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In 1680 he studied the Cassinian curve which is the locus of a point the product of whose distances from two fixed foci is constant. He worked on this as part of a study of the relative motions of the Earth and the Sun. The lemniscate of Jacob Bernoulli is a member of the Cassinian curves but this was not realised for 100 years.
Cassini also made a measurement of an arc of longitude in 1712 but obtained a result which wrongly suggested that the Earth was elongated at the poles. Twenty four years later Maupertuis obtained the correct result verifying Newton's predictions.
References elsewhere in this archive:
Tell me about the Cassinian Ovals
Tell me about the Lemniscate of Bernoulli
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References:
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