To enable him to calculate for himself, and to express & preserve his ideas, his contracts & accounts in writing.
Another part where Jefferson emphasizes the self reliance that the university intends to promote by making educated citizens who can fend for themselves and be able to keep track of their own personal business.
To harmonize & promote the interests of agriculture, manufactures & commerce and by well informed views of political economy to give a free scope to the public industry.
Jefferson's ideal america was an a republic where everyone was a farmer who could provide for themselves, so it makes sense that his university would promote harmony between all of these interests and promote well informed views so that everybody would be well informed about what was going on in the world and how they could affect it.
And where a sparse population would not, within such a compass, furnish subjects sufficient to maintain a school, a competent enlargement of [a] District must, of necessity, there be submitted to
The writers clearly would like if the student population of this new University could come solely from the area around the school as mentioned in the previous sentences, but the writers mention that if a sparse population cannot supply the school with a sufficient amount of students then they would be forced to enlarge the district that they are drawing students from but do so competently so that they could draw a sufficient student body. The writers had no idea what would become of the institution of higher learning in the United State, but they are invariably supporting out-of-state students which there are now an abundance of.
Chemistry, is meant, with its other usual branches, to comprehend the theory of Agriculture
Chemistry is explained in this context not as a natural science but for it's use to understand agriculture which was a practical skill at the time.