GE0 



OEO 



pearances observed in these rocks it is 

 concluded, that the waters in which they 

 were formed had risen with great rapidi- 

 ty, and had afterwards settled into a state 

 of considerable calmness. 



The collections and deposits derived 

 from the materials of pre-existing masses, 

 worn down by the powerful agency of air 

 and water, and afterwards deposited on 

 the land or on the sea coasts, ure termed 

 alluvial, and are, of course, of much later 

 formation than any of the preceding 

 classes. These deposits may be divided 

 into, 1. Those which are formed in moun- 

 tainous countries, and are found in vallies, 

 being composed of rolled masses, gravel, 

 sand, and sometimes loam, fragments of 

 ores, and different kinds of precious 

 stones. 2. Those which occur in low and 

 flat countries, being peat, sand, loam, bog 

 iron oar, nagelflech, calc-tuff, and calc- 

 nter: the three latter being better 

 known by the names breccia, tufa, and 

 stalactite. 



In this ingenious system, in which so 

 rnu,ch knowledge of the subject prevails, 

 and in which the marks of long and pa- 

 tient investigation ajre evident, a very 

 close accordance with geological facts is 

 generally observable. Some few difficul- 

 ties however occur, particularly it seems 

 with respect to the new trap formation ; 

 since, although the appearances which 

 this is intended to explain do not better 

 agree with any other supposition, still 

 the rising of the waters, whilst they yet 

 covered the summits of primitive moun- 

 tains, has much the appearance of a sup- 

 position made up for this particular pur- 

 pose ; and as, at the same time, it appears 

 to be warranted by no other phenomena, 

 it seems to require some further consi- 

 deration, before it is fully admitted. 



For more particular observations on 

 the various characters, and on the differ- 

 ent classes of rocks, see ROCKS. 



GEOMETRA, in natural history, one 

 of the families of the Phalaena genus of 

 insects. See PHALJENA. 



GEOMETRY, in its original sense, re- 

 lated simply to the measurement of the 

 earth, and was invented by the Egypti- 

 ans, whose lands being annually inundat- 

 ed, required to be frequently measured 

 out to the respective owners, so that 

 each might repossess his property. It 

 seems probable, that in the operations 

 attendant on that act of justice, many 

 discoveries were made relating to the 

 properties of figures, which gradually led 

 on to an extension of the science, and to 



the cultivation of the arts of navigation 

 and astronomy, which, indeed, first flou- 

 rished in that quarter. We are rather in 

 the dark as to many improvements made 

 in the infancy of geometry, and its at- 

 tendant speculations ; many tracts of sup- 

 posed value having been entirely lost, 

 though some faint traces and fragments 

 of their subjects, if not of their contents, 

 have from time to time been discovered. 

 The Grecians appear to have been enthu- 

 siasts in their reception of the new sci- 

 ence ; accordingly we find that Thales, 

 Pythagoras, Archimedes, Euclid, &c. ex- 

 erted themselves to instruct their coun- 

 trymen, and thus to prepare the way for 

 the philosophy of Ptolemy, Copernicus, 

 and others of the ancient school ; and of 

 Des Cartes, Leibnitz, and the immortal 

 Newton, in our more enlightened times. 

 At present, geometry is justly considered 

 to be the basis of many liberal sciences, 

 and to be an indispensable part of the 

 education of those who purpose exer- 

 cising even the more mechanical arts to 

 advantage. 



We shall submit to our readers a gene- 

 ral view of this most useful and fascinat- 

 ing attainment, and, by a gradual display 

 of its rudiments, open the field to further 

 advancement, which may be easily insur- 

 ed, by consulting those authors who have 

 become eminent for the display of what- 

 ever relates to the superior branches of 

 geometry. In the first instance, we shall 

 submit the following definitions, as laid 

 down by Euclid in his Elements, recom- 

 mending them to the serious attention of 

 the student; they being absolutely ne- 

 cessary towards his competent apprecia- 

 tion and understanding of the succeeding 

 propositions. 



DEFINITIONS. 



1. A point hath neither parts nor mag- 

 nitude. 2. A line has length, without 

 breadth. 3. The ends, or bounds, of a 

 line are points. 4. A right line lies evenly 

 between two points. 5. A superficies or 

 plane has only length and breadth. 6. 

 Planes are bounded by lines. 7. A plain 

 superficies lies evenly and level between 

 its lines. 8. A plain angle is formed by 

 the meeting of two right lines. 9. When 

 an angle measures 90 degrees, it is call- 

 ed a right angle. 10. When less than 

 90 degrees, it is said to be an acute 

 angle. 11. When more than 90 degrees, 

 it is called an obtuse angle. 12. A term, 

 or bound, implies the extreme of any 



