Anew andeafy vpay of demonjlrating form propofiti- 
ons in Euclid hy th^ learned Mr. Alli. a 
Member of the Philofophical Society of Dublin 
for pomotingnatural knowledge. 
THe Preeminence of Mathematical knowledge, and 
the certainty of its way of reafoning are manifeft 
from the few or no controverfies between the ProlBffors 
thereof (efpecially in pure unmixt Mathematic\s and 
from the eafy difcovery of paralogisms Som^ of the reafons 
of which certitude may be thele : btcsiuk quantity, thQ 
&bje8 about wliich it is converfant, is a fenfible obvious 
thing, and confequently the Iddas we form thefeof are 
clear and diftin(5l:, and day ly reprefehted to us in moft fa- 
miliar inftancesi betaufe it makes ufeof termes which 
are proper, adsequatej and unchangeable i its a:)cioms and 
pofiulata alfo are i^ry few and rational. It alTigns fuch 
caufes and generations^ oS ' Magnitudes as are eafily ap- 
prehended and readily admitted ; it rejeds all trifling in 
words aiid I^etarUdl fchemes - all comjedtures, authorities, 
prejudiices^ afid p^fliori y Laftly foexquifite an order and 
method in /^/?;^o;2//rir?i^/;2^ is obferved, that no propojitioti is 
pretended to be proved, which does not plainly fo^llcw 
from what was befofe demonft rated, as is manifeft in Eu- 
clid s Elements. Now as a farther inftance of the evi- 
dence of Mathematical Theoremes^ I believe it were not 
difficult to demonflrate any one of independently 
from the reft, without precedent i^^w^/s?'/ or propofiti- 
ons as an eflay of which I will here lubjoyn lome of the 
moft ufeful, and upon which the folution of moft pro^ 
^/^/w/jeipecially Al^^ehraical ones, do depend, and thofe 
alfo in the moil various and different ^artsoi Geometry, 
W^^, concerning the properties of angles,, circles, trian- 
gles, fquares, proportionalls, and folids. The Propofiti- 
ens v/hich I will endeavour to ^^'^wo/^/r^^f tlius indepen- 
dently 
