Balbus (Agrimensor)
Balbus was a Latin specialist writer, an agrimensor , or surveyor, late 1st century AD to early 2nd century AD, who mainly 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 Agrimensors and the page and line information in Brian Campbell's edition.)
Name, person, sources
Balbus is one of the lesser known authors in the Corpus agrimensorum Romanorum . The attempts to equate him or the addressee of his dedication, Celsus, with more well-known bearers of these names were not convincing. Therefore, only the information that he himself gives in his writing, mainly in the dedication, remains for his curriculum vitae.
There he describes himself and Celsus as experienced and knowledgeable canteens. Balbus is with the troops in the victorious campaign of the Roman emperor in Dacia (probably Domitian 86 AD or Trajan 101-102 AD). He stylized himself as an active participant in the war, who performs both military and field measurement tasks, such as constructing straight aisles ( rigores ) in impassable terrain (Balbus, pp. 204, 18-23).
But it is also important for him to put down the basics of his activity in writing, which he does not call professio = trade, specified art , like the agrimensor Siculus Flaccus , but as study = interest, scientific occupation (Balbus, p. 204,3).
The text has survived in numerous manuscripts, mostly without a heading and in fragments. In some manuscripts it is also incorrectly associated with the name Sextus Iulius Frontinus or Fronto. The manuscript in the Codex Arcerianus in Wolfenbüttel (see Corpus agrimensorum Romanorum ) with the beginning: Incipit liber, Balbi ad Celsum expositio et ratio omnium formarum is convincing . The assumption that Balbus was the author of a further work De asse , as well as that another text of the Corpus agrimensorum Romanorum , to which Marcus Junius Nipsus is attributed, came from him, are considered refuted.
Other works are uncertain as to their attribution, for example a list of cities (Liber coloniarum) from a Balbus Mensor, which may be identical to this Balbus. However, the content was not part of the exposure.
Fabius Calvus from Ravenna published a treatise on fractions in 1525, for which he gives a balbus as the source. However, this is not identical to this Balbus, as he lived in a later period (3rd to 4th century).
Other parts of the surviving corpus agrimensorum are probably from Balbus or go back to him.
Paul Gensel calls him in Pauly-Wissowa one of the most outstanding Roman agrimensors alongside Frontinus and Hyginus Gromaticus .
Expositio et ratio omnium formarum
The heading is the representation and theory of all floor plans . In fact, in contrast to the dedication, the text, which is rather impractical, is divided into 3 parts: a short definition of length, area and body measurements (Balbus, pp. 206,4-42), a translation and processing of a few parts of the geometry like them Euclid defined the elements in his work (Balbus, pp. 208.1-40) and attempted to combine this theory with agrimensory practice (Balbus, pp. 210.1-214.3).
Length, area and body measurements
It is believed that Balbus largely followed the writings of the Greek mathematician Heron of Alexandria . The Greek text was very likely inaccessible to him. But Latin versions were already available at the beginning of the imperial era. Like Heron, Balbus presents smaller and larger length measures based on the pes = foot . There are many similarities, for example the smallest unit for both authors is 1/16 foot with the designation finger (Latin: digitus , Greek: δάκτυλος ), but there are also differences. The names used for the unit are also mentioned by Pliny the Elder and extensively by Lucius Junius Moderatus Columella , and even partly by Cato the Elder and Marcus Terentius Varro .
Euclidean geometry
Omnis autem mensurarum obseruatione et oritur et desinit signo. signum est cuius pars nulla est (Balbus, pp. 208,1-2)
Every measurement begins and ends with the sign. A sign is that which has no part.
