An Improved Apparatus for use in Teaching Arithmetic.
Year: 1889

page_text: Date of Application, 15th Feb., 1889
Complete Specification Left. 21st Oct., 1889-Accepted, 7th Dec., 1889
PROVISIONAL SPECIFICATION.
An Improved Apparatus for use in Teaching Arithmetic.
We, KARL SCHULTE, teacher and ERNST AUG UST BOSIES, mechanical engineer,
both of Lüdenschoid, Westfalia Germany do hereby declare the nature of this invention
to be as follows :-
Our improved instrument for teaching arithmetic has for its object :
1) to serve the pupil as a means to control his problems and for exercise ;
2) to serve the teacher for demonstrating in synthesis and analysis addition,
multiplication and division;
3) to serve the teacher, without fatigating his voice, for exercising quickly with his
pupils, giving them the control over the answers to the questions asked.
On the accompanying drawing the instrument is represented.
Fig. I is a plan view of the outside;
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II section in the line of the bars;
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III is partly an outside view, partly a cross section of fig. I ;
IV a plan view, the cover taken off;
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V "", cross section of fig. 1V without the slides ;
VI longitudinal section through fig. IV.
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The instrument consists of a case A B C D closed at three sides and partly open at
the fourth side CD. Horizontal bars E, E. of same height as the sides divide the case
in a number of compartments F. In each of these compartments or cells fits a
slide G; the slides are a little longer than the compartments, and their projecting ends
are provided with a knop or button H, by means of which they can be conveniently
pulled forwards and backwards.
Each slide is provided with a little hole 1 near its inner end and corresponding holes M
are bored in the cover of the case so that a pin K can be put through both to
hold the slide fast. Instead of the hole in the slides long slits L may be cut
in them as shown by fig. 1.
The cover of the case is divided in a similar manner as the case by horizontal
lines and also by vertical lines of equal distance from each other, and in the square
fields thus received ciphers are written, namely in the upper horizontal row, exepting
the first square, the natural order of numbers 1, 2, 3 .
11.
The left or first vertical row of squares is left free; in the second horizontal row
of squares the cipher I is written in each field; in the third row the cipher 2; in the
fourth 3 etc. It follows thus that each vertical row, leaving out the upper fields
contains also the natural scale of numbers 1, 2, 3 .
Now the slides are divided vertically in the same manner as the cover O and each
field of the slide contains that number which is the produce of the multiplication of
one of the numbers in the first horizontal row-the multiplicators-with the number
in the fields of the corresponding row-t
-the multiplicands-above the respective slide
on the cover.
It follows from this that if a slide is pulled forwards and held in a certain field by
inserting the pin K, the last number visible on the slide must be the produce of the
number in the upper horizontal row and the respective number vertically below the
first in the field of the cover over the slide which has been drawn and fixed by
the pin.
By this arrangement it will be easily understood how addition, multiplication and
division can be taught with our instrument. Let us for instance show how to find the
product of 7x2=14?
In the row of squares containing the multiplicands 2 the teacher inserts the pin K
into the hole of that field which is vertically below the field in the upper row containing

