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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 a 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 ?

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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.) Únder 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 liné 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. cing, 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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