rying the Iame,botli the other roots (as in the Poftfcriptj : for 
every number or magnitude capable of a ^^^e root, is capable 
of two more, lee s^^^^^ iv^, following 
JO If the roots in the former Sedion , be aflumed in. 
Arithmetical progrefEon, and the asquation with its feveral 
Refoh'-ends be deprefled, there will come out a regular Series 
of Quadratick iEquations, whence an eafie metliod will rife 
of writing down fuch ranks as multiplied by an Arithmetical 
progreffion, fhall always beget the fame cubick iequation^ 
the Refolvend only varying. 
T T Let the roots of this leries of quadraticks be found as 
ufual in binomials, let thefe binomials be cubed.and then let 
it be obfervcd. whether the refult^ are conftaot portions of 
the fquare of the Refolvend and of the dioriftick limit : and if 
fo. Cardans Rules will have their defedl fupplyed. 
It In breaking a biquadratick, 'tis afferted that by leaving 
the Refolvend at liberty, it may be infinitely and rationally 
done, without the Aid oi the feparating cabick ^^quation» 
1 3 But fuppofing fuch feparating cubick m (tore, oi - 
which Bartholimfs in liis dioriftick hath given us great furni» : 
ture in Species^ why may not feveral roots of that asquatioii 
be affumed rational 5 and thence the biqiiadmtick brokea 
into as many pairs of quadratick equations r 
14- May not from hence a method arife of writing down 
2 Series of quadraticks that multiplied together fhail always 
beget the fame biquadratick Nomes, the Refolvend only 
yaryingPand hence thei^^^-^-^^^ of the ^quationis eafily defcribed. 
15- Here again (as in the n } if the binomial roots of thefe 
quadraticks be fquaredly fquared^ and thofe refolts ai-e con« 
Itant portions of the cube of the Refoivendj and the dio- 
riftick limit 3 it will be certain there may be general furd 
Canons for a^quations of the 4?/*. diraenlion, and MonfiarrClu^ 
^trufs (now at i^ondon) politively aflerts he hath a general 
method to obtain them for all DimenftoDs 
16 As Cardans are furd caiions deriv'd from the Refolvend, 
and dioriftick limit, fo it were worthy diiquifition, whether 
other furd Canons (of which many are fitted to particular 
cafes by your felf, Letbmtz. and others) do not arife out of the 
limits of thofe particular cafes and a^quations, and whether 
the glimpfe of a general Method might thence be deriv'd for 
all other ^equations, though encmnbred with negative quan- 
tities;^ which Mr. Gregory httle beiore his death, faid he had 
attained. 
17 The Learned Dr. Fell hath often afferted that after 
the Limits of an equation ara once obtaind, the.i it is ea- 
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