The construction of the wonderful canon of logarithms

1
8 Construction of the Canon.
2. Ofcontinuousprogressions, an arithmetical is one which
proceeds by equal intervals; a geometrical, one which
advances by unequal and proportionally increasing or
decreasing intervals.
Arithmetical progressions : i, 2, 3, 4, 5, 6, 7,
&c. ; or 2, 4, 6, 8, 10, 12, 14, 16, &c. Geometrical
progressions: i, 2, 4, 8, 16, 32, 64, &c. ; or 243,
81, 27, 9, 3, I.
3. /;« these progressions we require accuracy and ease in
working. Accuracy is obtained by taking large numbers
for a basis ; but large numbers are most easily made from
small by adding cyphers.
Thus instead of 1 00000, which the less experienced
make the greatest sine, the more learned
put 1 0000000, whereby the difference of all sines
is better expressed. Wherefore also we use the
same for radius and for the greatest of our geometrical
proportionals.
4. In computing tables, these large numbers may again be
made still larger by placing a period after the number and
adding cyphers.
Thus in commencing to compute, instead of
looooooo we put 1 0000000. 0000000, lest the most
minute error should become very large by frequent
multiplication.
5. In numbers distinguished thus by a period in their
midst, whatever is written after the period is a fraction,
the denominator of which is unity with as many cyphers
after it as there are figures after the period.
Thus 10000000.04 is the same as 1 0000000^;^ ;
also 25.803 is the same as 25x§^; also 9999998.
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