Others Maths Puzzle

I am the center of gravity, hold a capital situation in Vienna, and as I am foremost in every victory, am allowed by all to be invaluable. Though I am invisible, I am clearly seen in the midst of a river. I could name three who are in love with me and have three associates in vice. It is vain that you seek me for I have long been in heaven yet even now lie embalmed in the grave.

What am I?

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Others Other Question

Consider a rectangle out of which another small rectangle is carved out. This smaller rectangle can have any arbitrary orientation and any area. Considering the remaining area of the larger rectangle, you have to draw a straight line in a way such that it divides the remaining area of larger rectangle in two equal halves. And you have to provide a general solution that works for any small rectangle to be carved out. 0,6,24,120,210,336.?.