1.   THE Arabians applied themselves with much assiduity to the study of the sciences, and the situation of their climate led them to prefer astronomy, which they cultivated very early. There are a considerable quantity of their writings in our large repositories for books, which have never yet come under our notice, having still remained in manuscript in their original language: so great has been our neglect of them for some ages. Yet those who have been at the pains curiously to ransack those manuscripts, have been well rewarded for their trouble, by the acquisition they have thence made of many new and original ideas, and the information they have received of various inventions and discoveries, useful and entertaining. A learned gentleman at Oxford, who carefully examined the Arabian manuscripts in the famous library of that university, gives his sanction to this in a manner that should engage others to imitate his example in such researches. Among other motives naturally tending to produce the effect, he says, “the advantages recommending the study of astronomy to the people of the east were many. The serenity of their weather; the largeness and correctness of the instruments they made use of much exceeding what the moderns would be willing to believe; the multitude of their observations and writings, being six times more than what have been composed by Greeks and Latins; and, in short the number of powerful princes, who, in a manner becoming their own magnificence, aided them with protection. One letter is not sufficient, says he, to show in how many respects the Arabian astronomers detected the deficiency of Ptolomy, and the pains they took correct him; how carefully they measured time by water-clucks, sandglasses, immense solar dials, and even what perhaps will surpris you. the vibrations of the pendulum; and with what assiduity and accurately they conducted themselves in those nice attempts, which do so much honour to human genius in the taking the distances of the stars, and the measure of the earth.”

2.  Hence it is manifest that the vibration of the pendulum was employed by the ancient Arabians, long before the epocha we ordinarily assign for its first discovery; and the use it was applied to, was, exactly to measure time, the very purpose for which we employ it.

3.  The discovery of the refraction of light, is of more ancient origin than is generally imagined; for the cause of it appears to have’ been known to Ptolomy. According to Roger Bacon’s account, that great philosopher and geometrician gave the same explanation of that phenomenon, which Descartes has done since; for he says, that a ray, passing from a more rare into a more dense medium, becomes more perpendicular. Ptolomy, wrote a treatise on optics, which was extant in Bacon’s time; and Alhazen seems not only to have known that treatise of Ptolomy, but to have drawn thence whatever is truly estimated in what he advances about the refraction of light, astronomical refraction, and the cause of the extraordinary size of planets when they appear on the horizon. This last point, discussed with so much warmth between Mallebranche and Regis, had already been adjusted by Ptolomy.

4.  Ptolomy, and after him Alhazen, said, that “when a ray of light passes from a more rare, into a more dense medium, it changes its direction when it arrives upon the surface of the latter, describing a line which intersects the angle made by that of its first direction, and a perpendicular falling upon it from the more dense medium.” Bacon adds, after Ptolomy, that the angle formed by the coincidence of those two lines, is not always equally divided by the refracted ray; because in proportion to the greater or less density of the medium, the ray is more or less refracted, or obliged to decline from its first direction.” In this he approaches very near to the reason assigned by Sir Isaac Newton, who deducing the cause of refraction, from the attraction made upon the ray of light by the bodies surrounding it says, “ that mediums are more or less attractive in proportion to their density.”

5.  Ptolomy, acquainted with the principle of the refraction of light, could not fail to conclude, that this was the cause also of what was called astronomic refraction, or of the appearance of planets upon the horizon before they came there; having recourse therefore to this principle, he accounted for those appearances from the difference there was between the medium of air, and that of ether winch lay beyond it; so that the rays of light coming from the planet, and entering into the denser medium of our atmosphere, must of course be so attracted as to change their direction, and by that means bring the star to our view, before it really came upon the horizon. Alhazen tells us of a method whereby we may assure ourselves of this truth by observation. He bids us “take an armillary sphere, and upon it measure the distance of any star from the pole, when it passes nearest its zenith under the meridian, and when it appears on the horizon. This last, he says, will be its smallest distance.” He then makes it appear, that refraction is the cause of this phenomenon. Yet Alhazen advances nothing but what he derived from Ptolomy ; and neither one nor other of them have applied this important discovery in astronomy. so as to deduce from it, that the apparent elevation of the stars, when near the horizon, necessarily requires to be corrected.

6.  Roger Bacon, inquiring into the cause of that difference of magnitude in stars when seen on the horizon, from what they have when viewed over head, says, in the first place, that it may proceed from this: “that the rays coming from the star are made to diverge from each other, riot only by passing from the rare medium of ether into the denser one of our surrounding air, but also by the interposition of clouds and vapours arising out of’ the earth, which repeat the refraction and augment the dispersion of the rays, whereby the object must needs be magnified to our eye." “Though, says he afterward there has been assigned by Ptolemy and Alhazen, another cause for this; these authors thought that the reason of a star’s appearing larger at its rising or setting than when viewed overhead arose from this: that when the star is over head, there are no immediate objects perceived between it and us, so that we judge it nearer to us, arid are not surprised at its littleness ; but when a star is viewed on the horizon, it lies then so low, that all we can see upon earth. interposes between it and us, which making it appear at a greater distance, we imagine it larger than it is. For the same reason the sun and moon, when appearing upon the horizon, seem to be at a greater distance, by reason of the interposition of those objects, which are upon the surface of our earth, than when they are over head; and consequently, there will arise in our minds an idea of their largeness, augmented by that of their distance, and this of course must make it appear larger to us when viewed on the horizon, than when seen in the zenith.

