As a question has been started with regard to the au thor of the Elements, so the merit of the work has like wise been a subject of discussion. While some main tain that it is not only the most perfect system of elemen tary geometry, either of ancient or modern times, but as absolutely beyond the reach of improvement, except so far as to flee it from the blunders of ignorant commen tators ; others complain that the demonstrations are un necessarily long and prolix, frequently intricate and indi rect, and ill adapted to the purposes of instruction. Per haps in this dispute, too, both parties are wide of the truth. It must be acknowledged, on the one hand, that for (t rigid accuracy" of demonstration, perspicuity of language, and beauty of arrangement, the Elements of Euclid stand unrivalled, and that modern writers have excelled in these qualities, exactly in proportion as they have approached the Greek geometer. It must also be admitted, however, that in the present state of the mathe matical sciences, even these Elements are susceptible of improvement.
Though they are equally necessary as the foundation of all mathematical investigation in which magnitude is concerned, yet they do not bear the same proportion which they once did to the whole science. They still deserve, as much as ever, to be studied on their own ac count ; but as the field to which they open a way has vastly increased, and still continues to increase, it has become a matter of no inconsiderable moment to abridge, as much as possible, the labour necessary to acquire a knowledge of the elementary truths which they contain. On this account we are disposed to regard sonic modern treatises of geometry as possessing advantages unknown even to Euclid ; not that they excel, or even equal hint, in elegance and correctness of demonstration, but because they conduct the learner with greater facility to the ul terior and more objects of enquiry. With all these concessions, however, we are not prepared to ad mit an insinuation that has been sometimes thrown out, as if Euclid owed the continuance of his celebrity to an unreasonable and pertinacious adherence to a system, merely because it is ancient. To such prejudices has been ascribed, and we believe justly, the bondage in which the human mind was long held by the metaphysics of Aristotle. But to ascribe the reputation of Euclid to a similar cause, is to place him infinitely lower than he was ever destined to stand, and to assign to prejudice an au thority over mankind, which it never possessed. Bigotry and superstition may retard or suppress a spirit of ma thematical enquiry ; but we cannot admit the possibility of such a gross perversion of the human intellect, as to suppose that any thing but intrinsic excellence could se cure to an elementary system of geometry, the almost unanimous approbation of mathematicians for two thou sand years.
The other work to which Euclid is in anv degree in debted for his reputation with posterity, is his Book of Data. This treatise, like his Elements, had suffered much from the ignorance of commentators, as well as the depredations of time ; but, like the latter, revived with fresh vigour under the renovating hand of Dr Sim son of Glasgow. It is still perhaps unnecessarily pro lix, and not at all entitled to the estimation in which it was held by the ancients. At the same time it is cer tainly valuable, as containing the rudiments of the geo metrical analysis.
Of Euclid's books on Porisms, nothing can be col lected from ancient writers, except that he did treat of such propositions, and that they were regarded by the ancients, as forming a very important part of their analy sis. They were restored, or rather discovered anew, by Dr Simson, and published after his death by the late Earl Stanhope. See ANALYsIs, Ponisms, Sc.
Besides the subjects already mentioned, Euclid is known to have studied various other branches of the ma thematics, particularly the conic sections, optics, and as tronomy. See CONIC SECTIONS.
It would be impossible to enumerate all the editions through which the elements have passed, and the com mentaries that have been written upon them since the days of Proclus. Those of Commandini in 1572, and Gregory in 1703, deserve to be mentioned ; but it seems to be universally admitted, that Dr Simson's of Glasgow is superior to every other.
Of those who have written on geometry, with the view of accommodating it to the present state of the mathe matical sciences, Legendre, Lacroix, Mr Playfair, and Mr Leslie, may he mentioned as the most successful. Air West too, deserves to be noticed as the anther of an elementary treatise of mathematics, which has not hither to enjoyed the celebrity to which it is so justly entitled.
See Trans. of the Royal Soc. of Edin. vol. iii. part ii. p. 154. Simson's Euclid, Preface. Ilutton's Math. Diet. articles Euclid, Elements, Sc. Bossut Essai sur Ifi4 toire Generale des Mathenzatiques, Paris 1802. Dc la Caille, Lecons Elementaires des Muthematiques, Paris 1811. Mayfair's Geometry, Preface. Leslie's Geometry, Notes. Edin. Rev. vol. xx. p. 79, Sc. (R. G.)