With this, Balbus begins his Latin version of the definitions in Book I of the Euclidean work The Elements , in order to continue them through the definition of lines and angles up to the polygon. It is probably the oldest surviving treatise on the foundations of geometry in Latin. However, another piece of text has been preserved in the Corpus agrimensorum Romanorum ( Friedrich Blume , Karl Lachmann , Adolf August Friedrich Rudorff (eds.): Gromatici veteres , p. 377). It is mixed with texts that are assigned to the geometry of Boethius and is probably a translation of Boethius. The fact that the two texts are at least not directly dependent on one another can be seen from the different translations of the technical terms. Boethius speaks in the 1st definition of the punctum , Balbus of the indefinite signum . Boethius translates surface correctly with superficies , Balbus with summitas , which means the supreme thing , the top . Balbus cannot always follow the clarity of the definitions. The unambiguous definition 15:
A circle is a ... figure with the property that all stretches running from a point within the figure to the line are equal to each other (translation by Clemens Thaer )
"degenerates" into an indefinite one in Balbus:
circumferens, cuius incessus a conspectu signorum suorum distabit (Balbus, pp. 208, 17f)
the circular line is characterized by the fact that its course cannot be seen from the center.
Boethius' definition is much closer to the original.
Agrimensory practice
Balbus tries to use this theoretical concept for practical work, for example by tracing areas whose boundaries are neither straight lines nor segments of circles back to geometrically defined figures (Balbus, pp. 210, 23-29). The explanations are not always clear. The attached drawings also only partially fit, surprisingly none of the area calculations cited by Euclid, as recorded by Lucius Junius Moderatus Columella. Maybe this is because only part of the scriptures have survived.
Text output
- Friedrich Blume, Karl Lachmann, Adolf August Friedrich Rudorff (eds.): Gromatici veteres . The writings of the Roman surveyors, 2 volumes, Berlin 1848–52 (here volume 1, pp. 91-107)
- Brian Campbell, (Ed., Transl., Comm.): The writings of the Roman land surveyors. Introduction, translation and commentary (= Journal of the Roman Studies Monographs. 9), London 2000
literature
- Paul Gensel , article Balbus in Pauly-Wissowa , Volume 2, 1896, column 2820-2822
- Menso Folkerts : Balbus, Dictionary of Scientific Biography , Volume 1
- Moritz Cantor : The Roman Agrimensors and their position in the history of field measurement. Leipzig 1876.
- Menso Folkerts : The Mathematics of Agrimensors - Sources and Aftermath in Eberhard Knobloch , Cosima Möller (Ed.): In den Gefilden der Roman Feldmesser , Berlin / Boston 2014, ISBN 978-3-11-029084-4 .
- Friedrich Hultsch : Greek and Roman Metrology , Berlin 1882
- Karl Lachmann: About Frontinus, Balbus, Hyginus and Aggenus Urbicus In: Friedrich Blume, Karl Lachmann, Adolf August Friedrich Rudorff (ed.): Gromatici veteres. The writings of the Roman surveyors. 2 volumes, G. Reimer, Berlin 1848-52, Vol. 2, pp. 227-464 ( online ).
- Theodor Mommsen : The libri coloniarum In: Friedrich Blume, Karl Lachmann, Adolf August Friedrich Rudorff (Ed.): Gromatici veteres. The writings of the Roman surveyors. 2 volumes, G. Reimer, Berlin 1848-52, Vol. 2, pp. 227-464 ( online ).
Single receipts
- ^ Brian Campbell: The writings of the Roman land surveyors , pp. XXXIXf
- ^ Karl Lachmann: About Frontinus, Balbus, Hyginus and Agennus Urbicus , pp. 131-134
- ↑ Moritz Cantor: The Roman Agrimensors and their position in the history of field measurement , p. 100f
- ^ Folkerts in Dictionary of Scientific Biography
- ^ Theodor Mommsen: Die libri coloniarum , p. 148
- ↑ Friedrich Hultsch: Greek and Roman Metrology , p. 12
- ↑ Heron: Definitions of Geometric Designations , 130-132
- ↑ Columella: De re rustica libri duodecim , book 5.5-7
- ↑ Menso Folkerts: The mathematics of the agrimensors - sources and aftermath , p. 133
- ↑ Menso Folkerts: The mathematics of the agrimensors - sources and aftermath , p. 133
- ^ Karl Ernst Georges : Comprehensive Latin-German concise dictionary
- ^ Brian Campbell: The writings of the Roman land surveyors , p. 434, note 18