FOR THE

EXAMINATION OF THE PUPIL,

TO BE

ANSWERED VERBALLY.

The figures refer to the pages which contain the answers; and diagrams must be drawn by the pupil, when the questions cannot be properly explained without them.

PART I.

GEOMETRICAL DEFINITIONS:

What is Geometry?-What is a point,-a line? -How many kinds of lines are there?-What is a right or straight line?

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What is a curved line?-What are parallel lines?
-What is a superficies?-Can a superficies be
contained within one line?-What is a solid?
-What is an angle?

How many

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kinds of angles are there?-What is a right angle? What is an acute angle? - What is the complement of an angle? What is an obtuse angle?What is the supplement of an angle?... What is a triangle,—an equilateral triangle,—an isosceles triangle,-a scalene triangle, a rightangled triangle, an acute-angled triangle?.... What is an obtuse-angled triangle?—Which is the base, and which the perpendicular, of any figure? What is a figure of four sides denominated?What is a parallelogram,—a square, -a rectangle ?

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What is a rhombus,- —a rhomboid or rhomboides, -a trapezium,-a diagonal,-a trapezoid?....

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By what names are plane figures of more than four sides generally called?

Name the polygons?

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What is a regular polygon,-an irregular polygon,- —a circle,—the diameter ?

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What is the radius, and the arc, of a circle? What is a chord,-a segment,-a semicircle,a quadrant,-a sector?

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How is the circumference of every circle supposed to be divided?

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What are the names of the longest and shortest diameters that can be drawn within an ellipse?

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PART I.

GEOMETRICAL PROBLEMS.

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Draw a right line, and shew the manner of bi-
secting it
Make an angle, and shew the method of bisect-
ing it
How do you draw one line parallel to another, so
as to pass through a given point?
Shew the method of drawing one line parallel to
another, at a given distance
How do you erect a perpendicular, from a given
point, near the middle of a given line?
How do you proceed when the point is near the
end of the given line?
How do you let fall a perpendicular, from a point
nearly opposite to the middle of a given line?
How do you proceed when the point is nearly
opposite to the end of the line?
How do you find the centre of a given circle?
Shew the method of constructing a triangle, when
the three sides are given

How do you construct a triangle, when the base and perpendicular are given?

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Shew the manner of describing a square, when the side is given

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How do you make a rectangle, when the length and breadth are given?

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How do you make a regular rhombus, when its side is given?

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How do you construct an irregular rhombus,
when its side and perpendicular height are
given?
Shew the method of constructing a regular rhom-
boid, when its sides are giyen
How do you construct an irregular rhomboid,
when its base and perpendicular are given?...
Shew the method of constructing an ellipse, when
the transverse and conjugate diameters are
given
How do you make a regular pentagon, upon a
given line?

Shew the manner of describing a regular hexa-
gon, upon a given line
How do you construct a regular octagon, upon
a given line?
Shew the method of inscribing a circle in a given
triangle

How do you make a triangle equal to a given trapezium ?

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Shew the method of making a right angle by the
line of chords on the plane scale
Describe the method of making an acute angle...
How do you make an obtuse angle?

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How do you find the number of degrees contained in any augle?

How do you make a regular polygon of any number of sides, upon a given line?

Shew the method of inscribing a polygon of any number of sides in a given circle

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How do you find a mean proportional between

two given lines?

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How do you raise a perpendicular by a scale of equal parts?

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If the chord line and versed sine of any arch be given, how do you find the radius that will strike the arch?

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PART I.

GEOMETRICAL THEOREMS.

Draw two right lines to intersect each other; and shew which of the angles, made by the intersection, are equal

What side of a triangle is opposite to the great-
est angle?
When a right line intersects two parallel right
lines, which of the angles made by the inter-
section, are equal?
Draw a diagram, and repeat the fourth theorem
Draw a diagram, and repeat the fifth theorem
Draw a figure, and repeat the sixth theorem -
What is expressed in the seventh theorem ?
What does the eighth theorem express?
Repeat the ninth theorem

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Draw a diagram, and repeat the tenth theorem
What is expressed in the eleventh theorem ?
Draw a diagram, and repeat the twelfth theorem
Draw a figure, and repeat the thirteenth theorem
What property is contained in the fourteenth
theorem ?

Draw a diagram, and repeat the fifteenth theorem
Repeat the sixteenth theorem
What are the properties contained in the seven-

What properties are contained in the nineteenth

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and how are their areas estimated?
Repeat the table of lineal measure
Repeat the table of square measure
How do you find the area of a square?
When the area of a square is given, how do you

find its side?

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How do you find the area of a rectangle?
When the area of a rectangle and one of its sides
are given, how do you find the other side?
How do you determine the area of a rhombus or
rhomboides?

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If the area of a rhombus or rhomboides, and one
of its dimensions be given, how do you find
the other dimension ?
When the base and perpendicular of a triangle
are given, how do you find the area?
If the area of a triangle and one of its dimensions
be given, how do you find the other dimension?
How do you find the area of a triangle, when
the three sides only are given?

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Repeat the rule for performing multiplication
by logarithms

How do you perform division by logarithms?
How is the rule of three performed by logarithms?
Repeat the rule for involution, or raising powers,
by logarithms

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How is evolution, or the extraction of roots, per-
formed by logarithms?
When the two legs of a right-angled triangle are
given, how do you find the hypothenuse?
When the hypothenuse and one of the legs are
given, how do you find the other leg?
How do you find the area of a trapezium?
How may the area of a trapezium be found,
when it can be inscribed in a circle?