C ] 
termine the Orbs,either from the Focus given and two points 
or Tangents ; or without it by five points or Tangents or 
any number of Points and Tangents making together five. 
Then he fhewshow from the Time given to find the Point 
in a given Orb anPvvering thereto; which he performs accu- 
rately m tlie ParahoU.^nA by concife approximations comes 
as near as he pleafes in the Etliffe and HyferhoU: all 
which are Problems of the higheft concern in Aftronomy. 
Next he lays down the Rules of the perpendicular defcent 
of Bodies towards the Center, particularly in the cafe 
where the tendency thereto is reciprocally as the Iquare of 
the difiance ; and generally in all other cafes, fuppofing a 
general quadrature of Curve lines : upon which fuppofi- 
on likewift he delivers a general method of dilcovering 
the Orbs defcribed by a Body moving in fuch a tendency 
towards a Center, increafing or decreafing in any given 
relation to the diifance from the Center ; and then with 
great fubtilty he determines in all cafes the Motion of the 
Af fides (ox of the Points of greateft diftance from the Cen- 
ter in all theie Curves^ in fuch Orbs as are nearly Circular. 
Shewing the A^fides fixt, if the tendency be reciprocally as 
the iquare of the diftance; dire£t in Motion in any Ratio 
between the Squ^) re and the Cube and retrograde ; if un- 
dcr the Square : which Motion he determines exaftly from 
the Rule of the increafe ordecreafe of thtVisCemripeta. 
Next the Motion of bodies in given Surfaces isconfider- 
ed^as likewife the Ofcillatory Motion of Pendules, v^here is 
fliewn how to make a Pendulum Vibrate always in equal 
times, tho' the center or point of tendency be never fb near ; 
to which, the Demonftration of Mr. Hugens dc Cycloide is 
but a CorolUry. And in another Propofition is fhev/n the 
Velocity in each Point, and the time (pent in each part 
of the Arch defcribed by the Vibrating Body. After this 
the Effects of two or more Bodies, towards each of which 
there is a tendency, is confidered ; and 'tis made out that 
two Badies, fb drawing or attrafting each other, defcnbe 
O 0 2 about 
