On Transitions

(1) (most) Transitions have two parts and thus perform two tasks:

* Recapitulate + Announce

Here's a few definitions and examples from Sonnino, 180-11

Cicero: When what as been said is briefly recalled and we briefly propound what is to follow...This gives emphasis to our argument and makes it more memorable. Ad Herenium IV, 35

Wilson: When we go from one matter to another, we use this kind of phrase. Ex: "I have told you the cause of this evil, now I will tell you a remedy for the same". 182.

Scaliger: This figure adds nothing to the meaning but simply repeats what has been said and introduces what will be said. III, lxxvi.

We now turn to laws:

Robert Sanderson, Minister at Lincoln who wrote the textbook Logicae Artis Compendium that Isaac Newton studied, said [Editio Nona. (1680) p. 200]:

Lex Connexionis. Singulae partes Doctrinae aptis transitionibus connectantur. Crebris enim interruptionibus turbantur intellectus et memoria; apta vero colligatione et utrumque juvabitur, et Methodi ratio manifesta fiet. Operae facturus pretium qui docet, Methodi connexionem et rationem universam tabula aliqua sive diagraphe compendiaria discipulis repraesentabit.

The Law of Connections. Transitions aptly connect the individual parts of the message. For the frequent discontinuities (interruptions) disturbe the intellect and the memory. But the suitable colligation (bond/connection/band/conjunction) is the delight of the one and the other and the reasons of the Method become apparent. It will be rewarded he who represents the method of connexions and all the reasons to the disciples by means of table and diagraphs.

And also, Alsted in Systema Mnemonicum Duplex, 106-7:

Prima lex est lex homogeniae... secunda lex dicitur coordinationis...tertia lex dicitur transitionis. 

Milton says:

And if a rather long explication intervenes between these, they are to be joined together by bands of transition, for this restores and refreshes the hearer. 

A transition is either perfect or imperfect. One is perfect which briefly shows both what has been said and what follows, as does the beginning of this second book: "Up to this point has been treated the first part of the art of logic" etc. An imperfect transition is that which shows in some other way merely what has been said or what follows, such as that at the beginning of book i, chapter : "Simple arguments are as I have said" etc. 

So they are:

1. Perfect: It has both parts
2. Imperfect: Have only one part

(1b) There's another type of transition that introduces a digression that hinges on one term/thought of the last sentence, and in the next paragraph starts the digression rephrasing that term/idea and ellaborates it. 

EXAMPLES: (From Ramus Logicke, XVI) from Virgil Georgics, II

Thus far the tilth of fields and stars of heaven;
Now will I sing thee, Bacchus, and, with thee, 

And also (Georgics, III): (Imperfect: without the conclusion 

Thee too, great Pales, will I hymn, and thee, Amphrysian shepherd, worthy to be sung, 

And also (Georgics IV) 

Of air-born honey, gift of heaven, I now 

Take up the tale. 

And Cicero's Orator:

Since, therefore, we have thus shown the cause, we will now, if you please, explain the nature of it; 

And also (imperfect for it lacks an epilogue):

But now let us come to that worthy praetor and to those faults, which be more manifest to those that be here present, then to me although I have studied and prepared myself to declare the same

And also

there are many thing honorable judges which of necessity I most pretermit ...

 (2) Their goal is to guide and refresh the reader.

Therefore all that contributes to give:

1. A pause
2. A bird view of the overall plan of the text so far
3. An explanation
4. A short digression 

Can be used to. It's a sort of stop and dialogue with the reader to provide him with what he needs to effectively understand the plan and keep reading.

(3) When Milton explained how the Method properly arranges the prior and the posterior axioms, (i.e. dispositio), or the antecedent and consequent, he touches on transitions (Logic, II, XVII, p. 473 Columbia Edition). He indicates that we speak of the prior and posterior in five modes, that is the criteria to arrange them:

1. According to time: as an old man is before a youth [sic]. 
2. According to nature: as a cause is before an effect, a genus before a species.
3. According to consecutiveness: what is given when something else is necessarily given, (e.g. sun and light) and there's two possible (opposed) cases:
1. A thing may be before in production: parts before the whole, simple before the composite, means before the end.
2. A thing may be before in intention: the whole before the parts, compound before the simple, the end before the means.
4. Anything is prior in disposition or place which is nearer the beginning: as in narration, before in dignity, (magistrate to the citizen).
5. A thing is prior in cognition which is easier to grasp, either in itself or in us. 

