de todas las proposiciones y problemas de los libros quinto, septimo, octavo, nono, y dezimo del principe de la Mathematica Euclides (Barcelona: José Giralt, 1715?). For more information, see the digital exhibit of la Historia del Conocimiento Matemático:

[6] Tomás Vicente Tosca (1651-1723), renowned professor of mathematics at la Universidad de Valencia and author of several works on geometry, algebra, hydrology, and astrology, including the multi-volume Compendio mathemático (Valencia: Por Antonio Bordazar, año 1709), reprinted some twenty years later in Madrid with the same title (A. Marín, 1727).

[7] Archimedes (c. 287 BCE – c. 212 BCE) lived in Syracuse, Sicily. This grand tower is probably one of Archimedes’ creations. For an example of how this story circulated among English-language audiences, see Robert Aris Willmott, The Parlour Table Book (London: Joseph Rickerby, 1841), 317ff.

[8] Unfortunately, we are unable to identify this figure.

[9] Probably Alain Manesson Mallet (1630-1706), royal cartographer of Louis XIV and author of the Description de l’univers (Paris: Denys Thierry, 1683), which included several maps of South America and British North America, particularly Virginia.

[10] Athanasius Kircher (1602-1680) was a German scholar who studied the Orient, geology, and medicine.

[11] The legendary queen of Assyria in about 800 BC. She is celebrated as the author of most remarkable buildings and works of engineering near the Euphrates. See W. Robertson Smith, “Ctesias and the Semiramis Legend,” The English Historical Review, 2.6 (1887): 304.

[12] In the original text, Vendrell y Puig writes Bobeda (bóveda), probably referring to the Greek periboloi, or arches on the circular wall that encompassed Queen Semiramis’s buildings. See Bill Thayer, Diodorus Siculus Library of History, Loeb Classical Library Edition (Cambridge: Harvard University Press, 1933), accessed May 1, 2014 via*.html#ref17.

[13] In the source text, Alcázar, a type of castle or fortress in Spain. Its name is derived from the Arabic.

[14] A unit of measure approximately equal to the length of one elbow.

Full Colophon Information

Genre: Prose
Subjects: science
Period: 1766-1813
Location: New Spain, Spanish America
Format: essay
Translated and annotated by Claire Gillespie (William & Mary), using the manuscript copy held in Swem Library, Special Collections Resource Center