Daniel Santbech (

fl. ''Floruit'' (; abbreviated fl. or occasionally flor.; from Latin for "they flourished") denotes a date or period during which a person was known to have been alive or active. In English, the unabbreviated word may also be used as a noun indicatin ...

1561) was a Dutch

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, structure, space, models, and change. History On ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...

. He adopted the Latinized name of Noviomagus, possibly suggesting that he came from the town of

Nijmegen Nijmegen (;; Spanish and it, Nimega. Nijmeegs: ''Nimwèège'' ) is the largest city in the Dutch province of Gelderland and tenth largest of the Netherlands as a whole, located on the Waal river close to the German border. It is about 6 ...

, called ''Ulpia Noviomagus Batavorum'' by the

Romans Roman or Romans most often refers to: *Rome, the capital city of Italy * Ancient Rome, Roman civilization from 8th century BC to 5th century AD *Roman people, the people of ancient Rome *''Epistle to the Romans'', shortened to ''Romans'', a lette ...

. In 1561, Santbech compiled a collected edition of the works of

Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrument ...

(1436–1476), ''De triangulis planis et sphaericis libri quinque'' (first published in 1533) and ''Compositio tabularum sinum recto'', as well as Santbech's own ''Problematum astronomicorum et geometricorum sectiones septem''. It was published in

Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (B ...

by Henrich Petri and Petrus Perna. Santbech's work consisted of studies on

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

sundials A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a flat ...

surveying Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ...

, and

levelling Levelling or leveling (American English; see spelling differences) is a branch of surveying, the object of which is to establish or verify or measure the height of specified points relative to a datum. It is widely used in geodesy and cartogra ...

for water courses. It also includes descriptions of astronomical instruments, information for navigators and geographers, and general information about astronomy in the first years after

Nicolaus Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulat ...

. Santbech also studied the subject of gunnery and

ballistics Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing a ...

as a theoretic discourse as well as for the practical application of war, and utilized the foundations of geometry, with ample references to

Euclid Euclid (; grc-gre, Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the '' Elements'' treatise, which established the foundations of ...

and

Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...

, in order to do so. Santbech seem not to have been aware of similar studies by

Niccolò Fontana Tartaglia Niccolò Fontana Tartaglia (; 1499/1500 – 13 December 1557) was an Italian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then Republi ...

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Santbech's text included theoretical illustrations of trajectory, trajectories. These were depicted with abruptly acute angles and straight lines, allowing him to create a right-angled triangle from which

ranges In the Hebrew Bible and in the Old Testament, the word ranges has two very different meanings. Leviticus In Leviticus 11:35, ranges probably means a cooking furnace for two or more pots, as the Hebrew word here is in the dual number; or perhaps ...

were computed with the help of a table of

sines Sines () is a city and a municipality in Portugal. The municipality, divided into two parishes, has around 14,214 inhabitants (2021) in an area of . Sines holds an important oil refinery and several petrochemical industries. It is also a popular ...

. Santbech was of course fully aware that a

cannonball A round shot (also called solid shot or simply ball) is a solid spherical projectile without explosive charge, launched from a gun. Its diameter is slightly less than the bore of the barrel from which it is shot. A round shot fired from a lar ...

's true trajectory would not consist of a straight line and a sudden drop, but these depictions were meant to assist with mathematical calculations. In 1651,

Riccioli Giovanni Battista Riccioli, SJ (17 April 1598 – 25 June 1671) was an Italian astronomer and a Catholic priest in the Jesuit order. He is known, among other things, for his experiments with pendulums and with falling bodies, for his discussion ...

gave Santbech's name to the crater Santbech on the

Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

References

*Andreas Kleinert: Zur Ballistik des Daniel Santbech. In: Janus 63 (1976), pp. 47–59. n German

External links

The Geometry of War

* ttps://www.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.06.0023;layout=;loc=1;query=toc ''Problematum astronomicorum et geometricorum sectiones septem''(Full Latin Text at Perseus Project) ***Link Dead as of July 2021 {{DEFAULTSORT:Santbech, Daniel 16th-century Dutch astronomers 16th-century Dutch mathematicians Ballistics People from Nijmegen