EYO 



EUO 



possessed in a high degree what is gene- 

 rally called erudition. He had attentive- 

 ly read the most eminent writers of an- 

 cient Rome ; the civil and literary history 

 of all ages and of all nations was familiar 

 to him ; and foreigners, who were only 

 acquainted with his works, were astonish- 

 ed to find, in the conversation of a man, 

 whose Jong life seemed solely occupied 

 in mathematical and physical researches 

 and discoveries, such an extensive ac- 

 quaintance with the most interesting 

 branches of literature. In this respect, 

 no doubt, he was much indebted to a very 

 uncommon memory, which seemed to re- 

 tain every idea that was conveyed to it, 

 either from reading or from meditation. 

 He would repeat the ,/Eneid of Virgil, 

 from the beginning to the end, without 

 hesitation, and indicate the first and last 

 line of every page of the edition he used. 



Several attacks of a vertigo, in the be- 

 ginning of September, 1783, which did 

 not prevent his computing the motions 

 of the aerostatic globes, were, however, 

 the forerunners of his mild passage out of 

 this life. While he was amusing himself 

 at tea with one of his grand children, he 

 was struck with an apoplexy, which ter- 

 minated his illustrious career at seventy- 

 six years of age. 



M. Euler's constitution was uncommon- 

 ly strong and vigorous. His health was 

 good, and the evening of his longMife was 

 calm and serene, sweetened by the fame 

 that follows genius, the public esteem and 

 respect, that are never withheld from ex- 

 emplary virtue, and several domestic com- 

 forts, which he was capable of feeling, and 

 therefore deserved to enjoy. 



The catalogue of his works has been 

 printed in fifty pages, fourteen of which 

 contain the manuscript works. The print- 

 ed ones consist of works published sepa- 

 rately, and works to be found in the me- 

 moirs of several academies, viz. in thirty- 

 eight volumes of the Petersburgh acts, 

 (from six to ten papers in each volume ;) 

 in several volumes of the Paris acts ; in 

 twenty-six volumes of the Berlin acts, 

 (about five papers to each volume ;) in 

 the Acta Eruditorum, in two volumes ; in 

 the Miscellanea Taurinensia, in vol. ix. of 

 the Society of Ulyssingue ; in the Ephe- 

 merides of Berlin; in the Memoires de la 

 Socie'te Oeconomique, for 1766. 



EVOLUTE, in the higher geometry, 

 a curve, which, by being gradually open- 

 ed, describes another curve. Such is the 

 curve B C F ; (Plate V. Miscel. fig. 7.) for 

 if a thread, F C M, be wrapped about, or 

 applied to the said curve, and then un- 



wound again, the point M, thereof, will 

 describe another curve, A M M, called by 

 M. Huygens, a curve described from evo- 

 lution. The part of the thread, M C, is 

 called the radius of the e volute, or of tho 

 osculatory circle described on the centre, 

 C, with the radius, M C. 



Hence, 1. When the point, B, falls in 

 A, the radius of the evolute, M C, is equal 

 to the arch, B C ; but if not, to A B, and 

 the arch B C. 2. The radius of the evo- 

 lute, C M, is perpendicular to the curve, 

 A M. 3. Because the radius, M C, of the 

 evolute continually touches it, it is evi- 

 dent, from its generation, that it may be 

 described through innumerable points, if 

 the tangents in the parts of the evolute 

 are produced until they become equal to 

 their corresponding arches. 4. The evo- 

 lute of the common parabola is a para- 

 bola of the second kind, whose parameter 

 is .2-7 of the common one. 5. The evo- 

 lute of a cycloid is another cycloid equal 

 and similar to it. 6. All the arches of 

 evolute curves are rectifiable, if the radii 

 of the evolute can be expressed geome- 

 trically. 



EVOLUTION. See AIGEBHA. 



EVOLUTION, in the art of war, the mo* 

 tion made by a body of troops, when they 

 are obliged to change their form and dis- 

 position, in order to preserve a post, or 

 occupy another, to attack an enemy with 

 more advantage, or to be in a condition 

 of defending themselves the better. It 

 consists in doublings, counter-marches, 

 conversions, &c. A battalion doubles 

 the ranks, when attacked in front or rear, 

 to prevent its being flanked, or surround- 

 ed ; for then a battalion fights with a lar- 

 ger front. The files are doubled, either 

 to accommodate themselves to the ne- 

 cessity of a narrow ground, or to resist 

 an enemy which attacks them in flank ; 

 but if the ground will allow it, conversion 

 is much preferable, because, after con- 

 version, the battallion is in its first form, 

 and opposes the file leaders, which are 

 generally the best men, to the enemy ; 

 and likewise, because doubling the files 

 in a new or not well disciplined regi- 

 ment, they may happen to fall into disor- 

 der. 



E VOLVULUS, in botany, a genus of 

 the Pentandria Tetragynia class and or- 

 der. Nat iral order of Campanacese. Con- 

 volvuli, Jussieu. Essential character : ca- 

 lyx five-leaved ; corolla five-cleft, rotate ; 

 capsule three-celled; seeds solitary. 

 There are seven species, all natives of the 

 East or West Indies. 



EUONYMUS, in botany, English spin- 



