Sidebilder
PDF
ePub

3. Draw line DE, cutting AB in F.
4. From D, with radius DA, describe arc AB.
5. From E, with radius EF, describe an arc, cutting the

arc AB in G and H.
6. From C, with line GH as radius, cut the semicircle in 1.
7. Draw line Bl; it is a second side of the nonagon.
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 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.

7

B

2. From A, with radius AB, describe an arc, cutting the

semicircle in D, and bisect AB 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

Bl is a second side of the decagon.

6. Bisect B 1, and obtain 0, the centre of the circle.
7. Mark off, on the circumference, the divisions 1 2, 23, &c,

equal to B 1. Join 1 2, 23, &c., and a decagon is con-
structed on the given line AB.

Problem 77.
To construct a regular un-decagon on a given line AB.

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.
2. From A, with the same radius, describe an arc, cutting

the first arc in D and E.
3. Draw line DE, bisecting AB.

5

8

K

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 Bl; 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 0 (Pr. 1).

E

2. With centre 0, and radius 0 A, describe the circle.
3. From A, mark off the distance AB to DE, &c. Join

AD, DE, EF, &c., and a regular polygon will be com-
pletedin this case a hexagon.

Problem 79.
To construct a regular hexagon, its diameter AB being given.

1. Bisect AB in C (Pr. 1).

F

B

D

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

[blocks in formation]

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

« ForrigeFortsett »