AN IMPROVED GEOMETRICAL INSTRUMENT
Year: 1879

page_text: LETTERS PATENT to Louis Pierre Matton, Passage Gai, Fourvières, of Lyons,
in the Republic of France, for the Invention of "AN IMPROVED GEOMETRICAL
INSTRUMENT."
Sealed the 16th March 1880, and dated the 19th September 1879.
PROVISIONAL SPECIFICATION left by the said Louis Pierre Matton at the
Office of the Commissioners of Patents on the 19th September 1879.
LOUIS PIERRE MATTON, Passage Gai, Fourvières, of Lyons, in the Republic of
"AN IMPROVED GEOMETRICAL INSTRUMENT,"
France.
In making geometrical drawings it often becomes necessary to divide with
When divisions
exactitude given arcs or segments of circles into several parts.
into equal numbers are required the ordinary method, although somewhat long,
gives definite and exact results; but when it is necessary to divide into odd
numbers the method ceases, suppositions take its place, and the results are often
imperfect unless very great care is exercised by the draughtsman.
Hitherto no technical work has given a method for obtaining a division in odd
number of any kind of arc or angle (the trisectrix even has not been found), and it
is to meet this want in a general way that I have combined the instrument which
forms the subject of this Invention.
My instrument will be easily understood by reference to the accompanying Sheet
of Drawing.
At Figure 1 it is represented annexed to an ordinary protractor in order to
permit the valuation of the angle at the same time as its division.
Figure 2 shows the manner of using the instrument.
Whatever is stated with regard to the division of the arcs applies equally to that
of the angles measured by the said axes.
My improved instrument is in the form of a semi-circle cut out, as shown by the
nonshaded parts of the Drawing.
The part F, D, is a rule against which the instrument is applied; the shaded
part comprised within the semi-circumference M, B, N, of the instrument
presents three or more curves with fixed invariable centres and radii,
These curves and their radii possess the following properties :-
An arc of any kind C, A, E, taken or brought upon the circumference M, A, N,

page_text: being divided into two equal parts by the diameter A, B, will be divided by the aid
of the instrument into three, five, seven, or more equal parts by means of the
curves H, K, (trisectrix), G, L, (quintisectrix), X, Z, (septisectrix), and so on, by the
hereinafter described process, which necessitates no other graphical drawing than
the junction of the points C and E of the arc C, A, E, with the extremity B of the
diameter A, B, by the straight lines C, B, and E, B.
The chord of the arc P, S, limited by the intersection of these straight lines with
the curve H, K, will be exactly the chord of the arc C, A, E, (trisectrix). The
chord of the arc T, R, limited by the intersection of the same straight lines with
the curve G, L, will be the chord of the exact fifth of the arc C, A, E, (quintisectrix),
and the chord of the arc U, V, limited by the intersection of the said straight lines
with the curve X, Z, will be the exact chord of the seventh of the arc C, A, E,
(septisectrix) and so on.
It will be easily understood that whatever may be the extent of the arc or of the
angle to be divided the operation will all ways be effected in the same way, and
that it is sufficient when the instrument is of small dimensions to reduce the exten-
sion of the are concentrically in order to measure and divide it, because the angle
to be measured will not have changed its value. For this purpose it is only neces-
sary to draw the given lines and to extend them until they meet the given arc.
My instrument is therefore an instrument which will be very useful in the major
part of geometrical drawings, and should find its place in every box of mathematical
instruments.
I may make it of metal, ivory, wood, horn, vulcanized or hardened india-rubber,
or any other suitable strong material, and of any dimensions.
My instrument may be arranged for the division of arcs and angles into
4, 8, 10, 12, 14, and so on, and generally into any number of parts, odd or even, as
may be regarded.
The curves of my instrument have also the remarkable property of determining
the sides of polygons.

