A Fraction, Area, and Geometry Apparatus.
Year: 1898

page_text: A Fraction, Area, and Geometry Apparatus.
EDWARD FRANCIS, Schoolmaster, 8, Park Valley, Nottingham, do hereby declare
the nature of this invention to be as follows:-
An improved apparatus consisting of a frame upon which the moveable parts
of the apparatus can be exhibited.
The moveable parts consist of various sections of a square or any other plane
figure and these are so designed as to demonstrate and teach:
(1.) The various operations in fractions.
(2) The calculation, equality, and conversion of areas.
(3) The division of lines into parts.
(4) The principle of the vernier.
The apparatus may be constructed of any material, e.g., wood, metal, leather,
papier mache, &c. The frame may be of any form, generally, a square flanked
by two rectangular slides on which to show the moveable parts.
14 1000
EDWD. FRANCIS.
A Fraction, Area, and Geometry Apparatus.
I, EDWARD FRANCIS, of 8, Park Valley, in the City of Nottingham, School-
master, 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:-
This invention relates to an educational appliance to be used for practically
demonstrating or illustrating the calculation of fractional parts, superficial areas,
or the simple rules by which the said calculations are performed, it is also
applicable to demonstrate certain geometrical problems, such for example as the
division of lines into equal parts, or the principle and use of the vernier.
The invention will be best understood by reference to the accompanying draw-
ings, in which
Fig. 1 is an elevation, and
Fig. 2 a plan of a combined frame and casing on which the several parts of
the apparatus may be exhibited, and in which the whole of them
may
be

page_text: Figs. 3-1-5 and 6 are views showing square figures sub-divided into sections
according to my invention.
Figs. 7-8 and 9 illustrates the use of the figures shown in Figs. 3 to 6.
Fig. 10 is a view showing a square figure divided into sections so as to de-
monstrate the forty seventh proposition of the first book of Euclid.
Fig. 11 illustrates the use of the square figure shown in Fig. 10.
Fig. 12 is a view showing an approximately circular figure so divided into
segments as to demonstrate the rule or formula for calculating the area of a
circle.
Fig. 13 illustrates the use of the figure shown in Fig. 12.
Fig. 14 is a view of a square figure divided into sections.
Fig. 15 is a view of a square figure or black board divided by lines.
Fig. 16 shows a set-square which is to be used in connection with the square
figures.
The combined frame and casing shown in Figs. 1 and 2, comprises a shallow
square tray or box A, provided with a lid or cover which is formed in two
halves B B'.
Each of the halves B B of the cover is provided with a ledge B2, and is pivotted
at its outer bottom corner C to the corresponding corner of the box A, so that
they will turn down in a plane parallel to the box, into the position in which
that on the right B is shown, that is with the ledge B2 horizontal. Each half
of the cover is held in this position by a chain C, the ends of which are connected
to the box and cover respectively, or other suitable devices may be employed for
this purpose.
The combined frame and casing described is placed on an easel, the covers
turned down, and the parts of the apparatus required are taken from the box A
and exhibited by placing them on the ledge 12 of the covers B B¹.
The educational part of the apparatus is mainly comprised of objects made to
represent plane figures, which may be of any suitable shape and are hereinafter
described. They may be formed of wood or other suitable material of a convenient
thickness, and are cut into segments provided with distinct margins or borders,
and in some cases further divided by lines on the surface of the figure or parts
of the figures.
Fig. 3 shows a square figure D which is divided into eight equal parts a by
two diagonal lines and two lines parallel to the sides of the figure. Each
separate part a of the figure is provided with a distinct margin a¹ so that when
placed together it is plainly shown how many parts it is divided into.
This figure is used for demonstrating the calculation of fractions in fourths
and eighths, each part being taken to represent one eighth of the whole figure, and
two parts one fourth.
This square figure may also be made with the parts arranged in the form shown
in Fig. 7.
It can also be readily shown that two of the parts a form a square of one fourth
the area of the whole figure, and four of the parts a a square of one half the
area of the whole figure.
In the latter case it can be shown that the sides of the square having half the
area, are equal in length to half the length of the diagonal of the whole figure.
Fig. 4 shows a square figure E divided by lines parallel to its sides into nine equal
parts or squares, it is also actually divided along the lines bbc c and also
diagonally along the line d d.
This figure may be used in the same manner as the figure shown in Fig. 3,
but for fractions of thirds, ninths, and eighteenths, and although it is only divided
into six parts e a part or parts equal to any number of thirds, ninths or eighteenths
may be removed from the whole, and is more convenient to handle than if it
were cut into eighteen separate parts.
Fig. 5 shows a square figure F divided in a similar manner to Fig. 4 by lines
parallel to its sides into sixteen equal parts or squares, it is also actually divided
4

