Pierre Hérigone (

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

ized as Petrus Herigonius) (1580–1643) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

. Of

Basque Basque may refer to: * Basques, an ethnic group of Spain and France * Basque language, their language Places * Basque Country (greater region), the homeland of the Basque people with parts in both Spain and France * Basque Country (autonomous co ...

origin, Hérigone taught in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

for most of his life.

Works

Only one work by Hérigone is known to exist: ''Cursus mathematicus, nova, brevi, et clara methodo demonstratus, per notas reales et universales, citra usum cujuscunque idiomatis intellectu faciles'' (published in Paris in six volumes from 1634 to 1637; second edition 1644), a compendium of

elementary mathematics Elementary mathematics, also known as primary or secondary school mathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical c ...

written in French and

. The work introduced a system of

mathematical Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

and logical notation. It has been said that "Hérigone introduced so many new symbols in this six-volume work that some suggest that the introduction of these symbols, rather than an effective mathematics text, was his goal."

Florian Cajori Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics. Biography Florian Cajori was born in Zillis, Switzerland, as the son of Georg Cajori and Catherine Camenisch. He attended schools firs ...

has written that the work contains "a full recognition of the importance of notation and an almost reckless eagerness to introduce an exhaustive set of symbols..." Hérigone may have been the first to introduce the mathematical symbol to express an

angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

. He used both the symbol below and recorded the use of "<" as a symbol denoting "

less than In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. The main types of inequality ar ...

." He also introduced the upside-down "T" symbol (⊥) to express

perpendicularity In geometry, two geometric objects are perpendicular if they intersect at right angles, i.e. at an angle of 90 degrees or π/2 radians. The condition of perpendicularity may be represented graphically using the '' perpendicular symbol'', � ...

. In regards to the notation for

exponent In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, i ...

s, Herigone wrote a, a2, a3, etc. (though the numerals were not raised, however, as they are today). . Hérigone also created a number

alphabet An alphabet is a standard set of letter (alphabet), letters written to represent particular sounds in a spoken language. Specifically, letters largely correspond to phonemes as the smallest sound segments that can distinguish one word from a ...

for remembering long numbers in which

phoneme A phoneme () is any set of similar Phone (phonetics), speech sounds that are perceptually regarded by the speakers of a language as a single basic sound—a smallest possible Phonetics, phonetic unit—that helps distinguish one word fr ...

s were assigned to different numbers, while the

vowel A vowel is a speech sound pronounced without any stricture in the vocal tract, forming the nucleus of a syllable. Vowels are one of the two principal classes of speech sounds, the other being the consonant. Vowels vary in quality, in loudness a ...

s were supplied by the memorizer: 1 (t, d), 2 (n), 3 (m), 4 (r), 5 (l), 6 (j, ch, sh), 7 (c, k, g), 8 (f, v, ph), 9 (p, b), 10 (z, s). In Hérigone's work, we find the earliest written examples of mathematical terms. ''Parallelipipedon'', an archaic form of ''

parallelepiped In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term ''rhomboid'' is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. Three equiva ...

'', appears in an English work dated 1570. Hérigone himself used the spelling ''parallelepipedum''.

Hérigone and the camera obscura

In the ''Cursus mathematicus'', Hérigone describes a

camera obscura A camera obscura (; ) is the natural phenomenon in which the rays of light passing through a aperture, small hole into a dark space form an image where they strike a surface, resulting in an inverted (upside down) and reversed (left to right) ...

in the form of a

goblet A chalice (from Latin 'cup', taken from the Ancient Greek () 'cup') is a drinking cup raised on a stem with a foot or base. Although it is a technical archaeological term, in modern parlance the word is now used almost exclusively for the ...

(Chapter 6, page 113). Hérigone did not depict his goblet, but

Johann Zahn Johann Zahn (29 March 1641, Karlstadt am Main – 27 June 1707) was the seventeenth-century Germany, German author of ''Oculus Artificialis Teledioptricus Sive Telescopium'' (Würzburg, 1685). This work contains many descriptions and diagrams, ...

would illustrate the design in his ''Oculus Artificialis Teledioptricus Sive Telescopium'' (1685). Hérigone's goblet-camera obscura, more a

novelty Novelty (derived from Latin word ''novus'' for "new") is the quality of being new, or following from that, of being striking, original or unusual. Novelty may be the shared experience of a new cultural phenomenon or the subjective perception of an ...

than anything else, was constructed in such a way that you could spy on others while taking a drink. The device's 45-degree angle mirror had a stylized opening for the lens. The goblet had a cup made of glass where images could be seen. The lid bore a magnifying lens at the to

The lens and mirror of this dinner table device for spying was situated at the base of the goblet's stem and served to project a real-time image onto the ground glass screen in the cup of the goblet.

Committee work

Hérigone served on a number of scientific committees, including one set up to determine whether Jean-Baptiste Morin (mathematician), Jean-Baptiste Morin's scheme for determining

longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...

from the Moon's motion was practical. Members of this committee included Étienne Pascal and Claude Mydorge. He died in Paris. The crater Herigonius on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

is named after him.

Notes

Sources

Biography of Pierre Herigone
{{DEFAULTSORT:Herigone, Pierre 1580 births 1643 deaths 17th-century French astronomers 17th-century French inventors 17th-century French mathematicians French number theorists French-Basque people