(4) There are 3 classes of transitions, related to the granularity of the discourse.

1. Transitions for the axiom: it's the vinculum that joins the consequent with the antecedent
2. Transitions for the argument: joins axioms (minor and major premises)
3. Transitions for the method: it's the broadest and includes all the possibilities mentioned above and below. 

(5) A very useful account of overall method and transitions is given by Dr. Johnson:

"...It must begin, where it may be made intelligible without introduction; and end, where the mind is left in repose, without expectation of any farther event. The intermediate passages must join the last effect to the first cause, by a regular and unbroken concatenation ; nothing must be therefore inserted which does not apparently arise from something foregoing, and properly make way for something that succeeds it. 
  This precept is to be understood in its rigor only with respect to great and essential events, and cannot be extended in the same force to minuter circumstances and arbitrary decorations, which yet are more happy, as they contribute more to the main design; for it is always a proof of extensive thought and accurate circumspection, to promote various purposes by the same act; and the idea of an ornament admits use, though it seems to exclude necessity. 
  Whoever purposes, as it is expressed by Milton, to build the lofty rhyme, must acquaint himself with this law of poetical architecture, and take care that his edifice be solid as well as beautiful; that nothing stand single or independent, so as that it may be taken away without injuring the rest ; but that, from the foundation to tho pinnacles, one part rest firm upon another." #139. Tuesday July 16, 1751.

(6) Collingwood nicely observes that:

"Here lies the difference between the desultory and casual thinking of our unscientific consciousness and the orderly and systematic thinking we call science. In unscientific thinking our thoughts are coagulated into knots and tangles; we fish up a thought out of our minds like anchor foul of its own cable, hanging upside-down and draped in seaweed with shellfish sticking to it, and dump the whole thing on deck quite pleased with ourselves for having got it up at all. Thinking scientifically means disentangling all this mess, and reducing a knot of thoughts in which everything sticks together anyhow to a system or series of thoughts in which thinking the thoughts is at the same time thinking the connexions between them. Logicians have paid a great deal of attention to some kinds of connexion between thoughts, but to other kinds not so much." An Essay on Metaphysics, 22

(7) There are three main locations for them (adapted from reference below):

• Transitions within paragraphs: Act as cues by helping readers to anticipate what is coming (announces) before they read it. Within paragraphs, transitions tend to be single words or short phrases. (see table below)
• Transitions between paragraphs: Summarizes the previous paragraph (recapiltulates) and suggesting something of the content of the paragraph that follows (announces). It can be a word or two (however, for example, similarly), a phrase, or a sentence. Transitions can be at the end of the first paragraph, at the beginning of the second paragraph, or in both places.
• Transitions between sections: It may be necessary to include transitional paragraphs that summarize for the reader the information just covered (recapitulates) and specify the relevance of this information to the discussion in the following section (announces).

LOGICAL RELATIONSHIP	TRANSITIONAL EXPRESSION
Similarity	also, in the same way, just as … so too, likewise, similarly
Exception/Contrast	but, however, in spite of, on the one hand … on the other hand, nevertheless, nonetheless, notwithstanding, in contrast, on the contrary, still, yet
Sequence/Order	first, second, third, … next, then, finally
Time	after, afterward, at last, before, currently, during, earlier, immediately, later, meanwhile, now, recently, simultaneously, subsequently, then
Example	for example, for instance, namely, specifically, to illustrate
Emphasis	even, indeed, in fact, of course, truly
Place/Position	above, adjacent, below, beyond, here, in front, in back, nearby, there
Cause and Effect	accordingly, consequently, hence, so, therefore, thus
Additional Support or Evidence	additionally, again, also, and, as well, besides, equally important, further, furthermore, in addition, moreover, then
Conclusion/Summary	finally, in a word, in brief, briefly, in conclusion, in the end, in the final analysis, on the whole, thus, to conclude, to summarize, in sum, to sum up, in summary

Source: The Writing Center, University of North Carolina at Chapel Hill. Here