greetings! what follows is a minor addition to a recent posting and a
request for help.
-- Leibniz' calculemus
concerning recent postings on "leibniz' dream" to solve all disputes by
calculating let me add, that his dream -- in a way -- can be seen as having
a biographical background. he reports in a letter to gabriel wagner in GP
7, 514-527, here: 522, that once he had a dispute with a colleague which
was quite frustating and full of mutual misunderstanding until they
switched to an exchange in a rigorous syllogistic form ("we carried it to
the 12th prosyllogism and beyond").
-- method of trial and error/ method of double position
maybe someone on the list can help me with this.
charles hutton desribes in his "a course of mathematics" (11ed. London
1836) a method of solving equations in one variable by an approximation
method called by him "method of trial and error" or "method of double
position". the rules he actually states are due to bonnycastle's
"arithmetic" from 1810.
(one procceds like this: simply choose/guess, by TRIAL, two approximate
solutions to the equation in question, substitute these values for the
variable, calcute the equation, and then use the ERROR in excess or defect
for an algorithm that gives you a better approximation than the former one.
repeat until you've reached an accurate enough solution.)
an accompanying footnote by the editor of the 11th edition, olinthus
gregory, says that one can find a history of this method in g. peacocke's
"treatise on arithmetic" in the encyclopedia metropolitana. since i have
difficulties in getting peacocke's booklet via inter-library loan and
because i havn't found the keywords "method of trial and error/method of
double position" in the history of math books at hand my question is
whether someone on this list has a clue for me concerning (i) the history
of this method (e.g., its relation to babylonian, diophantian etc. regulae
falsi) and, especially, (ii) concerning the name for this method.
best, bb
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Bernd Buldt
FG Philosophie
Universitaet Konstanz
D-78457 Konstanz
Germany
Fon: [+49] (0)7531/88-2794 (Office)
Fax: [+49] (0)7531/88-4121
Fon/Fax:[+49] (0)7731/24116 (Private)
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