( 20©7 ) 
in he profecutes at largCj what was delivered in his Book Be 
Cjchide 5 formerly publifli't , continuing his Calculations 
(which were there begun) to a great number of Particular 
Cafes, which (for reafons then affigned) were there omitted, 
and which have not by any hitherto been computed. 
He doth the like , in the Figure of Right-Sines^ in the Fi- 
gure of Verfed Sines , and of Arches '-y a(iigning the Magni* 
tude of thofe Figures^ and of their Segments and Portions ; 
with their Vngnls^znA Solids by Converfwn 5 and the Centers 
of Gravity of all thefe*Whence(amongft many other things.^ 
are deduced thtfums of the Right Sines yVerfed Sines^ and 
Arches^ appertaining to any alligned Portion of a Circle 3 
and the Sums of their Squares^ Cubesy or other Pomrs; 
He doth the like m Spiral Figures, as well that of Archi- 
medes^ as an infinit number of other Spirals-^ fhe wing the 
Magnitude of the feveral Parts or SeSiors ; with their Cen- 
ters of Gravity 5 ( all applicable alfo to their refpeftive Sea» 
lar Solidji) and the refpeclive Paraholoeids with which they 
Symbolize, and by whofe Convolution they are made ; their 
Tangents alfo, with much more concerning them. He profe- 
cutes the fanie in part^ but more briefly^ in the CiJJoeid^ and 
Conchoezd,dt\Ax\i^Figure tangents as to the Magnitude 
of thofe Figures, and the Parts thereof ^ their Vnguls^Solidf^ 
and Centers of Gravity. He fhews particularly as to the Cif 
foeidfhow it doth fymbolize with the Cycloeid^ the parts of 
the one figure being equal to the refped:ive parts of the o* 
ther: And, as to the Conchoeid^ That its Plain is in Magni- 
tude (as v/ell as Longitude) Infinite 5 yet a Solid made by 
its Converfion, equal to a finit Cylinder. 
He fhews alfo the ^adrature of the Hyperbola^ and parts 
thereof^ thtlx Vnguls ^ Solids^ ^nd Centers of Gravity : As 
alib^an Hyperbolical Solid^made by the Converjion of a Streight 
Line about an Axis not in the fame Plain 5 (hewing the Mag- 
nitude oi th'^l Solid ^ and of its F^r/j , and their Centers of 
Gravity and the feveral SeBions of that Solid made by 
P/<?/»/in any affigned pofition^ being Parabola's^ Hyper bo- 
id Siy El/ipfes^ Circles^ P araUelograms^md triangles ; accord- 
ing to thedilFerent Pofitions of the Cutting Plains: With 
many 
