The first blank in this sentence is likely the easiest to fill in. It is a synonym parallel to "praise" in the final clause of the sentence. The author in question must have received much adulation for the works in question, meaning that she received much praise. These works are written for the general populace, making philosophical topics accessible to them. Such works are called "popular," not necessarily because they have won a popularity contest but because they are written for the people—for the "general populace."

The first blank is probably the more obvious of the two, for Henry's action is described as being quite careful. When we take great care about the details of something, we act in a meticulous manner, as Henry is doing in the story presented in this sentence. The second blank is likely a bit stranger, for we do not use the word "disposition" in this way very often. In a very general sense, a "disposition" can merely refer to the overall order found in a whole made up of various parts. Henry's actions are helping to create such a harmonious disposition in the whole group.

Stay as close as possible to the clues in a sentence. It is clear that the minister is preaching. This is indicated at the very close of the sentence. Therefore, you should stay with options that indicate some kind of verbal expression. Now, the options "colloquy" and "discourse" are not as good as "homily." A "homily" is a kind of sermon. Often, we think of Catholic priests giving homilies, as this word is still used in Catholic circles more frequently than in other religious groups. The word can be used for various kinds of religious preaching. It seems that the minister's homily had questionable components in it, at least in the estimation of some people. This must have led someone to think that he was a heretic, meaning that some people must have thought that he was setting forth teachings that were not the explicit ones of his particular religious tradition.

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.