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The basic idea of my argument for choosing A is that there is an semantical ambiguity about the verbial modifier 'over the century'
I think D, E are clearly grammatically unsound.
So A B & C are left.
Now, suppose they are all grammatically correct. In the sentence B, the problem is we are not sure about the time when 'a tripling' occurs.
Let's consider the following sentence:
#1，Over the course of the last two decades, the disintegration of the Soviet Union continued effecting the international politics.
The disintegration of Soviet Union didn't last for 20 years. What incessantly existed in the last 20 years was the effect of its disintegration. 'Over the course of the last two decades' is an adverbial modifier, and it is modifying the whole sentence, not the subject.
Back to the choice B:
Its main structure is:
over the course of 18th century (advervial modifier) a tripling (subject) was due to...(predicative).
And the adverbial is modifying the whole sentence, not the subject. So we are not sure when the 'tripling' happened.
But the author clearly wanted to tell us that 'the output of iron outwork' were incassently growing over the whole 18th century, and it tripled as a result.
So B is ambiguous.
There are two ambiguous points:
1. Sentence C fails to show the causal relationship between 'the output of iron' and 'those technique improvements'
As we can inform, the author tried to tell us the improvements of certain techniques CAUSE
the tripling of iron output.
But by using 'with', the sentence C fails to tell us the logic relationship between the 'improvements of techniques' and 'tripling of iron output'
#3 I passed the exam, with the pan borrowed from my roommate.
#4 I passed the exam, by using the pan borrowed from my roommate.
#5 I passed the exam, with very little preparation
In #3, there is no causal relationship between 'pass the exam' and 'pan borrowed from my roommate'. They are just coincident.
but by #4, I claim that there is some (magical) causal relationship between 'pass the exam' and 'using the pan...'
In #5, the preposition 'with' shows a little flavor of surprise: even though I had little preparation, I passed the exam. And here, no causal relationship at all.
Back to our question. By using 'with', Sentence C only shows the coincidence of those events (like the pan and to pass the exam), not their causal relationship which the author was dying to tell us.
2. the adverbial modifier in sentence C failed tell us when those techniques improvements happed.
As I mentioned above, the adverbial modifier is modifying the sentence. In sentence C, luckily, the adverbial 'over 18 century' is clearly modifying the sentence 'the output tripled', and this is what the author wanted to say.
But it is not modifying other adverbials, i.e. 'charcoal's being replaced by coal as the fuel used in the smelting of iron ore and several improvements in blowing machinery'. Therefore, we are still not sure about when these happened.
So C is out.
A's structure looked wierd, because the author intenionally put the three parts together without using a comma:
1 the output tripled...
2 as a result of the improvement of...
3 and because the coal replace...
Therefore the adverbial modifier 'over the cause of the 18th century' with a comma can modify these three simultaneously, and A clearly tells us that the tripling is a tripling over the 18th century, and that the improvement of blowing technique and the coal replacement both happened some times during the 18th century.
So although A looks very artificial, it clearly shows what the author wanted to tell us
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