7.  Most of the learned deny the ancients the advantage of having known the rules of perspective, or of having put them in practice although Vitruvius makes mention of the principles of Democritus and Anaxagoras respecting that science. in a manner that plainly shows they were not ignorant of them. “Anazagoras and Democritus," says he, “were instructed by Agatarchus the disciple of They both of them taught the rules of drawing, so as to imitate from any point of view the prospect that lay in sight, by making the lines in their draught, issuing from the point of view there, exactly resemble the radiation of those in nature; insomuch that, however ignorant any one might be of the rules whereby this was performed, could not but know at sight the edifices, and other prospects which offered themselves in the perspective scenes they drew for the deco ration of the theatre; where, though all the objects were represented on a plain surface, yet they swelled out, or retired from the sight, just as objects do endowed with all dimensions.” Again, he says, “that the painter Apatarius drew a scene for the theatre at Tralles, which was wonderfully pleasing to the eye, on account that the artist had so well managed the lights and shades, that the architecture appeared in reality to have all its projections.” Plato, in two or three places of his dialogues, speaks in such a manner of the effects of perspective, as makes it evident that he was acquainted with its principles. Pliny says, “that Pamphilus, who was an excellent painter, applied himself much to the study of geometry, and maintained, that, without its aid, it was impossible ever to arrive at perfection in that art ;“ which holds certainly true with respect to perspective. And a little farther he uses an expression, which can allude to nothing-but perspective; when he says, “that Apelles fell short of Asclepiodorus, in the art of laying down distances in his paintings.” Lucian, in his dialogue of Zeuxis, speaks of the effects of perspective in pictures. Philostratus, in his preface to his drawing, or history of painting, makes it appear that he knew this science; and in the description be gives of Menoetuis' picture of the siege of Thebes, he places full in sight the happy effects of perspective when studied’ with care. There he extols the genius of this painter, who, in representing the walls of the place invested, and scaled by soldiers, placed some of them full in view, others to be seen only as far as the knee, others only at- half length, and others whose heads only, or helmets, were seen, till the whole ended in the points of the spears of those who were not seen at all ; and he adds, that all this was the effect of perspective, which’ deceives the eye by means of the flexure of its lines which gradually approaching one another as they seem to recede from view, proportionally diminish the enclosed objects, and make them appear to retire.

8.  Aristotle was the first who proposed the famous problem respecting the roundness of that image of the sun, which is formed by his rays passing through a small puncture, even though the hole itself be square or triangular. Marolle, resolved this about the middle of the fifteenth century, by demonstrating that this puncture is the vortex 0f two cones of light, the one of which has the sun itself for its base, and the other the refracted image. Upon this, Mr. de Montucla ascribes to him the whole honour of the solution of this optical problem, formerly indeed proposed by Aristotle, but which that ancient philosopher, says he, “according to his wonted way, had but badly accounted for.” It is with regret that I find myself obliged to animadvert upon some very material mistakes, into which Mr. deMontuclahas slipt, whose judgment I so much revere on other occasions. For first of all, from his manner of quoting this problem of Aristotle, it appears that he neither consulted the Greek text, nor even the Latin version that accompanies it: insomuch, that I am at a loss to conceive where be came by this problem of Aristotle, as he produces it; and still more where he met with this obscure solution of it, which he imputes to that ancient philosopher. Aristotle’s only inquiry is, “why the sun, in transmitting his beams through a square puncture, does hot form a rectilineal figure “ And Mr. de Montucla, instead of this, makes him substitute quite another question, respecting the sun in a partial eclipse: Why his rays, in passing through such a puncture, should produce a figure exactly resembling that part of his disk, which remains yet obscured But of all this, there is not one word in Aristotle. Mr. de Montucla afterward affirms, that this question, the proper solution of which had till then been despaired of by naturalists, reduced them all to the necessity of saying with Aristotle, that “light naturally threw itself into a round form, or resumed the resemblance of the luminious body, as soon as ever it had surmounted the obstacle which put it under constraint.” Now this again is what Aristotle says nothing at all of. He gives two solutions of his own problem: the first of which is certainly the foundation, if not the entire substance of what Mr. de Montucla calls the discovery of Marolle. To enable the reader to decide whether I have wronged Mr. de Montucla, I present him with a literal ranslation of a passage of Aristotle’s, containing in it his first solution of this problem. “ Why is it that the sun, in passing through a square puncture, forms itself into an orbicular, and not into a rectilineal figure, as when it shines through a grate Is it not because the efflux of its rays, through the puncture, converges it into a cone whose base is the luminious circle ” This may serve to confirm, what I have formerly ventured to assert, that we but seldom do justice enough to the ancients, either through our entire neglect of them or from not rightly understanding them.

Chapter 19 - Of the Many Discoveries of the Ancients in Mathematics, &c

Chapter 19