Wanting to make their wills sincere, they first extended their knowledge.

致知在格物。

Extension of knowledge consists of the investigation of things.

[5] 物格而后知至。

When things are investigated, knowledge is extended.

知至而后意诚。

When knowledge is extended, the will becomes sincere.

意诚而后心正。

When the will is sincere, the mind is correct.

心正而后身修。

When the mind is correct, the self is cultivated.

身修而后家齐。

When the self is cultivated, the clan is harmonized.

家齐而后国治。

When the clan is harmonized, the country is well governed.

国治而后天下平。

When the country is well governed, there will be peace throughout the land.

[6] 自天子以至于庶人臺是皆以修身为本。

From the king down to the common people, all must regard the cultivation of the self as the most essential thing.

[7] 其本乱而末治者，否矣。其所厚者薄而其所薄者厚，未之有也。

It is impossible to have a situation wherein the essentials are in disorder, and the externals are well-managed. You simply cannot take the essential things as superficial, and the superficial things as essential.