1132 THE NEW ZEALAND GAZETTE. [No. 75

and apply the several geometrical terms required, and to give approxi-
mate verbal explanations of their meaning. They should also know how
to draw lines parallel or perpendicular to one another by means of set-
square and flat-ruler. Proceeding to simple geometrical figures, which
should be illustrated by models in cardboard or wood as well as by drawing,
they should know the square and the oblong as square-cornered figures of
four sides, all the sides being equal in the square, while in the oblong there
are two long sides equal and two short ones equal. The pupils should
draw these figures with sides of prescribed length. The meaning of
diagonal must be known, as also of triangle, equilateral, isosceles. The
two triangles into which a diagonal divides a square or oblong must be
recognised as right-angled triangles, and in the square as isosceles tri-
angles. So far as is possible without strict geometrical construction the
pupils must be able to draw at dictation, with ruler or as freehand
exercises, the several kinds of triangles here named, as well as to recog-
nise them. “Base,” “apex,” “altitude,” as applied to isosceles triangles,
should be known. The drawing exercises, with and without ruler, must
include combinations of straight lines forming borders and simple patterns.

In the Second Standard the freehand drawing is to include forms based
on the circle, semi-circle, and quadrant. The knowledge of terms—tested
by models, by diagrams, and by dictation—must include circumference,
radius, diameter, arc, chord, segment, semi-circle, and quadrant. The
rhombus and the rhomboid are to be studied: the rhombus, as like the
square, except as to its angles, and the rhomboid as similarly comparable
to the oblong; the rhombus as divided by one diagonal into two obtuse-
angled triangles, and by the other into two acute-angled triangles, all
isosceles; and the rhomboid as divided by one diagonal into two obtuse-
angled triangles, and by the other into two acute-angled triangles, two at
least of the triangles being scalene.

In the Third Standard the new figures for study are the trapezium and
the polygon, especially the regular hexagon and regular octagon. It
is to be known that any regular polygon may be divided into isosceles
triangles (equilateral in the hexagon), each of which has its apex in the centre
of the figure. The right angle is to be known as an angle of 90 degrees;
the sum of the angles round a point as equal to four right angles or 360
degrees; the sum of the angles of a triangle as 180 degrees (illustrated by
folding a triangular piece of paper so that the three corners may meet at a
point in one of the sides); and the sum of the angles of any four-sided
figure as 360 degrees (illustrated by tearing off the four corners of a tra-
pezium and putting them together at a point). The work of the standard
must include ruling, freehand, dictation, and memory exercises on the
geometry of form, and the freehand from set copies must include some
curves more difficult than such as can be produced by joining quadrants
together.

In the Fourth Standard the freehand drawing is to be more advanced
than that of the Third Standard. The definitions are to be given in strict
geometrical language, and are to include, in addition to all the terms used
in the first three standards, the pentagon, heptagon, decagon, dodecagon,
ellipse, major, and minor axes and foci. Practical use is to be made of set-
squares in the drawing of lines at angles of 90, 60, 45, 30, 15 degrees, and
others depending on these; and the pupils must be prepared with at least
thirty problems of practical construction. They ought also to be able to
work the problems from given dimensions to one or other of the following
scales: 3in., 1½in., or ¾in. to a foot; ¾in. to a yard (¼in. to foot); 1in.
to a mile (¹⁄₈in. to furlong). The problems required are the following:—
To bisect a given straight line or an arc.
To bisect a given angle.
To draw a perpendicular to a given straight line at a given point on it.
To draw a perpendicular to a given straight line from a given point out-
side it.
To draw a line parallel to a given straight line at a given distance from
it.
To draw a line parallel to a given straight line through a given point.
To make an angle at a given point in a given line equal to a given
angle.
To divide a given straight line into any number of equal parts.
To divide a given straight line proportionally to a given divided line.
To divide a circle into three, six, twelve, four, or eight equal parts.
To construct a triangle, its three sides being given.
To construct an equilateral triangle on a given side.
To construct an isosceles triangle, the base and the angle at the apex
being given.
To construct a square, the side being given.
To construct a square, the diagonal being given.
To construct a rectangle, the sides being given.