Chap. VIII.

GEOMETRY

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the ellipsis, hyperbola, and parabola,so useful in the study of conic sec-tions, or in the development ofmouldings used by the Greeks.The base of the cone may be dividedinto a number of equal parts, andfrom each point on them lines maybe drawn to the apex, and either ofthe above-named figures may thusbe portrayed.

To set out an oblique cone, theposition of the apex must be foundon the plan, and the same method

Fig. 884.

of proceeding must then be adopted as in the preceding example: after the seat ofall the lines has been found upon the plan, and their respective heights set out on theplanes which represent the vertical, they may be transferred to the figure.

Globes are constructed by drawing the paral- **

lelogram EFGH, which has its greater side EFtwice the smaller one E H. Divide the small sidesE H and F G each into two equal parts in thepoints I and K, and draw the line I K; divide thislength into twelve equal parts, and prolong it atpleasure. Take nine parts from the twelve onI K, and placing one foot of the compasses on anydivision, as 7, observe where the other foot cuts theline I K, as at L: from the point L as a centre,with the radius L7, describe the arc M7 N: thenwith the same radius L7, placing one foot on thepoint 6, observe where the other foot falls at O,and from this point O as a centre, with the radius0 6, describe the arc M6N, which will form thespindle M7 N6. Twelve of these spindles madewith the same radius, and according to the samerules, cut and folded together, will form the globe

Q.

When it is required to cover a dome or anyportion of a globe, these spindles or gores must becarefully drawn, and if the boarding or material isto be applied from the base towards the top, thediagram will show the method for cutting it out;if it is to be bent round, so as to exhibit horizontaljoints, the several portions will be those of cones, asalready described. Timber domes are frequentlyformed by adopting both processes, and many upona small scale exist in Italy , hooped round with thinboard, the first formation being that of a numberof gores, cut as shown in the figure EFGH; threeor four thicknesses of bent plank screwed firmlytogether will form a dome of sufficient strength tosustain a covering of lead or copper, and, whenassisted by an iron hoop at the base, will endure aconsiderable weight without yielding.

When the base of a dome is polygonal, the formsto be given to the gores may be easily found by asimilar process.

To project a Sphere orthographically on the Planeof the Equator : the centre from which the circle is

struck that represents the equator will be the projection of the pole ; and the two diameterswhich are perpendicular to each other will be projections of meridians 90° distant from eachother: each quadrant of the circle must then be divided on its circumference into sixequal parts, and lines drawn as radii from these points will be the projections of meridians of15°, 30°, &c. &c., dividing the equator into twenty-four equal parts, any one of which maybe assumed as the first meridian. To project the parallels of latitude, divide one of thequadrants into nine equal parts, and drop from the points of division as many perpendi-culars, which will cut the diameter of the circle; then from the pole as a centre, describeother circles through these points on the diameter, which will be the projections of parallelsof latitude at the distance of ten degrees.

By a series of parallel circles, crossed by others perpendicular to them, we may form a

Fig. 885

Fig. 887.

Fig. 886.