wkSR* through the femeimagine another Plain to pafr, and to 
cut the tone beneath the Vertex, as at O * then is the Wedge, con- 
taia'd between both thefe PWw( to wit VSROV, equal to \ of 
that Cilindricl or Prifrnatick Figure, whofe Altitude is equal to 
the Perpendicular VP tailing from the Vertex of the Cone to the 
Cutting PUixe, and whofe SORTS is the ^4 of the Fi- 
gure cur . in this cafe, an Hyperbola: when the Plain paffeth para- 
lei to the fide BV> zParahla-, when it will meet with VB produ- 
ced aPortion of an Ellipfis. By this means if a Brewers ton (ca- 
ken to be a Circular truncmConi) lean, and be not cover'd over 
with Liquor in its bottom, it may be computed by fubftra&ing 
the two known before -mention'd parts out of the whole: If it 
ftapd upright, and be divided by an Upright Plain into two Partiti- 
w,imagine it to be a whole Cone^ and firft, by the Method above, 
find the Segment, as of the whole, and afterwards of the additional 
To$-Cone*thtdi&xe&ce oi thofetwo gives the Content ©fthe 
Correfpondent Partition. 
3 . But if the Liquor cut both fides.the Ton leaning, as BCDE in Figure 1 1 1, 
fuppofe BAB to be the Triangle through the Axis of the whole Cone, then the 
E/liptickjOone ACD to the whole ABE is in a Triplicat ratio of the tide-line AB 
or AE to the Geometrical Meane between AC and AD, that is, 
As the Cube of the fide-line AB is to the Solidity of the whole Cone ABE, fo 
is the Cube of the Geometrical Mean between AC and AD, to the Solidity 
a£ the mptickCone ACD. ] 
And this readily followes from the Doctrine of Vivtam de Maxim* & 
'Minimis, where tis demonftrated, that any fuch FlliftickCones, cut out of an 
VprMtCcne, that have the ^r^V of their Triangles through the ^V^qual, 
are equal to e'ach other.- and likewife to that V fright Cone which hath the 
fame AreaonitsTriangle through the Axis on the former Plain thereof: 
And thefe Area's he calls their right Canons, 
And the mean Proportional by 2 3. E, 6. finds the fides of an Ifofceles Tri- 
angle in the Plain of the Axis equal to the Scalene Triangle ; and then thefe 
Cones are to each other in a Triplicate ratio of their Axes, Side-lines, or Bafe- 
lines, which ate proportional to their Axes 
The Areaoi zn HyperMabemg obtain'd, the Solidity of the Hyperbolical 
7^orSpindes(rmdeby the rotation of an Hyperbola about its Bafe) and 
their Trunci are computed, according to Cavallieri ( in his Geometrical exer- 
cifes, printed at Bcnonia, 1 64 7-) and the folid Zones of thefe Figures may be 
well taken to reprefent a Cask, 
la the S A V O T 9 
printed by 7". N. for John Martyr Printer to the Royal Society y and are 
to be fold at the BeH a little, without Temple-Bar t 1667. 
