Practica geometriae (Hugo von St. Viktor)
Practica geometriae (Hugo von St. Viktor) (hereinafter PG) is a text on geometric and astronomical subjects. It was created around 1125 by Hugo von St. Viktor in the Middle Latin language for early scholastic schools . However, this attribution is not entirely certain.
Basic attitude and tendencies
In the prologue the author formulates his intention: ... nostris tradere ... non quasi nouum cudens opus sed uetera colligens dissipata , ... not to produce anything new for our students, but to collect old, scattered things . This is related to the early school life, i.e. H. not accidental reading fruits are offered, but an ordered subject matter. To this end, Hugo von St. Victor divides geometry into a theoretical ( theorica ... spacia et intervalla dimensionum rationabilium sola rationis speculatione uestigat , theory ... which examines spaces and surfaces only after deliberations of the mind ) and a practical ( practica ... instrumentis agitur et ex aliis alia proportionaliter coniciendo diiudicat , practice ... the instruments used and the various proportionalities assessed ) (PG, Prenotanda , §2). Such a delimitation is new and is carried out for the first time in this publication. Hugo von St. Viktor divides his curriculum into the chapters altimetria , planimetria and cosmimetria ; He made this classification in his comprehensive work Didascalion, de studio legendi (Book 2, 13). Before that, the author presents a chapter prenotanda , in which he offers the students something from theoretical geometry that is necessary for understanding.
content
Prenotanda (preliminary remarks)
The chapter begins with theoretical geometrical definitions: line, point etc. after Euclid , The Elements , Book I, which Hugo von St. Viktor could have taken over from Gerbert d'Aurillac Geometria Geberti . After delimiting the practical geometry, some basic definitions follow, concerning the right triangle and the shape of the earth.
Altimetria, planimetria (height and area measurement)
§7 - §35 deal with the calculation of heights, §36 - §38 the calculation of areas. The similar triangles form the theoretical background . For practical implementation, the astrolabe is used and described: inter omnia instrumenta mensorum principalis (the first of all instruments used by measuring people) (§10). Hugo von St. Viktor was able to obtain this information from the text De astrolabia by Gernert d'Aurillac. However, only the back, the dioptra, is used with the alhidada or mediclinius that was used for the bearing .
Cosmimetria (earth surveying)
Hugo von St. Viktor wants to measure the world and starts from its center, the earth, which is surrounded by heavenly spheres. It deals with the circumference of the earth (§39), the diameter of the earth (§40), the distance between the earth and the sun (§41-§43), the size of the sun (§44-§45) and the earth's shadow (§46-§48) .
He specifies the circumference of the earth as 252,000 stages , as widespread in antiquity and associated with the name Eratosthenes . This is also one of the few sources he mentions, along with the anecdotal account of the geodetic measurements made by officials of the Egyptian ruler Ptolemy III. , possibly adapted from Martianus Capella ( The Marriage of Philologia and Mercury , Book 6 - Geometry). Hugo offers a second method to get the required database. The change in midday height of a bright star that stands high above the horizon all year round ( septentrio = pole star was chosen ) is measured with the aid of an astrolabe. There is no source for this in ancient literature.
The diameter of the earth is determined using the formula diameter * number of circles = circumference , with the number of circles π (Pi) being approximated by 3 1/7. Hugo von St. Viktor himself refers to his source Macrobius ("Commentary on Ciceros Somnium Scipionis ", XX, 16).
If these two quantities related to the earth had a good relation to reality, this cannot be said of the following distance earth-sun. The author adopts 4.82 million stages (on the order of 1 million km) from his ancient sources (including Macrobius, XX, 23) and is thus far removed from the astronomical unit . Since the sun circles around the earth in his view of the world, the circumference of this solar path can be calculated from the distance obtained. This value is related to the duration of the complete appearance of the solar disk above the horizon on the morning of the equinox and from this the diameter of the sun is determined (similar to Macrobius, XX, 26-31). Here, too, the author offers the alternative of using the diopter of an astrolabe to aim for the upper and lower edge of the sun.
Tradition and survival
The work has been handed down in numerous manuscripts. The Codex Paris Mazarine 717 (M) contains the text with several works by Hugo von St. Viktor. It was also compiled with the thematically matching texts of other authors, as in the Leiden Gronov 21 from the 12th century. a. with the Geometria of Gerbert d'Aurillac, a script by Hyginus Gromaticus and the Timaeus translation by Cicero .
In 1966 Roger Baron published a richly annotated edition of Practica geometriae . In 1991 a translation into the English language by Frederick A. Homann appeared. A translation into the German language is not available.
Text editions and translations
- Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PROPAEDEVTICA , Paris 1966
- Frederick A. Homann: PRACTICAL GEOMETRY, [Practica Geometriae] Attributed to Hugh of St. Victor , Milwaukee 1991
literature
- Nicolaus Bubnov: Gerberti Opera Mathematica , Berlin 1899
- Stephen K. Victor: Practical geometry in the high middle ages , Philadelphia 1979
Individual evidence
- ↑ Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PRODAEDEVTICA , Introduction, p. 4ff
- ↑ Frederick A. Homann: Practical Geometry , Introduction, p. 1
- ↑ Frederick A. Homann: Practical Geometry , Introduction, p. 17
- ↑ Stephen K. Victor: Practical geometry in the high middle ages , p. 3
- ↑ Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PROPAEDEVTICA , p 15 comments
- ↑ Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PROPAEDEVTICA , p 25 comments
- ↑ Frederick A. Homann: Ptactical Geometry , Appendix D.
- ↑ Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PROPAEDEVTICA , Introduction, p. 6f
- ↑ Roger Baron: HVGONIS DE SANCTO VICTORE OPERA PROPAEDEVTICA , Introduction, page 9