Improvements in Draughtsman's Triangles.
Year: 1898

page_text: Date of Application, 12th Sept., 1898-Accepted, 10th Dec., 1898
CUMI DELL
Improvements in Draughtsman's Triangles.
I, FREDERICK ZIEGLER, of Erfurt, in the Empire of Germany, do hereby declare
the nature of this invention, and in what manner the same is to be performed, to
be particularly described and ascertained in and by the following statement:-
My invention relates to an improved draughtsman's triangle for the purpose of
readily producing and transferring given acute angles, which may require to be
frequently repeated in various positions, as for instance in the operations of drawing
and plotting plans projections, and cross sections; or of drawing isometrical
projections, or in many other cases for which trapezes and right angled triangles
have been heretofore employed in order to avoid marking out by the aid of compasses
and protractors.
When using such trapezes and right angled triangles a special appliance is
required for each occurring angle; moreover in view of the fact that it is frequently
necessary to mark out and fix the sum or the difference of these small angles, the
use of the auxiliary appliances above referred to is rendered inconvenient and
lengthy.
The present invention has for its object a triangle, by the use of which it is
possible to find and transfer in a very simple rapid and accurate manner three such
angles of which one always forms the sum or difference of the other two-and
also to find and transfer that angle which must supplement each one of the said
three angles in order to form one right angle.
In order that my invention may be clearly understood and readily carried into
effect I will now proceed to describe the same fully with reference
accompanying drawings.
to the
Referring to Figures 1 and 2, Sheet 1, the three angles def of the triangle a b c
are so constructed, that the difference between each two angles, lying on one and
the same side of the triangle, is equal to one of the angles to be constructed.
therefore the latter be indicated as y 2, we have:-
If
If such a differential triangle be laid with one side, for instance c (Sheet 1) on a
given line A B and if the side 6 be supported in this position by means of a stationary
rule, and if subsequently the triangle be so reversed, that the side a lies, a*, on the
rule, the side c obtains a new direction c*, which cuts the line A B at an
angle x = d = e. The angles y or z may be produced in a similar manner by
means of laying one of the sides a or b, as the case may be, on the given line A B
and proceeding as already described.
If required the differential angles x y z may also be constructed by a mere dis-
placement or shifting of the triangle without reversing it as aforesaid.
Thus, for example, referring to Figure 3 Sheet 1 in order to form the angle x, lay
the triangle with its side c on the given line A B and the rule on the side a of the
,

page_text: triangle then turn or shift the triangle x from the right to the left in the direction of
the arrow, so that the side c lies on the rule, c*; then the side b* cuts the given
line A B at the desired angle x = d - e.
For the purpose of producing the angles y and z, one proceeds in exactly the same
manner.
In order that it may be possible in practice to instantly recognize how the triangle
should be laid on the given line, in order to obtain the desired direction (right or
left or above or below the given line), lines and arrows are arranged and marked on
the three sides and upon the two surfaces of the triangles; each of these lines or
arrows is parallel to and so indicates the direction that will be taken by the line that
will be produced if the edge of the triangle to which it belongs is applied to the
known line. These said parallel lines and arrows thus indicate in advance, that is to
say, prior to the operation of reversing or shifting the triangle, as the case may be,
what will be the direction occupied by the crossing line (forming the angle with the
known line) after the reversal or shifting has taken place. On each arrow the angle
to be found or put out, is indicated in degrees or otherwise and also its trigonometric
tangent. Instead of the parallel lines and of the arrows, any other suitable sign
may be provided.
Examples of the use of the difference triangles are shown in Figures 8 and 9
Sheet 1. The triangular forms Nos. 1 to 10 given on Sheet 2 contain the angular
proportions used by the railway administrations in most civilised states.
In Figures 4 and 5 Sheet 1 and Figures 5 and 6 Sheet 2 are shown triangles
having equal differential angles (x) on the sides b and c and the double angle (2 a)
on the third side a
These triangles serve for the special purpose of turning the differential angle x twice
out of the given line-either in one or both directions without altering the position
of the rule. They are therefore adapted mainly for the purpose of very conveniently
and accurately constructing the axes of the one-sided and two-sided double switches
and double-curve-switches for permanent ways.
For the purpose of designing the one-sided double switch, lay the one side with the
'simple angle x, for instance the side c (Figure 4 Sheet 1), on the given line A B, and
the rule on the side a, with the double angle 2a. Then turn the triangle from the
right to the left in such a manner, that the given line A B is first cut by the side b*
at the simple angle (x) and, on further turning, by the side a* of the double
angle (2x).
―
For the purpose of designing the two sided double switch, one of the two sides
with the simple angle (a), for instance the side c (Figure 5 Sheet 1) is laid on the
given line A B, but the rule, instead of being laid on the side a with the double
angle (2x) as in the preceding case is laid. on the side b with the simple angle (x).
Upon turning the triangle from right to left, the line A B is first cut at
the angle x d e branching off from the side a* to the right, and on further
turning the triangle, the line A B is cut by the side b* at the angle x = ƒ − d,
-branching off to the left.
Referring to the right angled triangle shown in Figures 1 to 4 Sheet 2 and
Figures 6 and 7 Sheet 1 (by the aid of which only one differential angle -x-
(tangent and its angle 90° x (tangent = 1: 1), forming together one right
1
n
22'
-
-
angle can be constructed) this can be manipulated in either of the following
ways:-
1. By turning or shifting. Lay the triangle first as shown in Figure 6 (Sheet 1),
with its hypotenuse c on the given line A B, and the rule on the adjacent line a, then
turn the triangle from right to left, as already described, until the hypotenuse lies

page_text: against the rule.
Then the line A B is cut by the adjacent side b* at an
angle x = = d e and simultaneously by the adjacent line a* at an angle 90° 1 x
these two angles together forming a right angle.
2. By reversing.
If, as shown in Figure 7 Sheet 1, the side a adjacent to the hypotenuse, is laid on
the given line A B, and the rule is laid on the hypotenuse c, the desired result is
only obtained by "reversing" the triangle (in the manner first described), so that
the hypotenuse is again located on the rule, the position being such, that the side b*
cuts the line A B at an angle x = =d- e, whilst simultaneously the side a* together
with the line A B forms the angle 90° x, the tangent of which forms the reciprocal
value of that is to say = 1:
n
1
n
-
In the employment of the oblique angled triangles for instance of slope-triangles,
such as shown in Figures 9 and 10 of the Sheet 2, the angles which supplement that
of the triangle to form a right angle are constructed by the aid of any right
angled triangle.
If it is desired, that the branched off line be of as large an extent as possible, it is
preferable to use the hypotenuse to produce the angle x according to the first described
method ("reversing," see Figure 2 Sheet 1).
Having now particularly described and ascertained the nature of my said inven-
tion and in what manner the same is to be performed, I declare that what I
claim is:-
1. A draughtsman's triangle so constructed that the difference between each two
of its angles lying on one and the same side of the triangle is equal to a given acute
angle, for the purpose specified.
2. The draughtsman's triangle above referred to, having guiding signs marked
and arranged on its three sides and on both surfaces thereof, for the purpose
specified.
3. Draughtsman's triangles constructed and operating substantially as herein before
described with reference to the accompanying drawings, for the purpose
specified.
HASELTINE, LAKE & Co.,
45, Southampton Buildings, London, W.C., Agents for the Applicant.