Which preposition to use with northeastward

across Occurrences 1%

The high crags which here shoulder the Wall are part of the Great Whin Sill, an intrusive dyke of dolerite which stretches from Greenhead northeastward across the county nearly to Berwick.

for Occurrences 1%

We crossed into Hungary, rolled northeastward for five or six hours into the Vag valley, with its green hills and vineyards and ruined castles, and finally came to a little place consisting almost entirely of consonants, in the Tatra foot-hills.

from Occurrences 1%

[Marginal note: Iamahey fiue and twenty dayes iourney Northeastward from Pegu.] which is in the countrey of the Langeiannes, whom we call Iangomes; it is fiue and twenty dayes

of Occurrences 1%

To the northeastward of the town, and on a shelf of the Lepaterique Mountains, which rise abruptly in that direction, and are covered with pine forests to their summits, is distinctly visible the Indian town of Lauterique,its position indicating clearly that it had been selected with reference to defensive purposes.

Which preposition to use with  northeastward