"Among the more noteworthy attempts at integration in modern times were those of Kepler (1609). In his notable work on planetary motion he asserted that a planet describes equal focal sectors of ellipses in equal times. This... demands some method for finding the areas of such sectors, and the one invented by Kepler was called by him the... "sum of the radii," a rude kind of integration. He also became interested in the problem of gaging, and published a work on this... and on general mensuration as set forth by Archimedes. ...[Kepler's] was a scientific study of the measurement of solids in general. ...composed "as it were" (veluti) of infinitely many infinitely small cones or infinitely thin disks, the summation of which becomes the problem of later integration."

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Added on April 10, 2026
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