It is well known in the scholarly literature that despite the fact that Boyle's name has become associated with the Mechanical Philosophy, that he defended general providence (and thus the existence of at least one final cause). And, as scholars have noted (and Boyle, too), in his many design arguments the Strasbourg clock figures prominently. Here's an example:
’tis like a rare Clock, such as may be that at Strasbourg, where all things are so skilfully contriv’d, that the Engine being once set a Moving, all things proceed according to the Artificers first design, and the Motions of the little Statues, that at such hours perform these or those things, do not require, like those of Puppets, the peculiar interposing of the Artificer, or any Intelligent Agent imployed by him, but perform their functions upon particular occasions, by vertue of the General and Primitive Contrivance of the whole Engine” (A Free Enquiry).
Boyle here uses the world-clock analogy in order to drive home the idea that God’s general providence works by general and original (this captures the sense of Boyle’s “primitive” in light of the “first design”) causes. (Locke uses the Strasbourg clock in yet another subtly different argument in Essay 3.6.3 & 3.6.9.)
But elsewhere, in the Usefulness of Natural Philosophy, Boyle adds two claims to his treatment of the Strasbourg clock that reveal his classical debt: (i) “the various motions of the wheels and other parts concur to exhibit the phenomena designed by the artificer in the engine…” (ii) “and might to a rude Indian seem to be more intelligent than Cunradus Dasypodius himself.” (Conrad Dasypodius was the designer of the famous Strasburg clock.) I return to that ignorant Indian below (while ignoring Boyle's shocking ignorance of the cultivation/civilization of India).
The phenomena exhibited by the (second) Strasbourg clock were primarily astronomical, that is, it was a gigantic planetarium in which heavenly motions and phenomena were faithfully represented (see the picture at the bottom of this post). I am not the first to note that Boyle is indebted to Cicero. But– to be anachronistic for a second – I have not found anybody noting that Boyle is really plagiarizing a specific argument by Cicero:
Our friend Posidonius has recently fashioned a planetarium; each time it revolves, it makes the sun, moon, and planets reproduce the movements which they make over a day and a night in the heavens. Suppose someone carried this to Scythia or to Britain. Surely no one in those barbarous regions would doubt that that planetarium had been constructed by a rational process. Yet our opponents [the Epicureans] here profess uncertainty whether the universe, from which all things take their origin, has come into existence by chance or some necessity, or by divine reason and intelligence. Thus, they believe Archimedes more successful in his model of the heavenly revolutions than nature’s production of these, even though nature’s role is considerably more ingenious than such representations.
There are many arguments from design. Let’s dub the main one articulated in the quoted passage the “Posidonian argument.” It deploys the “structural resemblance of state-of-the-art-planetary mechanism to the celestial globe.” For, it relies on the supposition that everybody (even barbarians) will grant that a sophisticated complex machine, which is a scientific representation of nature, must be the product of intelligent design, then (once granted) it turns to suggest that the represented complex (beautiful, well-adapted, etc.) machine must itself also have an intelligent author. (For a picture of what we think is Posidonius's planetarium and some reflections on the afterlife of the argument, see here. [See also Mohan's response.])
I stipulate that despite the presence of minor variants we know that we are dealing with the Posidonian argument if a design argument is accompanied (as it is in Cicero’s text) by a reference or allusion to Archimedes’ planetary sphere and/or Posidonius’ portable planetarium as well as a savage/ barbarian. (Obviously, there also treatments of Posidonius's planetarium without a focus on God's design.) Boyle substitutes the Strasbourg clock and a rude Indian, but preserves Cicero's argument form.
A few weeks ago I noted the logical structure and underlying significance of this Posidonian argument in the context of Dennett's reconstruction of a version of the argument in Descartes. For, the argument hinges on the fact that scientific theories and scientific representations presuppose God's order/design. Finding Boyle's adaptation of the Posidonian argument suggests further evidence for my claim that it is not a by-product of the scientific revolution, but it's right there at the heart of that process that was once called the mechanization of nature.
 Cicero The Nature of the Gods, translated by P.G. Walsh, (Oxford: Oxford University Press, 1978), 78; I have made some minor modifications.
 David Sedley (2007) Creationism and Its Critics in Antiquity, Berkeley: University of California Press, 207.
 As Sedley notes the represented world need not be itself a mechanism (207).
 According to Sedley (2007), 207, n. 6, Archimedes’ sphere is “likely to be the original Stoic example,” and the naming of Posidonius’ a “localizing touch.” (Posidonius was one of Cicero’s teachers.) In addition, see I.G. Kidd (1988) Posidonius II. The commentary: (i) Testimonia and Fragments 1-149, Cambridge: Cambridge University Press, pp. 74-5. See also the useful discussion in Sylvia Berryman (2010) The Mechanical Hypothesis in Ancient Greek Natural Philosophy, Cambridge: Cambridge University Press, 150-5. Details on Archimedes’ sphere can also be gleaned from (among others) Cicero (e.g., Republic 1.21-22; Tusculan Disputations 1.63), Sextus Empiricus, M. 9.115, and Proclus (A Commentary on the First Book of Euclid's Elements, Book I, Chapter XIII). (All available to Clarke, Hume, and Smith.) For more such references see https://www.math.nyu.edu/~crorres/Archimedes/Sphere/SphereSources.html.