The Beauty arising from Mechanism, apparently adapted to the Necessitys and Advantages of any Animal; which pleases us, even tho there be no Advantage to our selves ensuing from it; will be consider’d under the Head of Relative Beauty, or Design.*
Fowls.
XI. The peculiar Beauty of Fowls can scarce be omitted, which arises from the ||44vast|| Variety of Feathers, a curious Sort of Machines adapted to many admirable Uses, which retain a ||45vast|| Resemblance in their Structure among all the Species, ||46and|| a perfect Uniformity in those of the same Species in the corresponding Parts, and in the two Sides of each Individual; besides all the Beauty of lively Colours and gradual Shades, not only in the external Appearance of the Fowl, resulting from an artful Combination of shaded Feathers, but often visible even in one Feather separately. [27]
Fluids.
XII. If our Reasonings about the Nature of Fluids be just, the vast Stores of Water will give us an Instance of Uniformity in Nature above Imagination, when we reflect upon the almost infinite Multitude of small, polish’d, smooth Spheres, which must be suppos’d form’d in all the parts of this Globe. The same Uniformity there is probably among the Parts of other Fluids as well as Water: and the like must be observ’d in several other natural Bodys, as Salts, Sulphurs, and such like; whose uniform Propertys do probably depend upon an Uniformity in the Figures of their Parts.
Harmony.
XIII. Under Original Beauty we may include Harmony, or Beauty of Sound, if that Expression can be allow’d, because Harmony is not usually conceiv’d as an Imitation of any thing else. Harmony often raises Pleasure in those who know not what is the Occasion of it: And yet the Foundation of this Pleasure is known to be a sort of Uniformity. When the several Vibrations of one Note regularly coincide with the Vibrations of another, they make an agreeable Composition; and such Notes are call’d ||47Concords||. Thus the Vibrations of any one Note coincide in Time with ||48two Vibrations|| of its Octave; and two Vibrations of any Note coincide with three of its Fifth; and so on in the rest of the ||49aCon-[28]cords. ||50bNow no Composition can be harmonious, in which the Notes are not, for the most part, dispos’d according to these natural Proportions. Besides which, a due Regard must be had to the Key, which governs the whole, and to the Time and Humour, in which the Composition is begun: ||51ca frequent and inartificialc|| Change of any of which will produce the greatest, and most unnatural Discord.b|| This will appear, by observing the Dissonance which would arise from tacking Parts of different Tunes together as one, altho both were separately agreeable. A likea|| Uniformity is also observable among the Bases, Tenors, Trebles of the same Tune.
||52aThere is indeed ||53bobservableb||, in the best Compositions, a mysterious Effect of Discords: They often give as great Pleasure as continu’d Harmony; whether by refreshing the Ear with Variety, or by awakening the Attention, and enlivening the Relish for the succeeding Harmony of Concords, as Shades enliven and beautify Pictures, or by some other means not yet known: Certain it is however that they have their place, and some good Effect in our best Compositions.a|| Some other Powers of Musick may be consider’d ||54hereafter||.* [29]
XIV. But in all these Instances of55 Beauty let it be observ’d, That the Pleasure is communicated to those who never reflected on this general Foundation; and that all here alledg’d is this, “That the pleasant Sensation arises only from Objects, in which there is Uniformity amidst Variety:” We may have the Sensation without knowing what is the Occasion of it; as a Man’s Taste may suggest Ideas of Sweets, Acids, Bitters, tho he be ignorant of the Forms of the small Bodys, or their Motions, which excite ||56these|| Perceptions in him. [30]
Theorems.
I. The Beauty of Theorems, or universal Truths demonstrated, deserves a distinct Consideration, ||1being|| of a Nature pretty different from the former kinds of Beauty; and yet there is none in which we shall see such an amazing Variety with Uniformity: and hence arises a very great Pleasure distinct from Prospects of any further Advantage.
II. For in one Theorem we may find included, with the most exact Agreement, an infinite Multitude of particular Truths; nay, often ||2an Infinity|| of Infinites: so that altho the Necessity of forming abstract Ideas, and universal Theorems, arises perhaps from the Limitation of our Minds, which cannot admit an infinite Multitude of singular Ideas or Judgments at once, yet this Power gives us an Evidence of the Largeness of the human Capacity above our Imagination. Thus for instance, the 47th Proposition of the first Book of Euclid’s Elements contains an infinite Multitude of Truths, concerning the infinite possible Sizes of right-angled Triangles, as you make the Area greater [31] or less; and in each of these Sizes you may find an infinite Multitude of dissimilar Triangles, as you vary the Proportion of the Base to the Perpendicular; all which ||3Infinitys of|| Infinites agree in the general Theorem. ||4aIn Algebraick, and Fluxional Calculations, we shall ||5bstill find a greaterb|| Variety of particular Truths included in general Theorems; not only in general Equations applicable to all Kinds of Quantity, but in more particular Investigations of Areas and Tangents: In which one Manner of Operation shall discover Theorems applicable to ||6cinfinitec|| Orders or Species of Curves, to the infinite Sizes of each Species, and to the infinite Points of the ||7dinfinited|| Individuals of each Size.a||
Foundation of their Beauty.
III. That we may the better discern this Agreement, or Unity of an Infinity of Objects, in the general Theorem, to be the Foundation of the Beauty or Pleasure attending their Discovery, let us compare our Satisfaction in such Discoverys, with the uneasy state of Mind ||8in which we are||, when we can only measure Lines, or Surfaces, by a Scale, or are making Experiments which we can reduce to no general Canon, but ||9only|| heaping up a Multitude of particular incoherent Observations. Now each of these Trials discovers a new Truth, but with no Pleasure or Beauty, notwithstand-[32]ing the Variety, till we can discover some sort of Unity, or reduce them to some general Canon.
Little Beauty in Axioms.
IV. Again, let us ||10take|| a Metaphysical Axiom, such as this, Every Whole is greater than its Part; and we shall find no Beauty in the Contemplation. ||11For tho|| this Proposition ||12contains|| many Infinitys of particular Truths; yet the Unity is inconsiderable, since they all agree only in a vague, undetermin’d Conception of Whole and Part, and in an indefinite Excess of the former above the latter, which is sometimes great and sometimes small. So, should we hear that the Cylinder is greater than the inscrib’d Sphere, and this again greater than the Cone of the same Altitude and Diameter ||13with|| the Base, we shall find no pleasure in this Knowledge of a general Relation of greater ||14and|| less, without any precise Difference or Proportion. But when we see the universal exact Agreement of all possible Sizes of such Systems of Solids, that they preserve to each other the constant Ratio of 3, 2, 1; how beautiful is the Theorem, and how are we ravish’d with its first Discovery!
Easy Theorems.
||15aWe may likewise observe, that easy or obvious Propositions, even where the Unity is sufficiently distinct, and determinate, do not please us so much as those, which [33] being