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VI. A Demonflration of the i ith Propojition of 
Sir Ifaac Newton*^ Treatife of Qiiadratures* 
By Mr, Benjamin Robins. 
T his Propofition conMs of two Parts : Thefirft 
is as follows. 
Let there be any Curve ADI, whofe Abfcifle A B 
iliall be denoted by z, and its Ordinate B D by j 
which may be related in any manner to the Abfdlle. 
And calling this the firft Curve, let other Curves AEK, 
AFL, AGM, AHN, fe’c. be formed to the common Ab- 
fciffe A B, or z, by making the Ordinate B E of the 
fecond Curve always equal to the Area A BD of the 
firft divided by Unity ; the Ordinate BF of the third 
equal to the Area A B E of the fecond divided by U- 
nity ; the Ordinate B G of the fourth equal to the A- 
rea ABF of the third divided by Unity ; and lb on 
continually. Suppofe now, that other Curves AOS, 
A P T, A Q^V, A R W, be defcribed to the fame com- 
mon Abfcille AB or z; in which Curves the Or- 
dinate BO of the Curve AOS ihall be equal to 
z j , the Ordinate B P of the Curve APT equal 
z'' y, the Ordinate B Q of the Curve AQ^V equal 
to z’jy, the Ordinate BR of the Curve ARW e- 
qual to Z4J, And let the whole Area A Cl 
be denoted by A, the Area ACS by B, the Area 
ACT by C, the Area A C V by D, the Area 
A C W by E, ^c. Then the Series of Curves ADI, 
AEK, AFL, AGM, AHN are thus meafured : 
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