Is this semicolon used properly?

Your link is truncated, so I can't read the article for context, but, although the colon may be awkward, it is not grammatically incorrect. If you read the sentence immediately before the one you posted, it should explain why the colon was used.

For instance, I will give you another example, both without the context and with the context. You should be able to see the difference.

(Without context, it appears to be incorrect) "This is the reason why: both salt and baking soda are required to make a cake rise."

(With context, it is correct) "The cake was a disaster because the baker forgot to add salt. This is the reason why: both salt and baking soda are required to make a cake rise."

In the 1830's, the English scientists and inventor Charles Wheatstone discovered why the differences between the two images allows the brain to generate a sensation of depth.

In this case, a semi-colon should not be used at all. However this is semi colon ; and this is just a colon :

If a semi-colon was added instead of the colon the sentence would still be incorrect as a semi-colon integrates two separate ideas relating to the same topic or matter.

For example:

Sally likes Netball. Jams likes Football.

Sally likes Netball; James likes Football.

These phrases are perfectly fine as separate sentences however are closely related ideas and can be represented in the same sentence grammatically with the use of a semi-colon.