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roots of the equation ; and the feveral points, where 
the curve (hall approach the bafe, but (ball return 
without reaching it, will {hew the impojfible ones. 
Th is is a method I myfelf fell into ten or twelve 
years ago, and have conftantly ufed for finding the 
roots of fuch equations as I have had occafion to 
confider. But his method is preferable to mine in 
one refpeft, •viz. that whereas I always compute the 
value of the ordinates in numbers, he finds them by 
drawing certain right lines ; however, when there are 
both poffible and impoffible roots in an equation, as 
generally there are, thefe methods are both of them 
extremely embarrafling : the learned author there- 
fore wifhes, that fome method might be thought of, 
whereby fuch curves, as we are now fpeaking of, 
might in all cafes be defcribed by local motion ; but 
this, he tells us, he looked upon as fo very difficult 
a tafk, that he never attempted it. ^uod ad defcrip - 
tionern attinet , fays he, motum exccgitare t quo tales 
accurate dejignari pojjunt omnes [ hujujmodi curva] ad- 
mo dum difficile judicOy quare id neque tentavi. This 
hint, however, convinced me, that the thing was 
poffible ; I therefore determined to endeavour it. 
I foon found, that if rulers were properly centered, 
and fo combined together, that they fhould always 
continue reprefentatives of the feveral right lines, by 
which he difcovers the abovementioned ordinates, 
upon moving the firft, a point or pencil, fo fixed as 
to be carried along perpetually by the interfe&ion of 
the firft and laft rulers, would defcribe the required 
curve, let the number of dimenfions in the equation 
be what it will ; only the greater that number, the 
greater muft be the number of the rulers made ufe 
Vql. LX. I i of. 
