[ 88 3 
in this Book, as in Sir Ifaac Newtons Trincipia Ma- 
thematical. 
The Proofs made ufe of in his Demonftrations, are 
fometimes Algebraical, at other times Geometrical, 
according as he finds the one to be plainer and (hotter 
than the other. 
Book II. 
The fecond Book treats of the dired Method of 
Fluxions. And here he hopes the firft Principles of 
this Method are laid down, not only in a new, but 
very plain and concife manner. He proceeds to fhew 
the Ufe of Fluxions in the Solution of the common 
Problems of finding the Maxima and Minima of 
Quantities, the Radii of the Evolution of Curves, and 
the Radii of Refradion and Reflcdion. Under the 
firft of thefe Heads he tells us, particular Care has been 
taken to diftinguifh the. Maximums from the Mini- 
mums , a thing which has not been taken Notice of fo 
much as it ought to have been. And whereas fome 
Mathematicians, having made ufe of what they call in- 
finitely fmall Quantities, are forced to rejed fome- 
thing out of the Equation, for finding the Fluxion of 
a Redangle, whofe Sides are varying Quantities, Mr. 
Muller ufes only finite Quantities j and finds the Flu- 
xion of fuch a Redangle after a new manner, without 
rejeding any Quantity for its Smallnefs. He does the 
fame in finding the Fluxion of a Power. And to 
avoid the Ufe of infinitely fmall Quantities, introduces 
a new Principle, viz. That a curve Line may be con- 
fiderd as generated by the Motion of a Point carried 
along by two Forces or Motions, one in a Diredion 
always parallel to the Abfcifs, and the other in a Di- 
redion 
