Marcus Junius Nipsus

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Marcus Iunius Nipsus was a Latin specialist writer, an agrimensor (surveyor), who also dealt with mathematical aspects in his surviving writings. (Since the texts of the Agrimensors are poorly structured, the quotations in the following are given by the name of the Agrimensor, the abbreviation of the editor ( Ca for Brian Cambell, La for Karl Lachmann ) and the page and line number.)

Name, person, sources

Another Agrimensor is introduced with the introductory words Incipit Marci Iuni Nipsi liber II feliciter in the Corpus agrimensorum Romanorum (Nipsus, La , pp. 285, 1-3). Unfortunately, almost nothing is known about his person. He himself does not sprinkle any personal information into his scriptures, and no further testimonies have been received. The text proves to be a practical textbook due to the direct address ( Latin cum in agro assignato veneris , “if you go to an assigned piece of land” (Nipsus, La , p. 286,12)) and, according to popular opinion, falls into the 2nd century AD . Chr.

The work has only been handed down with gaps. The opinion of scholars as to which texts can be attributed to Nipsus differed. Some texts were discussed with him and attributed to the agrimensor Agennius Urbicus , and some other texts were assigned to him. In general, the tradition of Karl Lachmann is now accepted, who included the following three pieces of text in his edition:

  • Fluminis Varatio - dimension of the river
  • Limitis Repositio - cancellation (restoration, correction?) Of the limit
  • Podism - measurement of the feet, hypotenuse

He was able to use the oldest surviving manuscript, the Codex Arcerianus in Wolfenbüttel, for part of the edition . Other parts have only survived in more recent manuscripts. Jelle Bouma edited the first two parts with an English translation and detailed explanations.

The texts

Fluminis Varatio

Nipsus teaches a way to determine the breadth of a river whose opposite bank is inaccessible, for example because it is occupied by a warlike enemy. He looks for a striking sign on the opposite bank, such as a towering tree. This forms one corner of the right-angled triangle he is constructing. He leads one cathetus in a direct line across the river to his location. To construct the second cathetus, he cut a lane roughly parallel to the river bank from this location. In the middle of this aisle, he sets up his measuring device ( ferramentum , croma ) and determines the hypotenuse of the triangle by aiming for the distinctive sign over the river. Starting from this point, the Agrimensor constructs a second right-angled triangle that is similar to the first. The hypotenuse of the first triangle is continued as the hypotenuse and is held in place by appropriate marking in the terrain. One cathetus is the second half of the aisle parallel to the river bank. The second leg is thus fixed, can be measured by the Agrimensor and has the same length as the route across the river.

This solution is quite complex due to the formation of the long aisle and marking line. The more practical application of the mathematically “more demanding” ray theorem, which has been known for centuries, is dispensed with. The surveyor Balbus (Balbus, Ca , pp. 204, 24 f.) Also refers to the task of measuring the width of a river , without giving a solution, as does Sextus Iulius Frontinus (Iulus Frontinus, Ca , p. 14, 12 ff.).

Limitis Repositio

In the first part of this text (Nipsus, La , pp. 286,12–288,17), Nipsus describes how the agrimensor restores the borders and boundary stones in a long ago surveyed and overgrown area with disturbed boundary lines and missing stones. Starting from a few boundary stones, he looks for more by carving out long aisles based on their orientation. In the following (Nipsus, La , pp. 288,18–289,17) it is shown how plots of land are formed between limites of different lengths . It is accepted that the plots are not rectangular. The attached drawings illustrate the facts. In the third part (Nipsus, La , pp. 289.18–295.15), Nipsus introduces the “Agrimensor student” to the division of the assigned country by Decumanus and Cardo . He goes into various special cases and also explains the subseciva , the remnant pieces of land left over from the survey.

Podism

After some definitions of Euclidean geometry and determination of dimensions of measure , the text deals with the calculation of triangles. The source could largely be the Metrica or Geometrica of Heron of Alexandria . However, the excerpts are incomplete and distorted by multiple copies. While Heron deals with the mathematical theory, such as the Pythagorean theorem , Nipsus only brings number-based “recipes”. He particularly uses the Pythagorean triples , i.e. arrangements of three natural numbers that form the sides of a right triangle . In order to represent a formula of how a right triangle can be constructed as a smaller cathetus for any odd natural number , he laboriously uses the triple (III, IV, V) (Nipsus, La , p. 300, 1-5):

"Datum numerum, id est III, in se. Fit IX. hinc semper tollo assem. fit VIII. huius tollo semper partem dimidiam. fit IV. erit basis. ad base adicio assem. erit hypotenusa, pedum V "

“The opposite number, 3, is multiplied by itself. That gives 9. I'll take 1 away. That gives 8. I share that, gives 4. That is the second leg. I give 1, this is the hypotenuse: 5. "

Heron of Alexandria uses the triple (V, XII, XIII) for the same calculation. He also refers to the Pythagorean theorem:
a² + b² = c²
a² + ((a² - 1) / 2) ² = ((a² - 1) / 2 + 1) ²

In the whole text of the Nipsus the names Pythagoras and Euclid are not mentioned. His calculations probably have less of a practical meaning than are exercises for students. Thus (Nipsus, La , p. 298.1–299.3) it is calculated for two Pythagorean triples how further values ​​can be determined if the sum of the cathetus, the hyothenuse and the area are known.

Text output

  • Friedrich Blume, Karl Lachmann, Adolf August Friedrich Rudorff (eds.): Gromatici veteres. The writings of the Roman surveyors. 2 volumes, Berlin 1848–1852.

literature

Individual evidence

  1. ↑ Ulrich Schindel: Post-Classical Lessons in the Mirror of Gromatic Writings. P. 387.
  2. ↑ Jelle Bouma: Marcus Junius Nipsus - Fluminis varatio, limitis repositio. P. 15.
  3. ^ Karl Ernst Georges : Comprehensive Latin-German concise dictionary.
  4. ↑ Jelle Bouma: Marcus Junius Nipsus - Fluminis varatio, limitis repositio. P. 59 f.
  5. ↑ Jelle Bouma: Marcus Junius Nipsus - Fluminis varatio, limitis repositio. P. 143.
  6. ^ Moritz Cantor: The Roman Agrimensors and their position in the history of field measurement art. Pp. 104-107.
  7. ↑ Menso Folkerts: The mathematics of the agrimensors - sources and aftermath. P. 140.
  8. ↑ Heron of Alexandria, Geometrica 8.1.
  9. ^ OAW Dilke: The Roman land surveyors. P. 55.
personal data
SURNAME Nipsus, Marcus Junius
BRIEF DESCRIPTION Latin surveyor and specialist writer
DATE OF BIRTH 1st century or 2nd century
DATE OF DEATH 2nd century or 3rd century