FIFTEENTH LESSON.

TUSCAN COLUMN.

The Tuscan column is the simplest of the five orders of architecture; it is devoid of all ornament, and usually employed in buildings of the plainest kind.

1. A Tuscan column is divided into three parts: the capital, shaft, and base.

2. The capital (B) includes 30 minutes, and is divided into the

3. The upper fillet, together with the facia, is termed the abacus, and is the only square part of a Tuscan column.

4. The shaft (C) is 300 minutes in height, including the bead (U), of 4 minutes, and the fillet (V), of 2 minutes. The two latter portions together are termed the astragal.

5. The height of the column should be seven times its lower diameter.

6. The base (D) includes 30 minutes, and consists of a fillet (Y), 3 minutes; torus (Z), 12 minutes; and plinth (A), 15 minutes.

EXERCISES.

Character of Tuscan column. How divided? Point to each part. How is the capital divided? Proportion of ovolo? Fillet? Neck? Facia? &c. &c. Which forms the abacus ? Where is the astragal? Trace each on your boards. Proportion of height of a column to its diameter? Proportion of base? Its parts? Show the plinth. The torus. The fillet. Proportion of each? Copy Exercise 82. Explain each part.

See Appendix, L.

OF GEOMETRY WITH THAT OF DRAWING.

THE study of drawing, as before observed, benefits the student in several respects; but when it is combined with that of geometry, the advantages are incalculably greater.

For the cultivation of the intellectual powers, there is in my opinion nothing to equal the mathematics; the perfect accuracy required in correct demonstration, and the impossibility of success attending desultory attention or superficial research, must induce habits of the most valuable and sterling character.

The following Appendix will be found to resolve itself almost entirely into two parts. In the first place, it refers to the theorems in Euclid which may be easily combined with the geometrical forms already drawn by the pupils.

The second part is added to give a brief outline of the method of teaching mensuration, principally the area of superficies deducible from the given sides.

Any edition of Euclid's Elements will supply the enunciation and demonstration of each proposition, and it is hoped that little difficulty will be experienced in drawing out from the class by induction the principal geometrical properties of every form.

A course of practical geometry, alternating with the lineal drawing lessons, would quite repay the teacher's labour, and form a good basis for a more extended course of imitative study.

The excellent treatise by Mr. Nesbit will supply fuller information in the mensuration of superficies or solids.

In conclusion, I would respectfully but earnestly express a hope, that this short course of lessons may prove of some slight service to teachers, and assist them in their arduous and important duties. I also hope that circumstances may enable me at some future period to undertake a more advanced series, which shall supply to a greater degree the requirements of the present progressive state of education.

(A.)

1. Two right lines cannot enclose a space.

2. If two right lines be parallel to the same right line, they are parallel to each other. (See EUCLID, Book I. Prop. xxx.)

(B.)

1. The size or span of an angle is estimated by the number of degrees it includes in a circle, of which the angle forms the centre.

If a circle be divided into 360 equal parts, and a right angle be placed in the centre within it, it is evident that such an angle includes 90 parts, and is therefore called an angle of 90 degrees-half a right angle is called an angle of 45 degrees, &c. &c.

2. If a right line stand upon another right line, and make angles with it, these angles are either two right angles or together equal to two right angles. (See EUCLID, Book I. Prop. xiii.)

3. If two right lines intersect one another, the vertical angles are equal. (See EUCLID, Book I. Prop. xv.)

(C.)

1. The opposite sides and angles of a parallelogram are equal. (See EUCLID, Book I. Prop. xxxiv.)

2. A parallelogram is bisected by its diagonal. (See EUCLID, Book I. Prop. xxxiv.)

3. A parallelogram is double a triangle, if it be on the same base and between the same parallels. (See EUCLID, Book I. Prop. xli.)

MENSURATION.

Prob. I. To find the area of a square.

Rule. Multiply the length of one side by itself. The result is the required area.