3. Draw line DE, cutting AB in F. arc AB in G and H. &c., equal to B 1. Join 1 2, 23, &c., and a nonagon is constructed on the given line AB. Problem 76. To construct a regular decagon on a given line AB. 1. Produce the line AB, and from B, with radius BA, describe a semicircle, cutting it in C. 2. From A, with radius AB, describe an arc, cutting the semicircle in D, and bisect A B in E (Pr. 1). 3. From B, with radius BE, describe an arc, cutting arc BD in F. 4. Draw line EF. 5. From C, with radius EF, cut the semicircle in 1 ; then Bi is a second side of the decagon. 6. Bisect B 1, and obtain 0, the centre of the circle. equal to B 1. Join 1 2, 23, &c., and a decagon is con- Problem 77. 1. Produce the line AB, and from B, with radius BA, describe an arc, cutting the produced line AB in C, and being produced below A. the first arc in D and E. 4. From B, with half BA as radius, describe an arc cutting BD in G. 5. Bisect the arc BE in H; and draw AG, AH, cutting ED in K and L. 6. From C, with radius AL, cut off C 1 on the semicircle. 7. Draw line B1; it is a second side of the un-decagon. 8. Bisect B 1, and obtain 0, the centre of the circle. 9. Mark off, on the circumference, the divisions 1 2, 23, &c., equal to B 1. Join 1 2, 23, &c., and an un-decagon is constructed on the given line AB. Problem 78. To complete a regular polygon, its two sides AB, BC being given. 1. Bisect the lines AB, BC by perpendiculars meeting at O (Pr. 1). 2. With centre 0, and radius 04, describe the circle. AD, DE, EF, &c., and a regular polygon will be com- Problem 79. 1. Bisect AB in C (Pr. 1). 2. Through the point A draw a line DE perpendicular to AB (Pr. 2). 3. On CA, as an altitude, construct an equilateral triangle, having its vertical angle at C (Pr. 19). 4. From C, with radius CE or CD, describe a circle. 5. From point E, mark off the distance ED to FG, &c. Join EF, FG, &c., and a regular hexagon will be con structed, having the given diameter AB. Section VI.-ELLIPSES, &C. DEFINITIONS. In order to understand the following definitions clearly, we must refer to that SOLID which is called a CONE. 1. A cone is a solid figure, the base of which is a circle, but which tapers to a point from the base upward. Ex. ABC Note 1.-A straight line drawn from the centre of the base to the apex (or summit) is called its axis. Ex. AD NOTE 2.-When the apex is perpendicular to the base, the cone is said to be a right cone. NOTE 3.—When the axis is not perpendicular to the base, the cone is said to be an oblique cone. Note 4.—If a right cone be cut in two parts by a plane parallel |