No, only latitude. In order to get the longitude one needs very precise clocks to know what precise time it is, which they didn't have. Else the virtual movement of other stars due to the rotation of the earth ruins this, misestimating the time of the day by merely 10 minutes would put you off by up to 280km (at the equator). The latitude can be measured accurately without knowledge of the precise time because polaris is quite exactly above the earth's axis and therefore doesn't appear to move during its rotation.
Actually, only an object with rapid relative movement across the sky is
needed....i.e. The Moon...to determine time and longitude.
Chichester,F., Longitude without time, in: Journal of the Institute of
Navigation, Vol. 19 (1966), 106 -107 (with comments by D.H. Sadler, one
time superintendent of HM Nautical Almanac Office, p. 107 - 109).
Evans, J.J., Longitude without time, in: Journal of the Institute of
Navigation, Vol. 19 (1966), 392 - 394.
Sadler, D.H., Longitude without time, in: Journal of the Institute of
Navigation, Vol. 21 (1968), 234 - 235.
Ortlepp, Bruno, Longitude without time, in: Navigation (Washington),
Vol. 16 (1969), 29 - 31.
Wright, Frances W. , Examples of Moon Sights to Obtain Time and
Longitude, in: Navigation (Washington), Vol. 18, 292 - 297.
Kerst, D.W., Longitude Without Time, in: Navigation (Washington), Vol.
22 (1975), 283 - 292.
Luce, J.W., Longitude Without Time, in: Navigation (Washington), Vol. 24
(1977), 112 - 115.
Kerst, D.W., Comments on "Longitude Without Time", in: Navigation
(Washington), Vol. 25 (1978), 87 - 90.
A short section on lunar altitudes can also be found in:
H.M. Nautical Almanac Office, A Modern View of Lunar Distances, in:
Journal of the Institute of Navigation, Vol. 19 (1966), 131 - 153 (p.133
- 134)
Peace