To take the height of ( something ) = to measure its position relative to the horizon. The phrase could also be used in a figurative sense meaning 'to assess the importance, quality, type etc. of something'. As in this example from Ben Jonson's The Alchemist:
... [مشاهده متن کامل]
The doctor, I asssure you, shall inform you,
To the least shadow of a hair, and show you
An instrument he has of his own making,
Wherewith no sooner shall you make report
Of any quarrel, but he will take the height on't
Most instantly, and tell in what degree
Of safety it lies in, or mortality.
And how it may be borne, whether in a right line,
Or a half circle; or else may be cast
Into an angle blunt, if not acute. Alc. III. 2. 352 - 61.
In this, the alchemist and his assistant are attempting to trick a young jacakanapes to give them money, and they try to impress him with scientific mumbo - jumbo, pretending that they can, using an instrument, tell when it is safe to quarrel with someone. The Alchemist was written circa1609 - 10.
