The center of gravity of any body or geometrical magnitude is by definition the same as the centroid of a certain system of parallel forces. It will be convenient, therefore, to use the word centroid in most cases instead of center of gravity. […] The centroid of any area may be found by the following method: Divide the area into parts such that the area and centroid of each part are known. Take the centroids of the partial areas as the points of application of forces proportional respectively to those areas. The centroid of this system of forces is the centroid of the total area, and may be found by the method of Art. 172.

Then there was Betty who was constantly in a fit when she invariably became speechless. Not to mention, Sally's mouthsore and the severe dog-bites suffered by Maria.

First, let us define its 1-dimensional analog, that is, a topological graph. A graph 𝛥 is a 1-dimensional stratified topological space with finitely many 0-strata (vertices) and finitely many 1-strata (edges). […] A graph such that any vertex belongs to at least two half-edges we call an s-graph. Clearly the boundary ∂𝛺 of a surface 𝛺 with marked points is an s-graph. A morphism of graphs 𝜑:𝛥'→𝛥 is a continuous epimorphic map of graphs compatible with the stratification; i.e., the restriction of 𝜑 to any open 1-stratum (interior of an edge) of 𝛥' is a local (therefore, global) homeomorphism with appropriate open 1-stratum of 𝛥.

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