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a scalene triangle ? (12.) What is a right-angled triangle? (13.) Which side is the hypotenuse ? (14.) What are the other sides called ? (15.) What is an obtuse-angled triangle? (16.) What is an acute-angled triangle? (17.) What is the vertex of a triangle? (18.) What other name has it? (19.) What is generally meant by the base ? (20.) In what kind of triangles may it be changed? (21.) What is the altitude of a triangle ? (22.) What is the perimeter of a figure? (23.) What is a chord ?

Section 3. (1.) What is a quadrilateral figure? (2.) What is a parallelogram ? (3.) How many kinds of quadrilaterals are there ? (4.) Name the four which are parallelograms. (5.) Name the two which are not parallelograms. (6.) What is a square ? (7.) What is a rectangle ? (8.) What other name has it? (9.) What is a rhombus? (10.) What angles are always equal to each other ? (11.) What is a rhomboid ? (12.) What is a trapezium ? (13.) What is a trapezoid ? (14.) Give another name for a quadrilateral figure. (15.) What is a diagonal ? (16.) What is a diameter of a parallelogram?

Section 4. (1.) What is the area of a figure ? (2.) How are such measurements calculated ? (3.) What is the area of a square whose side contains 6 linear inches ? (4.) What is the area of a rectangle whose adjacent sides are 6 feet and 5 feet? (5.) What are concentric circles ?

Section 5. (1.) What is Euclid's definition of multilateral figures or polygons ? (2.) What is a regular polygon ? (3.) What is an irregular polygon? (4.) How many sides may a polygon have? (5.) What is the limit to the number of sides that we usually meet with ? (6.) What is a nonagon ? (7.) What name is given to a figure of eleven sides? (8.) Of twelve sides ?

Section 6. (1.) What is a cone? (2.) What is meant by its axis ? (3.) When is à cone said to be right ? (4.) When is it said to be oblique ? (5.) Under what circumstances will a section of a cone be a circle ? (6.) What is an ellipse'? (7.) How many diameters has it? (8.) What is the long diameter called ? (9.) What name is given to the short diameter ? (10.) What are the foci ? (11.) What is a parabola ? (12.) What is its double ordinate ? (13.) What is its ordinate ? (14.) What is its abscissa ? (15.) What is a hyperbola ? (16.) What is its diameter ? (17.) What do we mean by the “conic sections ?(18.) What is an oval? (19.) Why is it so called ?

Section 7. (1.) How many kinds of inscribed figures are there? (2.) When is a rectilineal figure said to be inscribed in another rectilineal figure ? (3.) When is a rectilineal figure said to be inscribed in a circle ? (4.) When is a circle said to be inscribed in a rectilineal figure? (5.) What is a sector of a circle ?

Section 8. (1.) How many kinds of described figures are there? (2.) When is a rectilineal figure said to be described about another rectilineal figure? (3.) When is a rectilineal figure said to be described about a circle? (4.) When is a circle said to be described about a rectilineal figure ?

Section 9. (1.) What is ratio ? (2.) On what does the ratio of any two quantities depend ? (3.) What is understood by a “ part ?(4.) What is Euclid's definition of proportion ? (5.) When are four quantities said to be proportionals? (6.) What is the last term called ? (7.) Which are the extremes ? (8.) Which are the means? (9.) What product equals the product of the means ? (10.) What is meant by a mean proportional ? (11.) What is a proportional in Practical Geometry ? (12.) What is meant by the fourth proportional greater ? (13.) What is meant by the fourth proportional less ? (14.) What is meant by the third proportional greater ? (15.) The third proportional less ?

Section 10. (1.) What is Euclid's definition of similar rectilineal figures ? (2.) What rectilineal figures are similar ? (3.) What other rectilineal figures can be made similar ?

Section 11. (1.) In Euclid I. 35, what is meant by the same parallels? (2.) In what direction is the altitude reckoned ? (3.) Under what circumstances is a triangle half of a parallelogram?

QUESTIONS IN SOLID GEOMETRY.

