The Pythagorean Theorem, Plane Triangles and Sixteenth-century Gauging Rods

Meskens, Ad

doi:10.1093/teamat/11.2.83

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“…To simplify the calculations, a quadratic scale of graduations was etched on the gauging rod; i.e., the numbers 1, 4, 9 ..... n 2 were written at the 1st, 2nd, 3rd, depth points which were not perfect squares were constructed either geometrically using the Pythagorean theorem [15] or algebraically using a table. 2 To avoid multiplication of length and depth, a so-called change rod (Fig.…”

Section: Measuring Practice In the 16th Centurymentioning

confidence: 99%

“…In 1551, for example, the beer excise accounted for 44% of the total, with wine bringing in 25%. In the second half of the 16th century, the share of the wine excise dropped to 15% [7,[15][16]. These relative figures obscure the fact that during the last quarter of the 16th century, the income from the beer excise dropped by nearly one third, from 3,174,054 to 2,158,722 Brabant groats [26,521].…”

Section: Antwerp and The Wine Tradementioning

confidence: 99%

“…Most likely this implies the use of some kind of quadratic rod. The subdivisions on a quadratic rod, for which the square roots of the natural numbers have to be found, are easily constructed using the Pythagorean theorem [15]. Nevertheless tables giving square roots to three decimal places existed, so that the subdivisions could also have been found by simple measurement.…”

Section: Testing For a New Gaugermentioning

confidence: 99%

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Wine gauging in late 16th- and early 17th-century antwerp

Meskens¹

1994

Historia Mathematica

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Renaissance European cities imposed an excise on wine and beer. Wine gaugers were employed to measure the contents of barrels. Antwerp was no exception. It organized competitions to appoint new gaugers. Results of two such competitions are given and show that the results for full barrels were satisfactory. It is also shown that the gaugers' remuneration was not very high, since, most probably, they regarded gauging as a source of extra income. Despite the fact that competitions were held, doubts about the competence of gaugers remained. Some gaugers, Michiel Coignet among them, tried to improve measuring practices. In a second section it is demonstrated, using three approximations for barrels and using infinitesimal calculus, that the gaugers' formula for calculating the volume of a barrel yielded results which were presumably within the measuring errors. This is not the case for their formula for partly filled barrels. © 1994 Academic Press, Inc.In de Renaissance hieven de steden een accijns op wijn en bier. Om de inhoud van de wijnvaten te meten werden wijnroeiers in dienst genomen. Antwerpen was hierop geen uitzondering. Het organiseerde wedstrijden om nieuwe wijnroeiers aan te werven. De resultaten van twee zulke wedstrijden worden besproken en tonen aan dat de metingen voor voile vaten bevredigend waren. Er wordt aangetoond dat het loon van de roeiers laag was zodat ze het waarschijnlijk als bijverdienste beschouwden. Ondanks het feit dat er wedstrijden georganiseerd werden, bleef er twijfel over hun competentie bestaan. Sommige wijnroeiers, zoals Michiel Coignet, probeerden de roeimethoden te verbeteren. In een tweede deel zal aangetoond worden, door gebruik te maken van drie benaderingen, dat de meetresultaten meestal binnen de meetfout lagen. Dit was niet het geval voor gedeeltelijk gevulde tonnen. © 1994 Academic Press, Inc.

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Section: Measuring Practice In the 16th Centurymentioning

confidence: 99%

Section: Antwerp and The Wine Tradementioning

confidence: 99%

Section: Testing For a New Gaugermentioning

confidence: 99%

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