points to the main part of the sentence. I can't believe the student read this over and found it comprehensible. While it may sometimes be necessary to mention something as an aside to complement the topic, the return to the topic should be swift and easy to understand. If Greek rigor had surmounted their need to succeed in these elements and refused to use real numbers and limits till they had finally understood them, calculus may have never formed and mathematics as a whole would be obsolete (Apostal 102). "Centuries" is the plural of "century not the possessive. "Demonstrate" would be better. It should say: "The Royal Society hosted a guest each week." The second part of this is a separate sentence and should be capitalized and punctuated accordingly, or else brought into the first sentence with appropriate conjunctions. I have tried to categorize the errors as best as I could. A "cardinal sin" is a sin of fundamental importance. "Achievements" or "discoveries" would be better.
"Quite a busy man" is a bit colloquial. This could in the devil's snare thesis be confused with Smith Senior dying from a fall. Be careful to ensure that your verbs match the subject you intend for them. The university re-opened after the plague in 1667. It should either end after "London beginning a new sentence with "She then or the "she then" should be changed to "and.". "Predominant" is not the best word in this case anyway. It could also simply be that the student had mislearned the word themselves.
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