of the spherical angle at the pole of the ecliptic which is contained by the circles of longitude of the two ftars; therefore this angle is alfo given, and by the fourth cafe of oblique-angled spherical triangles, the distance of the two ftars is found; likewife the spherical angle contained by the arc which is their distance, and by the arc which is the complement of the latitude of one of them, is found by the first case of oblique-angled spherical triangles. And because the distance of the two ftars whose longitudes and latitudes are given has been found, and that the distance of the third ftar from each of them is given, the three fides of the spherical triangle, in whose angular points these three stars are, are each of them given; therefore the angle contained by the arc which is the distance of the two first stars, and by the arc which is the distance of one of thefe from the third ftar, is found by the eleventh cafe of obliqueangled spherical triangles; and if this angle be taken from the angle contained by the arc which is the diftance of the two first ftars, and by the arc which is the complement of the latitude of one of them, (which angle was already found), the remaining

angle

angle contained by the arc which is the distance of the star, whose longitude and latitude is fought from the one of the first two, and by the arc which is the complement of this ftar's latitude, is given: and the fides containing this laft angle are each of them given; therefore the fide oppofite to the given angle is found by the fourth cafe of oblique-angled fpherical triangles: and this fide is the complement of the lati tude of the star whofe latitude is fought; therefore its latitude is found. And because the diftance of the ftar whofe latitude and

longitude was fought from the pole of the ecliptic has been found, and that its diftance from the one of the firft ftars is gi ven, and likewife that the angle adjacent to this last fide has been found, the angle adjacent to the other fide, viz. the angle at pole of the ecliptic, is found by the second cafe of oblique-angled fpherical triangles; and the measure of this angle upon the ecliptic is the difference of longitude of the ftar, whose latitude and longitude was fought from that of the one of those stars whofe latitudes and longitudes were given; therefore the latitude and longitude of the third ftar is found.

FINI S.