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This page (plate 14) illustrates projections obtained by cutting a cone with an oblique plane.
Detail of the title page of part I of the General Trattato di Numeri (General Treatise on Number and Measure) (1556) of Niccolo Tartaglia (1500-1557). This is an extensive work on elementary mathematics that was popular in Italy for several decades after its publication.
Here Tartaglia is showing how to determine the area of an irregular curved shape.
Gottfried Wilhelm Leibniz carried on an active correspondence within the intellectual community of his time. In particular, two of his main correspondents were the brothers Jacob and Johann Bernoulli. Johann began corresponding with Leibniz in 1693.
In this December 1696 letter from Leibniz to Bernoulli, there is a discussion of integration by parts applied to functions having powers of x and powers of the logarithm.