The construction of the wonderful canon of logarithms

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Construction of the Canon.
less of the other, and the greater of the one to
of the other.
Thus let the
j,
line a b c \>&
divided into two
parts, a b and b c.
a-
the greater
Let a b lie between the limits
123.5 the greater and 123.2 the less. Also let b c
lie between the limits 43.2 the greater and 43.1
the less. Then the greater being added to the
greater and the less to the less, the whole line a c
will lie between the limits 166.7 ^^^ 166,3,
The two limits of one quantity are multiplied into the
two limits of another, when the less of the one is multiplied
into the less of the other, and the greater of the one into
the greater of the other.
^ ^ Thus let one of the quantities a b lie
between the limits 10.502 the greater
and 10.500 the less. And let the other
a c lie between the limits 3.216 the
greater and 3.215 the less. Then 10.502
being multiplied into 3.216 and 10.500
into 3.215, the limits will become
33.774432 and 33.757500, between which the area
oi a b c d will lie.
10. Subtraction of limits is performed by taking the greater
limit of the less quantity from the less of the greater, and
the less limit of the less quantity from the greater of the
greater.
Thus, in the first figure, if from the limits of a c,
which are 166.7 and 166.3, you subtract the limits
oi b c, which are 43.2 and 43.1, the limits of « ^
become 123.6 and 123.1, and not 123.5 ^"^^ 123,2,
For although the addition of the latter to 43.2
and