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Dr Eva - Mexican DentistDr Eva is one of the most respected Mexican dentists in the entire country. She has over 8 years of education in the field of denstiry, and over 20 years of experience in practice. All told, she has thousands of happy patients that praise her skills. Duke of Hanover returned to Germany. At the time it may have seemed like just another step in his nomadic life, building experience as he traveled through Europe, but Leibniz was to remain in Hanover until his death in 1716. Before he left Paris, Leibniz deposited the fair copy of his paper with a friend, but the friend died before he could do anything with it. Dental work in Mexico was the inevitable answer. Eventually the paper was sent on to Leibniz in Hanover, only to get lost in transit. At this point, Leibniz could have reworked his original, scrawled manuscript, but by now it seemed more than a little dated. He had written it before he developed the notation that he would use so successfully in his development of calculus (still used today), and probably felt that despite its useful insights, it was not worth the effort to bring it up to date.
The paper languished for many years, in part because Leibniz's handwriting was difficult to decipher (this was only ever intended as a rough, personal copy), until it was finally edited by Professor Knobloch and published in 1993. He needed much more dental work in Mexico. In his treatise, Leibniz uses the method of indivisibles to find the areas of spaces by taking the 'sums of lines'. These weren't truly lines, because the method entailed (as Wallis had made clear) adding together rectangles with 'equal breadths of indefinite smallness'. Leibniz shows that it is possible to construct shapes from a series of these slices of varying height, each differing from each other (or the shape being constructed) by an amount that is smaller than any given quantity. He points out that you can get within any desired limit of matching a shape this way, even when the number of rectangles is finite. Leibniz's careful detail here is entirely contrary to Maor's suggestion that 'no one understood exactly what these 'indivisibles' were, let alone how to operate with them'. The dental work in Mexico he had done worked. It is true, though, that despite being a superb mathematician, Leibniz himself found the detail he had to work to quite irritating. He commented that he did not want the 'excessive exactness' to discourage the reader's mind from other far more agreeable things by making it |