EUC 



EUD 



tor 'Eradtosthenes, Achimedes, Apollo- 

 nius, Ptolemy, Theon, &c. &c. He re- 

 duced into regularity and order all the 

 Fundamental principles of pure mathe- 

 matics, which had been delivered down 

 by Thales, Pythagoras, Eudoxus, and 

 other mathematicians before him, and ad- 

 ded many others of his own discovering 1 : 

 on which account it is said he was the 

 first who reduced arithmetic and geome- 

 try into the form of a science. He like- 

 wise applied himself to the study of mix- 

 ed mathematics, particularly to astrono- 

 my and optics. 



His works, as we learn from Pappus 

 and Proclus, are, the Elements, Data, In- 

 troduction to Harmony, Phenomena, Op- 

 tics, Catoptrics, a Treatise of the Division 

 of Superficies, Porisms, Loci ad Super- 

 ficiem, Fallacies, and four books of Co- 

 nies. 



The most celebrated of these is the first 

 work, the " Elements of Geometry ;" of 

 which there have been numberless edi- 

 tions, in all languages ; and a fine edition 

 of all his works, now extant, was printed 

 in 1703, by David Gregory, Savilian Pro- 

 fessor of Astronmy at Oxford. 



The " Elements," as commonly pub- 

 lished, consist of fifteen books, of which 

 the two last, it is suspected, are not Eu- 

 clid's, but a comment of Hypsicles of 

 Alexandria, who lived 200 years after Eu- 

 clid. They are divided into three parts, 

 viz. The contemplation of Superficies, 

 Numbers, and Solids ; the first four books 

 treat of planes only; the fifth of the pro- 

 portions of magnitudes in general; the 

 sixth of the proportion of plane figures; 

 the seventh, eight, and ninth, give us the 

 fundamental properties of numbers ; the 

 tenth contains the theory of commensura- 

 ble and incommensurable lines and spa- 

 ces ; the eleventh, twelfth, thirteenth, 

 fourteenth, and fifteenth, treat of the doc- 

 trine of solids. 



There is no doubt but, before Euclid, 

 elements of geometry were compiled by 

 Hippocrates of Chius, Eudoxus, Leon, 

 and many others, mentioned by Proclus, 

 in the beginning of his second book ; for 

 he affirms, that Euclid new ordered many 

 things in the Elements of Eudoxus, com- 

 pleted many things in those of Theatetus, 

 and besides strengthened such proposi- 

 tions as before were too slightly, or but 

 superficially, established, with the most 

 firm and convincing demonstrations. 



History is silent as to the time of Eu- 

 clid's death, or his age. He is represent- 

 ed as a person of a courteous and agreea- 

 ble behaviour, and in great esteem and 



familiarity with King Ptolemy ; who once 

 asking him whether there was any short- 

 er way of coming at geometry than by his 

 Elements, Euclid, as Proclus testifies, 

 made answer, that there was no other 

 royal way or path to geometry. 



EUCOMIS, in botany, a genus of the 

 Hexandria Monogynia class and order. 

 Natural order of Coronariae. Asphodeli, 

 Jussieu. Essential character : corolla in- 

 ferior, six-parted, permanent, spreading; 

 filaments united at the base into a nectary 

 growing to the corolla. There are four 

 species, all natives of the Cape. 



EUDIOMETRY. The measurement of 

 the quantity of oxygen contained in at- 

 mospheric air, or indeed in any gas in 

 which it is not intimately combined, is 

 named eudiometry, and the instrument 

 by which it is performed, the eudiome- 

 ter. To attain such a measurement, it is 

 merely necessary to present to atmosphe- 

 ric air some substance, which combines 

 with its oxygen, and which either does 

 not afford any gaseous product, or affords 

 one that is easily abstracted and measur- 

 ed. Differect substances have been ap- 

 plied to this purpose. 



The fluid originally employed by 

 Scheele, in the analysis of the air, the so- 

 lution of sulphuret of potash, or, what is 

 rather more convenient, the sulphuret of 

 lime is perhaps superior in accuracy to 

 any, at least if the air be not too long ex- 

 posed to it, and be not in too small a quan- 

 tity proportioned to the quantity of fluid. 

 Phosphorus is applied by a very simple 

 apparatus, but, by its solubility in nitro- 

 gen gas, it adds to the bulk of the resi- 

 dual air, for which a correction must be 

 made. Nitrous gas was employed by 

 Priestley; it exhibits the result immediate- 

 ly, but is liable to several sources of fal- 

 lacy. Hydrogen gas was employed by 

 Volta : a given measure of it being put 

 along with a quantity of the air designed 

 to be submitted to trial into a graduated 

 tube, and inflamed by the electric spark, 

 the diminution of volume indicating the 

 quantity of oxygen ; 100 measures of oxy- 

 gen require rather less than 200 measures 

 of hydrogen for saturation ; about 40 mea- 

 sures of hydrogen are therefore sufficient 

 to saturate the oxygen contained in 100 

 measures of atmospheric air, but it is pro- 

 per to use an excess of hydrogen, as 

 otherwise part of the oxygen is liable to 

 escape combination. From 60 of hydro- 

 gen, with 100 of atmospheric air, Mr. 

 Dalton states that the residuum, after ex- 

 plosion, is 100, 21 of oxygen combining 

 with 39 of hydrogen. The method is 



