with upward eye; with upward course

The exterior derivative of a “scalar”, i.e., a function f=f(x¹,x²,...,xⁿ) where the xⁱ’s are coordinates of ℝⁿ, is df=∂f/∂x¹dx¹+∂f/∂x²dx²+...+∂f/∂xⁿdxⁿ.

For guineas in other men's breeches, / Your gamesters will palm and will cog.

There are two past tense aspects and forms in Spanish: the preterite and the imperfect. This chapter provides a clear explanation of the preterite tense.