The construction of the wonderful canon of logarithms

12 Construction of the Canon.
easily which arise by subtraction of an easy part of the
number from the whole number.
14. We call easy parts of a number, any parts the denominators
of which are made up of unity and a number of
cyphers, such parts being obtained by rejecting as many of
the figures at the end of the principal number as there are
cyphers in the denominator.
Thus the tenth, hundredth, thousandth, loooo*,
1 00000* 1 000000* 1 0000000* parts are easily
obtained, because the tenth part of any number is
got by deleting its last figure, the hundredth its
last two, the thousandth its last three figures, and
so with the others, by always deleting as many of
the figures at the end as there are cyphers in the
denominator of the part. Thus the tenth part of
99321 is 9932, its hundredth part is 993, its thousandth
99, &c.
15. Tlie half twentieth, two hundredth, and other parts
denoted by the number two and cyphers, are also tolerably
easily obtained ; by rejecting as many of the figures at the
end of the principal number as there are cyphers in the
denominator, and dividing the remainder by two.
Thus the 2000* part of the number 9973218045
is 4986609, the 20000* part is 498660.
16. Hence itfollows that iffrom radius with seven cyphers
added you subtract its 1 0000000* part, and from the
number thence arising its 1 0000000* part, and so on, a
hundred numbers may very easily be continued geometrically
in the proportion subsisting between radius and the
sine less than it by unity, namely between 1 0000000 and
9999999 and this series of proportionals we name the
;
First table.
Thus