Budapest Régiségei 30. (1993)

TÁRGYI EMLÉKEK ÉS LELETEK = DENKMÄLER UND FUNDE - Madarassy Orsolya: Tabula gromatici az aquincumi canabaeból 297-315

Following this logic, the last circle may be labelled as Thulé (Figure 2). These attributes suggest that the instrument was made following the works of Strabo and Vitruvius, so that is the earliest time it could have been manufactured was the first half of the 1st century A. D. The entire cross-section of mathematics, geography and astronomy in Antiquity is presented in the works of Claudius Ptolemaios (approximately A. D. 160; Map 2).

12 When the "B" side of this fragment is compared to the data produced by Ptolemaios , the following observations can be made: 1) Ptolemaios reported latitudes in terms of degrees, minutes and seconds. This accuracy is based on a theoretical mathematical calculation which estimates the proportion between the angle and circle's diameter with deviations of 0,5°. The precision of this Antique circular function table, also known as a table of chords, is not based on the accuracy of real measurement data but results from a series of square root calculations. 2) The logic followed in the division of clima declinations by Ptolemaios is based on the changing proportions between days and nights during the time spans between the summer solstice and winter solstice. Consequently, after the traditional Meroe - Syene Alexandria - Rhodos - Athens line, the Ptolemaian latitudes follow a system differing from that of the fragment analyzed in this study. 3) Ptolemaios marked the various latitudes by geographical concepts rather than city names. Since the logic of this instrument differs from the inner logic of works by Ptolemaios, its manufacturing must be dated to times preceding his activities. In light of these observations the terminus post quern for this artifact is later than the works of Strabo and Vitruvius (early A. D. 1st century). The terminus ante quern dating for this artifact, on the other hand, precedes subsequent research carried out by Ptolemaios (60's of the 2nd century). inscription No. CIL XIII

11173 is worth considering when attempting the functional interpretation of this artifact. It may be found on the B side of a bronze disc denoting the geographical latitudes of provinces (?). The Equator, that is the equinox line, was drawn on the A side. The markings of the winter and summer solstice form a 24° angle with this line, while the outher circle is subdivided by a 90° set of incisions (Figure 3). A similar bifacial bronze disk was published by Jean Luc Massy in the 1985 volume of Gallia (Figure 4). Three quarters of that artifact is covered by the latitudinal data from provinces or geographical units, while a horologium is located in the upper section of the disk, which was constructed exploiting the sun dial principle of a shadow as is shown by the markings of clima-declinatio and months. When side "A" of the Aquincum marble plate is projected onto this horologium it becomes possible to interpret these angles: a monthly sub-division becomes apparent within the ecliptic angle (Figure 5). When the aforementioned sources are studied from a conceptual rather than a chronological point of view, it may be concluded that while Ptolemaios summarized the theory of science history available at the time, Vitruvius as a specialist, laid emphasis on practical applications. In the case of the sun dial's design it is very clear that Vitruvius presents a simple, sketchy figure while the same problem is tackled by Ptolemaios using detailed mathematical descriptions and by projecting a spherical surface onto a plane. In light of this observation it is not difficult to identify the straight line on side "A" as the extension of a "theoretical" gnomon, which is joined by the ecliptic angle at its two ends. The inner divisions therefore correspond to months, while the basic circle represents the celestial meridian. A 10° division occurs between the two inner arches of the external circles. Although the next such division falls near the fracture line, it may be assumed that similar, 10° divisions occurred in the next, missing section as well. On the basis of CIL XIII 11173 the X C incision may be interpreted as the sum of 2 angles within that section. When this arch on the fragment is extended into a rectangle, the next incision may be completed as [L] XXX. Since the base line is not finished beyond the 2 divisions, one may hypothesize that another arch with even finer subdivisions was drawn on the section which was broken off and lost (Figure 6), Consequently, it was the basic data of the analemma which were incised on side "A". These included subdivisions by year (Radius 5: equinoxes, Radii 2 and 8: solstices) and by month (Radii 3, 4 and 6, 7). In addition, a compass may be recognized which is of help in constructing finer divisions (days, hours). In addition to the auxiliary sketch incised when this marble instrument was manufactured, additional construction lines were drawn across its surface during subsequent use. In addition to the angle between the straight line (Radius 9) and the vertical line of the gnomon, the angle between this line and the horizon (47,5°) should also be considered. This latter angle corresponds to the geographical latitude of Aquincum. Using this particular information and the basic design, a local horologium can be constructed for Aquincum. Two additional arches also appear on side "A". These markings were probably left by a bronze compass. The length of the chord corresponding to 90° in one of the inner circles (meridian) equals the length of the radius that belongs to the circle connecting the 10° and 2° incisions. The other chord originates from the intersection point between the Aquincum auxiliary line and the median circle. Its length corresponds to the geographical latitude of Aquincum as marked on side "B". 303