(1.) To what has the preceding portion of the work been confined ? (2.) What kind of objects next comes under consideration ? (3.) What is the great difference between a plane figure and a solid object? (4.) Name the distinct ways in which a solid may be represented. (5.) Explain clearly the difference between drawing an object perspectively and geometrically. (6.) How many distinct drawings must we make in order to draw a solid object geometrically? (7.) Explain clearly what is meant by plan, and what by elevation. (8.) What do we understand by the “ planes of projection ?(9.) Name them. (10.) How may the horizontal plane be illustrated ? (11.) How may the vertical plane be illustrated? (12.) What do we understand by the “line of intersection ?" (13.) By what other names is it known ? (14.) What do we mean by the projections of an object? (15.) By what is every solid bounded ? (16.) By what is every surface bounded ? (17.) By what is every line limited ? (18.) What do we mean by the projector of a point ? (19.) How may a point be found, its projections being given? (20.) When a line is parallel to the horizontal and vertical plane, to what are its projections parallel ? (21.) Under what circumstances must we suppose the vertical plane to revolve upon the line of intersection of the planes of projection ? (22.) What shows the distance of a point from the horizontal plane ? (23.) What shows the distance of a point from the vertical plane ? (24.) What is understood by the term rabatting ?

(25.) What solids are most commonly used to illustrate the principles of Solid Geometry ? (26.) What is a cube? (27.) What is a prism ? (28.) What is a pyramid ? (29.) What is a sphere ? (30.) What is a cone? (31.) What is a cylinder ?

(32.) What are co-ordinate planes ? (33.) What do we understand by the traces of a line ?' (34.) How are they distinguished ? (35.) What do we understand by the traces of a plane ? (36.) How are they distinguished ? (37.) When the projections of a line are given, what may be found ? (38.) If a plaue be parallel to the ground line, to what are its traces parallel ? (39.) If a trace be perpendicular to the ground line, to what are its traces perpendicular ?

(40.) Name four other regular solids which are used to illustrate the principles of Solid Geometry. (41.) What is a tetrahedron ? (42.) What is an octahedron ? (43.) What is a dodecahedron ? (44.) What is an icosahedron ?

(45.) What do we understand by a section ? (46.) What do we mean by penetrations of solids ?

ETYMOLOGY OF GEOMETRICAL TERMS.

Abbreviations—L. for Latin ; G. for Greek; F. for French.

Abscissa, from L. abscissus, a, um, torn off; from L. ab-scindo, to tear off. Acute, from L. acutus, a, um, sharp or pointed; from L. acuo, to make

sharp. Adjacent, from L. adjacens-entis, lying near; from L. ad, to; and jaceo,

to lie. Alternate, from L. alternatus, a, um; from L. alterno, to do anything by

turns. [L. alter = other.] Altitude, from L. altitudo, dinis, height; from L. altus, a, um, high. Angle, from L. angulus, a corner; from G. angkylos, a bend. Apex, from L. apex, the tip or top of a thing. Arc, from L. arcus, a bow. Area, from L. area, a vacant piece of ground; originally a place where corn

was dried; from L. areo, to be dry. Axis, from L. axis ; G. axon, an axle.

Base, from L. basis, a foundation; from G. baino, to step.
Bisect, from L. bis, twice; and L, seco (sectus), to cut.

Centre, from L. centrum ; G. kentron, a sharp point. [G. kenteo = to prick.]
Chord, from L. chorda; G. chordē, an intestine, also a string of a lyre.
Cinquefoil, from F. cinq, five; and F. feuille, a leaf. [L. folium = a leaf.]
Circle, from L. circulus, a ring ; from G. kirkos, a circle.
Circumference, from L. circumfero, to carry round; from L. circum, around;

and L. fero, to carry. Coincide, from L. co (con), together; and L. incido, to fall into or upon.

[L. in = in; and L. cado = to fall.] Concentric, from L. con, together; and L. centrum ; G. kentron, a sharp

point. Cone, from L. conus, G. könos, that which comes to a point.

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