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"In a body of equal thickness, as a board, or a slab of marble, but otherwise of an irregular shape, the centre of gravity may be found by suspending it, first from one point, and then from another, and marking, by means of a plumb line, the perpendicular ranges from the point of suspension. the centre of gravity will be the point where these two lines cross each other." -Comstock 1850

Center of Gravity

"In a body of equal thickness, as a board, or a slab of marble, but otherwise of an irregular shape,…

"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and when it has come to rest, drop a plumb line from the point of suspension and mark its direction on the surface. Do the same at any other point, and the centre of gravity will lie where the two line intersect." —Quackenbos 1859

Center of Gravity

"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and…

"To find the center of gravity of any irregular plane figure, but of uniform thickness throughout, divide one of the parallel surfaces into triangles, parallelograms, circles, ellipses, etc., according to the shape of the figure; find the area and center of gravity of each part separately, and combine the center of gravity thus found in the same manner." —Hallock 1905

Center of Gravity of an Irregular Plane

"To find the center of gravity of any irregular plane figure, but of uniform thickness throughout, divide…

"In a body free to move, the center of gravity will lie in a vertical plumb-line drawn through the point of support. Therefore, to find the position of the center of gravity of an irregular solid, as the crank, Fig 8, suspended it at some point, as B, so that it will move freely. Drop a plumb line from the point of suspension and mark its direction. Suspend the body at another point, as A, and repeat the process. The intersection C of the two lines will be directly over the center of gravity." —Hallock 1905

Center of Gravity of a Solid

"In a body free to move, the center of gravity will lie in a vertical plumb-line drawn through the point…

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex decagon. This polygon has some symmetry.

Irregular Convex Decagon

Illustration of an irregular convex decagon. This polygon has some symmetry.

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Irregular Convex Dodecagon

Illustration of an irregular convex dodecagon. This polygon has some symmetry.

Illustration of an irregular concave heptagon.

Irregular Concave Heptagon

Illustration of an irregular concave heptagon.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon. This polygon has some symmetry.

Illustration of an irregular convex heptagon.

Irregular Convex Heptagon

Illustration of an irregular convex heptagon.

Illustration of an irregular hexagon. This is also an example of a concave polygon.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Hexagon

Illustration of an irregular hexagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular convex hexagon.

Irregular Convex Hexagon

Illustration of an irregular convex hexagon.

Illustration of an irregular convex hexagon with symmetry.

Irregular Convex Hexagon

Illustration of an irregular convex hexagon with symmetry.

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped rulers, called irregular curves. A series of points is first determined through which the curved line is to pass. The line is then drawn through these points by using such parts of the irregular curve as will pass through several of the points at once, the curve being shifted from time to time as required." — Hallock, 1905

Irregular Curves

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Concave Nonagon

Illustration of a nonregular/irregular convcave nonagon. A nonagon is a closed geometric figure with…

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Convex Nonagon

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9…

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9 sides.

Irregular Convex Nonagon

Illustration of a nonregular/irregular convex nonagon. A nonagon is a closed geometric figure with 9…

Illustration of 2 regular congruent nonagons that have the same center. One nonagon has been rotated 20° in relation to the other.

2 Congruent Rotated Nonagons

Illustration of 2 regular congruent nonagons that have the same center. One nonagon has been rotated…

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular concave octagon.

Irregular Concave Octagon

Illustration of an irregular concave octagon.

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular concave octagon. This polygon has some symmetry.

Irregular Concave Octagon

Illustration of an irregular concave octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon.

Irregular Convex Octagon

Illustration of an irregular convex octagon.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular convex octagon. This polygon has some symmetry.

Irregular Convex Octagon

Illustration of an irregular convex octagon. This polygon has some symmetry.

Illustration of an irregular pentagon. This is also an example of a concave polygon with symmetry.

Irregular Concave Pentagon

Illustration of an irregular pentagon. This is also an example of a concave polygon with symmetry.

Illustration of an irregular concave pentagon.

Irregular Concave Pentagon

Illustration of an irregular concave pentagon.

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Irregular Convex Pentagon

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Irregular Convex Pentagon

Illustration of an irregular pentagon. This is also an example of a convex polygon with symmetry.

Illustration of an irregular convex pentagon.

Irregular Convex Pentagon

Illustration of an irregular convex pentagon.

Illustration of an irregular convex polygon with 16 sides that has symmetry. It could be used to show rotation of a square.

Irregular Convex Polygon

Illustration of an irregular convex polygon with 16 sides that has symmetry. It could be used to show…

Illustration of a quadrilateral with diagonals AC and BD.

Quadrilateral With Diagonals

Illustration of a quadrilateral with diagonals AC and BD.

"Irregular reflection or diffusion results from the incidence of radiant energy upon an irregular surface, as is illustrated. Bodies are made visible to the eye mainly by the light that they thus diffuse." -Avery 1895

Irregular Reflection or Diffusion

"Irregular reflection or diffusion results from the incidence of radiant energy upon an irregular surface,…