In his address to King Charles I, in his Grammelogia I, Delamain emphasizes
the ease of operating with his slide rule by stating that it is “fit for
use . . . as well on Horse backe as on Foot.” Speaking “To the Reader,” he
states that he has “for many yeares taught the Mathematicks in this Towne,”
and made efforts to improve Gunter’s scale “by some Motion, so that the
whole body of Logarithmes might move proportionally the one to the other,
as occasion required. This conceit in February last [1629] I struke upon,
and so composed my Grammelogia or Mathematicall Ring; by which only with an
ocular inspection, there is had at one instant all proportionalls through
the said body of Numbers.” He dates his preface “first of January, 1630.”
The fifth and sixth pages contain his “Description of the Grammelogia,” the
term Grammelogia being applied to the instrument, as well as to the book.
His description is as follows:
The parts of the Instrument are two Circles, the one moveable, and the
other fixed; The moveable is that unto which is fastened a small pin to
move it by; the other Circle may be conceived to be fixed; The
circumference of the moveable Circle is divided into unequall parts,
charactered with figures thus, 1. 2. 3. 4. 5. 6. 7. 8. 9. these figures
doe represent themselves, or such numbers unto which a Cipher or Ciphers
are added, and are varied as the occasion falls out in the speech of
Numbers, so 1. stands for 1. or 10. or 100., &c. the 2. stands for 2. or
20. or 200. or 2000., &c. the 3. stands for 30. or 300. or 3000., &c.
After elaborating this last point and explaining the decimal subdivisions
on the scales of the movable circle, he says that “the numbers and
divisions on the fixed Circle, are the very same that the moveable are, .
.” There is no drawing of the slide rule in this publication. The
twenty-two numbered pages give explanations of the various uses to which
the instrument can be put: “How to performe the Golden Rule” (pp. 1-3),
“Further uses of the Golden Rule” (pp. 4-6), “Notions or Principles
touching the disposing or ordering of the Numbers in the Golden Rule in
their true places upon the Grammelogia” (pp. 7-11), “How to divide one
number by another” (pp. 12, 13), “to multiply one Number by another” (pp.
14, 15), “To find Numbers in continuall proportion” (pp. 16, 17), “How to
extract the Square Root,” “How to extract the Cubicke Root” (pp. 18-21),
“How to performe the Golden Rule” (the rule of proportion) is explained
thus:
Seeke the first number in the moveable, and bring it to the second number
in the fixed, so right against the third number in the moveable, is the
answer in the fixed.
If the Interest of 100. li. be 8. li. in the yeare, what is the Interest
of 65. li. for the same time.
Bring 100. in the moveable to 8. in the fixed, so right against 65. in
the moveable is 5.2. in the fixed, and so much is the Interest of 65. li.
for the yeare at 8. li. for 100. li. per annum.
The Instrument not removed, you may at one instant right against any
summe of money in the moveable, see the Interest thereof in the fixed:
the reason of this is from the Definition of Logarithmes.
These are the earliest known printed instructions on the use of a slide
rule. It will be noticed that the description of the instrument at the
opening makes no references to logarithmic lines for the trigonometric
functions; only the line of numbers is given. Yet the title-page promised
the “resolution of Plaine and Sphericall Triangles.” Page 22 throws light
upon this matter:
If there be composed three Circles of equal thicknesse, A.B.C. so that
the inner edge of D [should be B] and the outward edge of A bee
answerably graduated with Logarithmall signes [sines], and the outward
edge of B and the inner edge of A with Logarithmes; and then on the
backside be graduated the Logarithmall Tangents, and againe the
Logarithmall signes oppositly to the former graduations, it shall be
fitted for the resolution of Plaine and Sphericall Triangles.
After twelve lines of further remarks on this point he adds:
Hence from the forme, I have called it a Ring, and Grammelogia by
annoligie of a Lineary speech; which Ring, if it were projected in the
convex unto two yards Diameter, or thereabouts, and the line Decupled, it
would worke Trigonometrie unto seconds, and give proportionall numbers
unto six places only by an ocular inspection, which would compendiate
Astronomicall calculations, and be sufficient for the Prosthaphaeresis of
the Motions: But of this as God shall give life and ability to health and
time.
The unnumbered page following page 22 contains the patent and copyright on
the instrument and book:
Whereas Richard Delamain, Teacher of Mathematicks, hath presented vnto Vs
an Instrument called Grammelogia, or The Mathematicall Ring, together
with a Booke so intituled, expressing the use thereof, being his owne
Invention; we of our Gracious and Princely favour have granted unto the
said Richard Delamain and his Assignes, Privilege, Licence, and
Authority, for the sole Making, Printing and Selling of the said
Instrument and Booke: straightly forbidding any other to Make, Imprint,
or Sell, or cause to be Made, or Imprinted, or Sold, the said Instrument
or Booke within any our Dominions, during the space of ten yeares next
ensuing the date hereof, upon paine of Our high displeasure. Given under
our hand and Signet at our Palace of Westminster, the fourth day of
January, in the sixth yeare of our Raigne.