( 178 ) 
on he found theTheoremeabovemention’d, and by means of 
thisTheoreme he found the Reduction of Fractions and Surds 
into converging Series, by Divifion and Extraction of Roots ; 
and then proceeded to the Extraction of affected Roots. And 
thefe Reductions are his third Rule. 
When Mr. Norton had in this Compendium explained thefe 
three Rules, and illuflrated them with various Examples, he 
laid down the Idea of deducing the Area from the Ordrnate, 
by confidering the Area as a Quantity, growing or increafing 
by continual Flux, in proportion to the Length of the Ordi- 
nate, fuppofing the Abfciffa toincreafe uniformly in propor- 
tion to Time And from the Moments of Time he gave the 
Name of Moments to the momentaneous Increafes, or infinite- 
ly fmall Parts of the Abfcifia and Area ; generated in Moments 
of Time. The Moment of a Line he called a Point, in the 
Senfe of Cavallerius, tho’ it be not a geometrical Point, but a 
Line infinitely ihort, and the Moment of an Area or Superfi- 
cies be called a Line, in the Senfe of Cavallerius, tho’ it be 
not a geometrical Line, but a Superficies infinitely narrow- 
And when he confider’d the Ordinate as the Moment of the 
Area, he underftood by it the Redangles under the geome- 
trical. Ordinate and a Moment of the Abfcifla, tho’ that Mo- 
ment be not always exprefled. Sit ABD, faith he, Curva 
qtwvis, dr AH KB reftangulum cujus 
laius AH vel KB eft unitas. Etcogila 
re ft am DBK uniforms ter ab AH mot am 
areas ABD dr AK defer ibere ; dr quod 
[reda] BK ( i)Jit momentum quo [area] 
AK(x), dr [reda] BD (y) momentum 
quo [area curvilinea] ABD gradatim 
augetar; dr qwd ex moment 0 BD perpetim dato poffts, per pr ace- 
dentes [tres] Regulas, aream ABD ipfo defer ipt am inveftigate , 
five cum area AK(x ) moment 0 1 defer ipt a conferre. This is his 
Idea of the Work in fquaring of Curves, and how he ap- 
plies this to other Problems, he expreflesin the next Words. 
Jam qua ratione , faith he, (uPerftcies ABD ex moment 0 fuo per- 
t>ttim 
