La Perspectiua, y Especularia de Euclides. Traduzidas en vulgar castellano, y dirigidas a la S.C.R.M. del Rey don Phelippe nuestro señor. Por Pedro Ambrosio Onderiz su criado

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Author: Euclid of Alexandria (323-283 BC)

Year: 1585

Publisher: En casa de la viuda de Alonso Gomez

Place: Madrid


[4] (of [6]), 57 (of 60) leaves (with 3 facsimile leaves at end). ii6 (-ll2-3?), A-P4 (-P2-4) with illustrations throughout. Small octavo (7 1/4" x 5 3/4"), bound in period vellum, later end-papers.

The first translation into Spanish of Optics and Catoptrics. "Optica" is ascribed to Euclid; the 'Catoptrica' ('Reflections') is not by Euclid but is, rather, a later compilation from ancient works on the subject. "Optica et Catoptrica" is the earliest surviving Greek work on perspective, and until the arrival of Newton's Opticks, the most important. The translator of the present work, Pedro Ambrosio Onderiz, was appointed by King Philip II to a chair in the newly established Academia de Matemáticas, and was expressly charged with the translation of scientific works into Spanish. The only earlier work by Euclid that had been translated into Spanish was the 1576 Los seis libros primeros de la geometria; prior to that, the only printing of Euclid in Spain was a truncated Mathematicae quaedam selectae, done in 1566.

Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is 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. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigor. Very few original references to Euclid survive, so little is known about his life. He is mentioned by name, though rarely, by other Greek mathematicians from Archimedes (c287 BC-c212 BC) onward, and is usually referred to as "ὁ στοιχειώτης" ("the author of Elements"). The few historical references to Euclid were written by Proclus c450 AD, centuries after Euclid lived.

Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of the Elements. Most of the copies say they are "from the edition of Theon" or the "lectures of Theon", while the text considered to be primary, held by the Vatican, mentions no author. Proclus provides the only reference ascribing the Elements to Euclid. Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid–Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers. The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries discovered in the 19th century.


Some soiling and wear to vellum; title page backed with paper restoring some marginal chipping, a number of leaves with archival repairs to worming in gutter margins or to loss at upper corners and a few other places, some minor staining; good condition, with respectable restoration.