Which preposition to use with perpendicularity

in Occurrences 2%

At the return of peace the prices leaped with parallel perpendicularity in all the markets from $400-$500 in 1814 to twice that range in 1818, only to be upset by the world-wide panic of the following year and to descend to levels of $400 to $600 in 1823.

to Occurrences 1%

why don't you walk the plank at once, and prove yourself sober?" vociferated a long-tailed wag, determined not to slip this opportunity of having a shot on the sly at his first lieutenant, who had only a night or two before put his perpendicularity to a similar test.

Which preposition to use with  perpendicularity