page_text: the multiplicator 7., and then he draws the slide which will be caught by the pin,
and the last number then visible on the slide will be 14.
In order to show that the multiplication is merely an abbreviated addition, that for
instance 30 is composed of times 6, the teachier proceeds as follows: In that of the
horizontal fields containing the multiplicands 6 the teacher marks the one which is
below the square containing the multiplicator 5 in the upper row, then he
gradually inserts the pin, beginning at the left, into the holes of all the squares
of the multiplicand and draws the slide every time until the 5th field thus showing
that 1×6=6; 2x6 or 6+6-12; +6 or 6+6+6=3x6=18; +6 or 16+66+6=
4×6=24; +6 or 6+6+6+6+6=5×6=30.
In a similar manner the teacher proceeds to explain the division.
How often is 6 contained .in 30? 5 times! for-5 times the slide below the row
containing the 6 can be shifted from square to square inwards .if 30 was the 'last
visible figure on it, until the remainder is 0.
Dated this 11th day of February 1889.
"KARLI. MAYER,
Agent for Applicants.
COMPLETE SPECIFICATION.
An Improved Apparatus for use in Teaching Arithmetic.
We, KARL SCHULTE, teacher and ERNST. AUGUST.BOSIES, mechanical engineer, both
of Lüdenscheid Westalia, Germany do hereby declare the nature of tliis invention.and
in what manner the same is to be performed, to be particularly described and
ascertained in and by.the following statement :-
The present invention has for its object::
1) to serve the pupil.as a means to control this problems and for exercise;
2) to serve the teacher for demonstrating in synthesis and tanalysis..to the,pupil
addition, multiplication and division ;
3) to serve the teacher without fatigating his voice for exercising, (quickly with .his
pupils, giving themselves the control over the answers to the questions asked.
On the annexed drawing the instrument is represented.
Fig: Iis a plan view of the outside.;
Fig. ista section tint the: line of the division bars;
Fig. IIIis: partly an outside view and partlya.cross section of-fig..I.;
Fig. IV is a plan view, the covertaken off
Fig. Visa cross section through the case fig..IV without the slides ;;
Fig. VI is a longitudinal section through fig. IV.
The apparatus consists of a case A.B.CD closed at three sides and partly open
at the fourth side. Horizontal bars E E of same height as the sides divide the case
in a muniber of compartments F. In each of these compartments fits a slide G ;
the slides are a little longer than the compartments and their projecting ends are
provided with a knop or button .H, by means of which they can be conveniently
pulled forwards and backwards.
Each slide is provided with a little hole 1 near its inner end and corresponding
holes are bored in the cover of the case. so that a 'pin Kamay.be put through
both to hold the slide fast. Instead of the. holerin the slides flong slots..L..may
be cut in them as shown by figs. L.& IV.
The cover of the case is divided in a similar manner as the case by horizontal
lines and also by vertical lines of equal distance and in the square fields so arising
ciphers are written, namely in the upper horizontal .row, exepting.the.first square, the
figures 1, 2, 3. ..n; the left vertical row of squares is left free ; .in .the..second
row of squares the cipher 1 is inscribed in each square; in the third row the
cipher 2 in the fourth the number 3 and so on.
It follows thus that each vertical row, leaving out the upper field, contains the
natural scale of numbers 1, 2, 3 . . . . (n-1). Now the slides are divided vertically

page_text: n the same manner as the cover O and each field of the slide contains the
umber which is the product of the multiplication of one of the numbers in the
first horizontal row-(multipliers 1, 2, . . .)—with the number in the fields of
the corresponding horizontal row above the slide on the cover.
It follows from this that if a slide is withdrawn and then held in a certain field by
inserting the pin K, the last number visible on the slide will be the product of the
number in the upper horizontal row and the respective number vertically below the
first one in the field over the slide which has been drawn and fixed by the pin.
By this arrangement it will be easily understood how addition, multiplication
and division can be taught.
Let us for instance show how to find the product of 7 x 2=14.
In the row of squares containing the multiplicands 2 the teacher puts the pin K into
the hole of that field which is vertically below the field in the uppermost row being
marked by the multiplier 7 and then he draws the slide until it will be held by the pin
in its hole, and the last figure visible on the slide then is 14.
To show that the multiplication is merely an abbreviated addition, that for instance
30 is composed of 5 times 6, the teacher proceeds as follows: In that of the horizontal
fields containing the 6, the multiplicands, the teacher marks the one which is below
the square containing the 5 in the uppermost row, then he gradually inserts the
pin, beginning at the left, into the holes of all the squares of the multiplicand row 6
and draws the slide every time up to the fifth field, thus showing, that 1×6=6; 2×6
or 6+6=12, +6 or 6+6+6=18, +6 or 6+6+6+6=4×6=24+6 or 6+6+6+6
+6=5×6=30.
In a similar manner the teacher proceeds to explain the division:
How often is 6 contained in 30? five times! for 5 times the slide below the fields
containing the 6 can be shifted from square to square when 30 was the last visible
figure on it until the rest is 0.
Having now particularly described and ascertained the nature of my said Inven-
tion, and in what manner
the saine is performed, I declare that what I
claim is:
"The instrument for use in teaching arithmetic consisting of:
1) the case A B C D having one side B C open,
2) the compartiments F, FI being formed by division bars E,
ני
3) the covering plate O, being divided horizontally and vertically in squares of
same width as the compartments F, F¹..., the upper row of the so formed squares,
exepting the first square on the left side, containing the natural scale of
numbers 1, 2, 3, n and in like manner the squares in the vertical rows,
exepting always the first squares on the left side, below the upper horizontal row are
each provided with the natural scale of numbers also; each field being further provided
with a hole M.
4) the slides G fitting into the compartments F, F' . . and being divided by
vertical lines of same distance as the lines on the covering plate in fields con-
taining the products of the number in the upper horizontal row, as multiplier, with
the numbers in the respective squares in the other, rows, as multiplicand; the slides
being also provided with holes 1 or slots L in order to fix their position by
inserting a pin K through the holes M and I or the slots L respectively."
Dr. K day at Oetober
at Catabor
KARL I. MAYER,
Agent for K. Schulte & E. A. Bosies.
KARL I. MAYER,
Agent for K. Schulte & E. A. Bosies.