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. rente in some other respects, and esteemed theObservations of Apian and Kepler , who madethem too inaccurate for clearing up so subtil apoint; I was content on first publistsing this Com-pendium in the Year 1705, only to point out this asmy opinion, supported by some degree of proba-bility, and advised posterity to be strictly on thewatch for its return, which I expected about theyear 1758.

But he goes on and fays, that since the firstpublishing the Compendium, he had found out amethod of easily and accurately computing themotions of Comets in any Ellipsis whatever: Andthat in turning over the Catalogues of ancientComets, he had found three more preceding theothers in the same order and intervals; to wit, in1305, about Eajler ; in 1380, the month uncer-tain ; and another in 1456, in the month ofJune ; and this made him resume his former opi-nion with more confidence than formerly, so thatin the whole he had obtained a catalogue of sixComets, which appeared in the years 1305, 1380,1456, 1531, 1607, 1682; and being thus pre-pared, instead of the parabolic Orbit which he

had

As to what Carpenters, Masons, and other artificers performwithout the knowledge of any properties of Lines at all, it isfrom the rules that thinking men have laid them down, andwhich they are content to use on their faith, without pretendingor being capable to examine into the truth of the demonstra-tion, for many people can dexterously put in practice the in-ventions of others, if you will take the pains to instruct them,the’ they fall short of a capacity to be inventors themselves.

Now the computation of a Comet’s motion in an Ellipsiswas heretofore very difficult, which made Dr, Halley computethem as moving in the curves of Parabola’s, therefore it warnot strictly accurate on that account.