Napier's Circle.pdf

Napier's Circle

1. Napier’s Circle

2. John Napier
John Napier, a 16
th
Century
Scottish scholar,
contributed a host of
mathematical discoveries,
among them the world’s
first calculator.
John Napier (1550 – 1617)

3. He is credited with creating the first
computing machine, logarithms and was
the first to describe the systematic use of
the decimal point.
Other contributions include a mnemonic
for formulas used in solving spherical
triangles and two formulas known as
Napier's analogies.
“In computing tables, these large numbers may again be made
still larger by placing a period after the number and adding
ciphers. ... 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 ciphers after it as
there are figures after the period.”

4. RIGHT SPHERICAL TRIANGLE
a
c
b
B
A
C
a
b
co - A
co - c
co - B
Where:
co – A = complement of A
co – B = complement of B
co – c = complement of c
Napier’s Circle

5. NAPIER’S RULE
NR1: The sine of any middle part is equal to the
product of the tangents of the adjacent
parts.
SAM = PTAP
NR2: The sine of any middle part is equal to the
product of the cosines of the opposite
parts.
SAM = PCOP