Book, Tafel der Viertel-Quadrate

Book, Tafel der Viertel-Quadrate

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Before the widespread availability of electronic calculators, scientists, engineers, and businessmen relied on a variety of printed mathematical tables. For multiplication, some used books like this one, which lists the quarter squares of all whole numbers from 1 to 200000 (perhaps 1 to 199,000). The product of two numbers a and b can be written:
ab = ¼ ( (a+b)^2 – (a-b)^2) = ¼ (a+b)^2 – ¼ (a-b)^2.
The two quantities in the last equation are what one would look up in the table.
Published tables of quarter squares date at least to 1817, when Antoine Voisin in Paris and J.A.P. Bűrger in Zurich presented works on the subjects. They were soon followed by John Leslie in Edinburgh.
Joseph Blater’s first published tables of this sort are represented by this volume from 1887. The book was translated into French and into English the following year.
This example of Blater’s tables was owned by the German- American statistician, mathematician and computer pioneer Carl Hammer (1914-2004).
Denis Roegel. A Reconstruction of Blater’s Table of Quarter-squares (1887). [Research Report] 2013.
Trűbner & Company Monthly List, vol. 13, #12, December, 1889, p. 163. This, and several earlier issues of the listing, announces the English edition. This page also has an extract from a review of the book by J.W. L. Glaisher.
Currently not on view
Object Name
date made
Blater, Joseph
place made
Austria: Vienna state
Physical Description
paper (overall material)
overall: 2 cm x 26 cm x 31.7 cm; 25/32 in x 10 1/4 in x 12 15/32 in
ID Number
nonaccession number
catalog number
Credit Line
Gift of Carl Hammer
See more items in
Medicine and Science: Mathematics
Mathematical Charts and Tables
Data Source
National Museum of American History
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