The easier blank for this sentence is likely the second one. Clearly the philosopher has a great admiration for Rousseau's thought. This leads him to admire it greatly. Such a person almost certainly thinks that Rousseau's thought is perfect. Hence, he thinks that it is "flawless" (i.e. without error or blemish). Someone who has this kind of opinion will be very devoted to Rousseau's thought. Thus, he would "adhere" to it—not physically but, in a way, mentally. "Adhesion" is a good word in this regard, as it can be used to describe such devotion.

Probably the most tempting wrong answer for this question is "emasculating." Whenever something is "emasculating," it takes away the masculinity from something or someone. This is not exactly what is being stated.  It is basically being said that the clothes have an ambiguous character. You really can't tell if they are for men or for women. When something is "androgynous" it could be for either gender. The word is actually made up of parts meaning "man" and "woman." Think of the words "androgen" (male hormones) and "gynecologist" (a doctor specifically treating issues pertaining to females). If the clothes were androgynous, they likely fit the measurements of both males and females. Hence "proportions" is a fine option for the second blank.

The fact that Timothy could overwhelm his listeners with his ideas is a very important clue regarding the answer you are looking for. Apparently, he has a very fertile and fruitful intelligence. The word "fecund" means this. You likely know the abstract known "fecundity," which describes the state of being fruitful in this manner. It seems that he expresses his ideas and insights without much reserve. Whenever someone is so uncontrolled with "outflow" in this manner, such a person can be called prodigal. Often, this word is used to describe someone who spends a lot of money, as in the biblical story of the "Prodigal Son," who did just this with his inheritance.

The second blank is probably easier to solve than is the first one. The problem is being solved in a new way. The word "novel" means new. The word comes from the Latin "novus," which is an adjective meaning new. This kind of solution is "genius," not in the sense of being exceptionally insightful and creative in its novel manner of solving the old problem.

It is easiest to start with the first blank for this question. The kind of reasoning that we do when we apply general ethical principles to particular circumstances is called "casuistry." You can think of it as meaning applying to individual cases. Often, this word is used to describe a kind of sophistical reasoning—that is, a kind of reasoning that only appears to be true. The word "casuistry" can describe a truly necessary undertaking.

The words involved in this sentence are not very difficult. By the simplest reading of the text, it is saying that the phenomenon was not unique but was evidenced by numerous other examples of the same happening or occurrence. The word "singular" can mean unique, as when we say, "It was a singular experience," meaning the kind of experience that will likely not be had again.

Remember that you should always stay as close to the direct meaning of the sentence as possible. You really do not have many details about this trip except that it has the details of the course to be taken on a trip through space. Thus, it is best to stay as close to the idea of space travel as possible, thus describing the map as a "celestial" map.  This word comes from the Latin for the heavens. As regards the trip to the galaxy, it is best just to call it an "expedition." Particularly given the fact that this trip seems to have a plan and organization, the word "expedition" is quite appropriate.

The second blank is probably the easier of the two. The scholar apparently is able to progress toward the completion of his work. We really do not know much else about what he will do—whether he will publish it, announce it, or whatever else might be the case. Hence, the word "consummation" is the best option among those given. The "consummation" is the gathering up of various things into a whole. Often, this can be used to describe the completion of some task. (You can see how the word is related to the idea of "summing up.") The word "veritable" means true. In a strange twist of linguistic fate, it actually means metaphorically true. It is a word that intensifies a metaphor like this. The implication is that scholar was metaphorically able to "coast in" on the information that seems to have come to his attention at some point.

For the first blank, we are only looking for a simple synonym for the word "exhaustion." No further details should be inferred unless necessary. "Lassitude" is just such a state, one that is wholly without energy. The second blank might seem strange, but the word "impotent" is indeed the best option. "Impotence," strictly speaking, merely means without power. The "-potent" portion of the word is related to the Latin for able to do. Thus, we have English words like "potential," "potent," "potentate," and even the related word "possible." Thus, the state of lassitude left Gregory wholly impotent.

For this sentence, stick as close to the literal meaning of your clues as is possible. We are only told that the mayor had made an announcement. Thus, a generic word for "announcement" will be the best option among those provided. "Promulgation" fits this well. To promulgate something is to send it forth, and generally, this relates to a promulgated message. As for the second blank, it seems that the city was surprised by the promulgation. The word "nonplussed" works well here, though you should note that this word generally indicates a very extreme amount of surprise, to the point of meaning that someone is unable to function because of the great amount of surprise.