19
References and Notes, in Chronological Order
[1] Briggs, H., Logaritmorum ChHias Prima, London, 1617
[2] Gunter, E., Canon Triangulorum, sive Tabulae Sinuum et Tangentium
artificialium a Radium 10000.0000 ad scrupuia prime quadrantis, W. Jones,
London, 1620.
Note: Gunter introduced in his table the addition of the term 10 to all
trigonometrical logarithms (for example sin(30) -0.3010300 10 9.6989700),
a convention which has persisted until today although Gunter's original
justification is now lost: in the 17th century the sine value was proportional to the
radius of the circle enclosing the angle. As negative numbers were generally
disliked at the time, the radius was chosen to be 1010 (10.000.000.000) so that
all logarithmic values were increased by 10 and even the smallest trigonometrical
logarithm in a table ended up positive. This convention has made calculations on
combinations of numbers and trigonometrical functions less intuitive: when
mathematical notation progressed from proportional statements to more general
formulae, the logarithmic table manuals needed warnings to subtract always 10
from the logsine and other trigonometrical entries. For some reason Gunter put
the wrong radius value 108 (in stead of 1010) in his introductory text (which
generally went unnoticed).
[3] Briggs, H., Arithmetica Logarithmica, sive Logarithmorum Chiiiades Triginta,
Pro numeris natural! serie cescentibus ab unitate ad 20,000' et a 90,000 ad
100,000, W. Jones.
"Thus, if there is anyone, who wants to complete the gap between the
Twentieth and the Ninetieth Chiliads, and on the calculation of these, the
value of the work accomplished would itself be considered, to make me
sure that it had been carried out in a worthy manner; I will show him how
easy it is to add a Chiliad, lest the venture should fall by an ineffective
attempt; in the same way that another [Chiliad] be undertaken and
completed by someone else. I even have the paper, which has been
prepared with this end in sight, and with squares with distinct straight lines,
this I can carefully send. And when all the intervening space has been filled
up, I will give the work, if it has been done properly, to be printed again".
[4a] Decker, E. de, Eerste deel van de Nieuwe Telkonst, inhovdende verscheydene
manieren van rekenen, waer door seer licht konnen volbracht worden de
Geometrische ende Arithmetische Questien, with a promise for part II: the "Great
Table", P. Rammaseyn, Gouda, 1626.
[4b] Decker, E. de, Nieuwe Telkonst, inhoudende de logarithm! voor de ghetallen
beginnende van 1 tot 10000, ghemaeckt van HENRICO BRIGGIO Professor van de
geometrie tot Ocxfort. Mitsgaders de Tafel van Hoeckmaten ende Raeck/ijnen door
het ghebruyck van Logarithm!, de Wortel zijnde van 10000,0000 deeien, gemaeckt
van Edmund. Guntero, Professor vande Astronomie tot Londen, P. Rammaseyn,
Gouda, 1626 (published by De Decker together with the Nieuwe Telkonst I, again
with a promise for part II: the "Great Table").
