The construction of the wonderful canon of logarithms

Notes. 85
On some Terms made use of in the Original Work.
Napier's Canon or Table of Logarithms does not contain the
logarithms of equidifferent numbers, but of sines of equidifferent arcs
for every minute in the quadrant. A specimen page of the Table is
given in the Catalogue under the 1614 edition of the Descriptio.
The sine of the Quadrant or Radius, which he calls Sinus Totus, was
assumed to have the value 1 0000000.
Numerus Artificialis, or simply Artifidalis, is used in the body of the
Constructio for Logarithm, the number corresponding to the logarithm
being called NumefTis Naturalis.
Logarithmus, corresponding to which Numerus Vulgaris is used, is
however employed in the title-page and headings of the Constructio, and
in the Appendix and following papers. It is also used throughout the
Descriptio published in
1614; and as the word was not invented till
several years after the completion of the Constructio (see the second
page of the Preface, line 12), the latter must have been written some
years prior to 16 14.
For shortness, Napier sometimes uses the expression logarithm
arc for the logarithm of the sine of an arc.
of an
The Antilogarithm of an arc, meaning log. sine complement of arc,
and the Differential of an arc, meaning log. tangent of arc (see Descriptio,
Bk. I., chap, iii.), are terms used in the original, but as they
have a different signification in modern mathematics, we do not use
them in the translation.
Prosthapharesis was a term in common use at
the beginning of the
seventeenth century, and is twice employed by Napier in the Spherical
Trigonometry of the Constructio as well as in the Descriptio. The
following short extract from Mr Glaisher's article on Napier, in the
'
Encyclopedia Britannica,' indicates the nature of this method of
calculation.
The ' ' new invention in Denmark " to which Anthony Wood refers as having
given the hint to Napier was probably the method of calculation called
prosthaphaeresis (often written in Greek letters irpotrOaipaipetns), which had its
origin in the solution of spherical triangles. The method consists in the use of
the formula sin a sin 6 = ^ {cos {a-b)- cos (a + b)}, by means of which the multiplication
of two sines is reduced to the addition or subtraction of two tabular
results taken from a table of sines ; and as such products occur in the solution