page_text: SPECIFICATION in pursuance of the conditions of the Letters Patent filed by
the said Louis Pierre Matton in the Great Seal Patent Office on the 16th
March 1880.
LOUIS PIERRE MATTON, Passage Gai, Fourvières, of Lyons, in the Republic of
France. "AN IMPROVED GEOMETRICAL INSTRUMENT."
In making geometrical drawings it often becomes necessary to divide with
exactitude given arcs or segments of circles into equal parts. When divisions into
equal numbers are required the ordinary method although somewhat long gives
definite and exact results, but when it is necessary to divide into odd numbers the
method ceases, suppositions take its place, and the results are often imperfect unless
very great care is exercised by the draughtsman.
Hitherto no technical skill has given a method for obtaining a division in odd
number of any kind of arc or angle (the trisectrix even has not been found), and
it is to meet this want in a general way that I have combined the instrument
which forms the subject of this Invention.
My instrument will be easily understood by reference to the accompanying Sheet
of Drawing.
At Figure 1 it is represented annexed to an ordinary protractor in order to
permit the valuation of the angle at the same time, as its division.
Figure 2 shows the manner of using the instrument.
Whatever is stated with regard to the division of the arcs applies equally to that
of the angles measured by the said axes.
My improved instrument is in the form of a semi-circle cut out, as shown by
the non-shaded parts of the Drawing.
The part F, D, is a rule against which the instrument is applied; the shaded
part comprised within the semi-circumference M, B, N, presents three or more
curves with fixed invariable centres and radii. These curves and their radii possess
the following properties:-
An arc of any kind C, A, E, taken or brought upon the circumference M, A, N,
being divided into two equal parts by the diameter A, B, will be divided by the
aid of my instrument into three, five, seven, or more equal parts by means of the
curves H, K, (trisectrix), G, L, (quintisectrix), X, Z, (septisectrix), and so on, by
the hereinafter described process, which necessitates no other graphical drawing
than the junction of the points C and E of the arc C, A, E, with the extremity B of
the diameter A, B, by the lines C, B, and E, B.
The chord of the arc P, S, limited by the intersection of these lines C, B, with
the curve H, K, will be exactly the chord of the arc C, A, E, (trisectrix). The
chord of the arc T, R, limited by the intersection of the same lines C, B, with the
curve G, L, will be the chord of the exact fifth of the arc C, A, E, (quintisectrix),
and the chord of the arc U, V, limited by the intersection of the lines C, B, with
the curve X, Z, will be the exact chord of the seventh of the arc C, A, E, (septi-
sectrix), and so on.
It will be easily understood that whatever may be the extent of the arc or of the
angle to be divided the operation will always be effected in the same way, and that
it is sufficient when my instrument is of small dimensions to reduce the extension
of the are concentriccally in order to measure and divide it, because the angle to be
measured will not have changed its value. For this purpose it is only necessary to
draw the given lines and to extend them until they meet the given arc.
My improved instrument will therefore be very useful in the major part of
geometrical drawings, and should find its place in every box of mathematical
instruments.
I may make it of metal, ivory, wood, horn, vulcanized or hardened india rubber,
or any other suitable strong material, and of any dimensions.

page_text: My improved instrument may be arranged for the division of arcs and angles into
4, 8, 10, 12, 14, and so on, and generally into any number of parts, odd or even,
as may be required.
The curves of my instrument have also the remarkable property of determining
the sides of polygons.
Having now described and ascertained the nature of my said Invention, and in
what manner the same is or may be performed,
I claim as secured to me by the hereinbefore in part recited Letters Patent,-
The use of an improved geometrical instrument, combined and arranged to
operate substantially as and for the purposes herein before set forth.
In witness whereof, I, the said Louis Pierre Matton, have hereunto set my
hand and seal, this Ninth day of March, in the year of our Lord One
thousand eight hundred and eighty.
Signed, in my presence, by the
above written L. P Matton,
this Ninth day of March, One
thousand eight hundred and
eighty, at Lyons, in the
Republic of France.
CHARLES S. HADEN,
H.B.M. Vice Consul,
L. P. MATTON. (L.S.)