What is the Method, and what is so personal, brilliant, and transgressive about it? The Method is mechanical; Archimedes finds the area of the parabolic segment by weighing it in his mind. He thinks of the curved parabolic region as a material object — I’m picturing it as a thin sheet of metal carefully trimmed into the desired parabolic shape — and then he places it at one end of an imaginary balance scale. Or, if you prefer, think of it as being seated at one end of an imaginary seesaw. Next he figures out how to counterbalance it against a shape he already knows how to weigh: a triangle.
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