Encyclopaedia Britannica, or, a Dictionary of arts, sciences, and miscellaneous literature : enlarged and improved. Illustrated with nearly six hundred engravings > Volume 18, RHI-SCR

AMUSEMENTS OF SCIENCE.
55
eoffl«tri- longer fide rr four Indies, its fiiorter =r two inches, and
cat its hypothenufe =r fquare root of 20 (4*472135) j and
' ^ie triangle, as G, will have its longer fide — two
^ ‘ inches, its fliorter = one inch, and its hypothenufe =
fquare root nf 5 (2.236068) : the fides of the remaining
triangle will be refpe&ively 5 inches, 4.472135 inches,
and 2.236068 inches.
To form a Square of fine equal Squares.
) form a Divide one fide of each of four of the fquares, as
mare of ^ B, C, D, (fig. 23. N° I, and 2) into two equal parts,
and from one of the angles adjacent to the oppofite fide
r, 2$. draw a ftraight line to the point of divifion j then cut
thefe four fquares in the dire&ion of that line, by which
means each of them will be divided into a trapezium and
a triangle, as feen fig. 23. N° 1.
Laftly, arrange thefe four trapeziums and thefe four
triangles around the whole fquare E, as feen fig. 23. N°
2. and you will have a fquare evidently equal to the five
fquares given.
To defcribe an Ellipfs or Oval geometrically.
49'
ethod of The geometrical oval is a curve with two unequal
Icribing axes, and having in its greater axis two points fo fitua-
ova^ ted, that if lines be drawn to thefe two points, from each
point of the circumference, the fum of thefe two lines
will be always the fame. See Conic Sfxtions.
g. 24. Let AB (fig. 24.) be the greater axis of the el-
lipfis to be defcribed *, and let ED, interfefting it at
right angles, and divide it into two equal parts, be
the lefler axis, which is alfo divided into two equal
parts at C *, from the point D as a centre, with a radi¬
us rr AC, defcribe an arc of a circle, cutting the greater
axis in F and f; thefe two points are w?hat are called
the foci. Fix in each of thefe a pin, or if you operate
on the ground, a very ftraight peg ; then take a thread
or a cord, if you mean to defcribe the figure on the
ground, having its two ends tied together, and in length
equal to the line AB, plus the diftance Yf; place it
round the pins or pegs Yf; then ftretch it as feen at
FG f and with a pencil, or ftiarp-pointed inftrument,
make it move round from B, through D, A, and E, till
it return again to B. The curve defcribed by the pencil
on paper, or on the ground, by any fharp inftrument,
during a whole revolution, will be the curve required.
This ellipfis is fometimcs called \\\e gardener's oval,
becaufe, when gardeners defcribe that figure, they em¬
ploy this method.
An oval figure approximating to the eliipfe, may be
defcribed at one fweep of the compaffes, by tvrapping
the paper on which it is to be defcribed round a cylin¬
drical furface. If a circle be defcribed upon the paper
thus placed, affirming any point as a centre, it is evident
that when the paper is extended on a plain furface, we
fhall have an oval figure, the fliorter diameter of which
will be in the direction of the axis of the cylinder on
which the oval was defcribed. This figure, however,
is by no means an accurate oval, though it may ferve
Xrery well as the border of a drawing, or for fimilar pur-
pofes, where great accuracy is not required,
ntriv- In no feience are amufing contrivances more requi-
:«for fite to facilitate the progrcfsof the young pupil than in
“ find£eotttetry* We are therefore difpofed to regard, with
geokc- Particblar attention, every attempt to illuftrate and ren¬
der popular the elements of this fcience. We may lay
with Mr Edgeworth, that though there is certainty no
royal road to geometry, the way may be rendered eafy
and pleafant by timely preparations for the journey.
Without fome previous knowledge of the country, or of
its peculiar language, we can fcarcely expeft that our
young traveller fhould advance with facility or plea-
fure. Young people ftiould, from their earlieft years,
be accuftomed to what are commonly called the regular
folids, viz. the tetrahedron, or regular four-fided‘folid ;
the cube, or regular fix-fided folid ; the oeftabedron, or
regular eight-fided folid 5 the dodecahedron, or regular
I2-iided folid ; and the icofahedron, or regular 20-fided
folid. Thefe may be formed of card or wood, and Mr
Don, an ingenious mathematician of Briftol, has con-
ftruded models of thefe and other mathematical figures,
and explained them in an Effay on Mechanical Geome¬
try. Children fliould alfo be accuftomed to the figures worth's ‘
in mathematical diagrams. To thefe fliould be added Practical
their refpeftive names, and the whole language of the ^Jucatinn,
fcience ffiould be rendered as familiar as poffible *. canp^xvi.
We have lately met with a contrivance for rendering x,e Petit
familiar to children the terms of geometry by means of Euclid,
an eafy trick. This contrivance is called Le Petit Eu- Gg* 2S*
did, and confifts of two circular cards which are repre-
fent at fig. 25. Plate CCCCLXXII, and fig. 26.
Plate CCCCLXXIII. Each of thefe circles is divided
into eight compartments, marked I, 2, 3, 4, 5, 6, 7, 8,
and within each compartment are reprefented feveral
mathematical figures or diagrams. In the centre of the
card reprefented at fig. 25. is the word quef ion, and in
that at fig. 26. the word anfwer. On the latter the
figures are diftinguilbed by numbers, referring to their
explanations in the following table.
N°
1. The cone.
2. Curve line.
3. Quadrant.
4. A point.
5. Dotted cofine.
6. Dotted lecant.
7. Cube.
8. Pyramid.
9. A perpendicular.
10. Acute-angled triangle.
11. Decagon.
12. Hexagon.
13. Square.
14. Right-angled triangle.
15. Sphere.
16. Circular fegment.
17. A angle.
18. Dotted length.
19. Paralltlopipedon,
20. Dotted radius.
21. A feclor.
22. Heptagon.
23. The bafe.
24. Dotted abfciiTe.
2 9. Ifofceles triangle.
26. Dotted line fubtending
an angle.
27. Dotted ordinate.
28. Enneagon, or regular
9-fided figure.
4 A ■:
N°
29. The foci of an ellipfe.
30. O£!agon.
31. Rhomboid.
32. Equilateral triangle.
33. Pentagon.
34. Spindle.
35. A fealene triangle.
36. Parallelogram,
37. Obtuffe-angled triangle.
38. Dotted height.
39. Hyperbola.
40. Dotted conjugate dia¬
meter.
41. Dotted hypothenufe.
42. Dotted parameter,
43. Rhombus.
44. Dotted diameter.
45. Dotted fine.
46. An obtufe angle.
47. Parabola.
48. Cylinder.
49. External* angle.
50. Dotted tangent.
51. Straight line.
52. Ellipfis.
53. Dotted diagonal.
54. Circle.
55. Dotted tranfverfe dia¬
meter.
56. Prifm.
i 57. Dotted