page_text: along the lines f f g g h h and diagonally along the line ii. This figure is
thus divided into eight parts and may be used for fractions of eighths, sixteenths,
and thirty-seconds.
Fig. 6 shows another square figure I divided in a similar manner.to Fig. 4 by lines
parallel to its sides but into twenty-five equal parts or squares, it is also actually
divided along the lines kk, 1 1, m m, nn, and diagonally along the line p P
into ten parts q.
This figure gives fractional parts of the whole, of fifths, tenths, twenty-fifths,
and fiftieths.
The figures described in addition to the demonstration of the calculation of
fractions, may be used for practically demonstrating the calculation of superficial
areas.
For example it may be demonstrated that the area of a triangle is equal to the
base multiplied by half the height, or the height multiplied by half the base.
The former is shown in Figs. 8 and 9.
In Fig. 8 is shown a triangle made up of parts of the figure shown in Fig. 5,
the two upper parts are then moved into the position shown in Fig. 9 which
makes a rectangle of half the height of the triangle.
The divided edges of the several square figures shown may be placed together
in order to demonstrate the use of the vernier. This may be further demonstrated
by a scale G (see Figs. 1 and 2) on the cover B' of the casing A, and a second
scale on a movable ruler G¹ sliding on the ledge B2.
The division of lines into equal parts may also be demonstrated by the triangular
figure shown in Fig. 8 in which it may be shown that in order to divide the
liner in four equal parts the liners may be first projected, then divided, and the
points of division projected from the liners by parallel lines on to the line r r.
The division of lines may also be demonstrated by the use of the set-square
shown in Fig. 16, in connection with one of the rectangular figures, say Fig. 13
on which the bevel side of the square is indicated by a dotted line t.
Fig. 10 shows a square figure J which is divided as shown into three parts u
in order to demonstrate the forty seventh proposition of the first book of Euclid.
Each part u is provided with a distinct margin ' and in addition there are two short
lines to make a continuation of the dividing lines. The problem is demonstrated by
putting the several parts together as shown in Fig. 14, the two squares in the latter
being equal to the one in Fig. 10.
Fig. 11 is an approximately circular figure K divided into any convenient
number of segments or triangles v, in order to demonstrate that the area of a
circle is equal to half the circumference multiplied by the radius.
Ono half of the segments are connected by a flexible band w secured to their
bases, the other half of the segments are also connected in a similar manner
by a flexible band ; by placing the two halves of the figure together in the
form shown in Fig. 15, a parallelogram is formed having a width and height
equal to the circumference and radius respectively.
Fig. 12 shows a square figure figure L divided into twenty four rectangular
parts y each provided with a distinct margin y¹ for the purpose hereinbefore
stated.
This figure may be used in the same manner as the figures hereinbefore
described
Fig. 13 shows a square figure M or blackboard, divided by lines into one
hundred squares, and may be used to demonstrate certain of the problems herein-
before referred to, by means of the assistance of chalk lines drawn on the surface
of the board.
Having now particularly described and ascertained the nature of the said
invention and in what manner the same is to be performed I declare that what
I claim is:-
1. In apparatus such as described a combined framing and casing comprised of

page_text: a box or tray such as A to contain the apparatus a lid or cover formed in two
parts such as B provided with ledges such as 62 and pivotted so as to turn
down and provide a framing on which to exhibit the several parts of the apparatus
substantially as described.
2. In apparatus such as described a square or other suitable shaped figure such
as I divided into a number of equal parts and each part provided with a distinct
margin substantially as and for the purpose described.
3. In apparatus such as described a square figure such as E divided by lines
into a number of equal squares and actually divided on lines such as bb, c c
parallel to one side and diagonally on the line d d substantially as and for the
purpose described
4. In apparatus such as described a square figure such as J divided into three
parts u as shown in Fig. 10 and each part provided with a distinct margin
substantially as and for the purpose described.
5. In apparatus such as described an approximately circular figure such as K
divided into segments such as one half the segments being connected by a
flexible band and the other half by a band a substantially as and for the
purpose described.
.
6. The combination and arrangement of parts constituting the complete educa-
tional apparatus substantially as and for the purpose described and illustrated
in the accompanying drawings.
Dated this the 29th day of December 1898
EDWD. FRANCIS.
Boult & Wade,
Agents for the Applicant.