Final answer:
The question appears to involve the concept of proportions within mathematics, particularly how to find the unknown value in a proportion such as '1:2=4:x', by using cross-multiplication.
Step-by-step explanation:
The question regarding the proportion of sail area increase over a 350-year period seems to be related to advancements in maritime technology, implicating the transition from square sails to triangular lateen sails that improved maneuverability at sea. However, the question could also relate to the mathematical concept of proportions and scale factors.
To find the proportion by which the sail area increased, we would need specific data about the original and final sail areas. Given that the question provides multiple ratios (1.5:1, 1:1.5, 2:1, 1:2) but lacks context, it's not possible to determine the correct proportion of the sail area increase directly. The problem statement given as an example, '1:2=4:x', is an equation that can be solved to find the missing value (x) in the proportion. This type of question typically involves cross-multiplication to find the unknown.