GEO 
phyry slate and trap tuff. These rocks 
are said to have been formed during the 
settling of the water consequent to a vast 
deluge, which is supposed to have taken 
place when the surface of the earth was 
covered with animals and vegetables, and 
when much diy land existed. From vari- 
ous appearauces observed in these rocks 
it is concluded, that the waters, in which 
they were formed, had risen with great 
rapidity, 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, are termed allu- 
vial, and are, of course, of much later for- 
mation than any of the preceding classes. 
These deposits may be divided into, 1. 
Those which are formed in mountainous 
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 coun- 
tries, being peat, sand, loam, bog iron 
ore, nagelflech, calc-tuff and calc-sinter: the 
three latter being better known by the 
names breccia, tufa, and stalactite. 
In this ingenious system, in which so 
much knowledge of the subject prevails, 
and in which the marks of long and patient 
investigation are evident, a very close ac- 
cordance with geological facts is generally 
observable. Some few difficulties 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 the 
.primitive mountains, has much the ap- 
pearance of a supposition made up for this 
particular purpose ; and as, at the same time, 
it appears to be warranted by no other 
phenomena, it seems to require some further 
consideration, before it is fully admitted. 
For more particular observations on the 
various characters, and on the different 
classes of rocks, see Rocks. 
GEOMETRA, iji. natural history, one of 
the families of the Phalama genus of in- 
sects. See Phal/f,xa. 
GEOMETRY, in its original sense, re- 
lated simply to the measurement of the 
earth, and was invented by the Egyptians, 
whose lands being annually inundated, re- 
quired to be frequently measured out to the 
GEO 
respective owners, so that each might re- 
possess 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 flourished in that quarter. We are ra- 
ther 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 enthusiasts in 
their reception of the new science; accord- 
ingly, we find that Thales, Pythagoras, Ar- 
chimedes, Euclid, &c. exerted themselves 
to instruct their countrymen, and thus to 
prepare the way for the philosophy of 
Ptolemy, Copernicus, and others of the 
ancient school; and of DesCartes, Leibnitz 
and the immortal Newton, in our more en- 
lightened 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 
exercising even the more mechanical arts 
to advantage. 
We shall submit to our readers a general 
view of this most useful and fascinating at- 
tainment, and, by a gradual display of its 
rudiments, open the field to further ad- 
vancement, which may be easily insured by 
consulting those authors who have become 
eminent for the display of whatever relates 
to the superior branches of geometry. In 
the first instance, we shall submit the fol- 
lowing definitions, as laid down by Euclid 
in his Elements, recommending them to the 
serious attention of the student; they being 
absolutely necessary towards his competent 
appreciation and understanding of the suc- 
ceeding propositions. 
DEFINITIONS. 
1. A point hath neither parts nor magni- 
tude. 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. 6. A superficies, or plane, has only 
length and breadth. 6. Planes are bounded 
by lines. 7. A plain superficies lies even- 
ly and level between its lines. 8. A plain 
angle is formed by the meeting of two right 
lines. 9. When an angle measures 90 de- 
grees, it is called a right angle. 10. When 
less than 90 degrees, it is said to be an acute 
