Royal Society. 21 
two parallel infinite lines be fuppoled drawn on fuch an infi- 
nite plane, the area, intercepted between them, will be likewile 
infinite, but at the fame time infinitely lefs than that fpacc 
intercepted between two infinite lines, inclined at never ib Imall 
an angle ^ becaufe in the one cafe, the given finite diftance of 
the parallel lines diminilhes the infinity in one degree of dimen- 
fion, whereas, in a fe^tor, there is infinity in both dimenfions5 
and confequently, the quantities are the one infinitely greater 
than the other, and there is ratio between them : From the fame 
confideration arife the three leveral fpecies of infinite Ipace or ib- 
lidity, as hath been faid^ for a parallelopiped, or a cylinder, 
infinitely long, is greater than any finite magnitude, how great 
foeverj and all fucb folids, fuppoled to be formed on given bafes, 
are to each other as thofe bafes 5 but if two of thele three dimen- 
fions be wanting, as in the fpace intercepted between two pa- 
rallel planes infinitely extended, . and at a finite diftance 5 or with 
infinite length and breadth, with a finite thicknefs 5 all fuch fo- 
lids will be to each other as the given finite dimenfions 5 but thefe 
quantities, tho' infinitely greater than the other, arc yet infinitely 
lefs than any of thofe, wherein all the three dimenfions are infi- 
nite j fuch are the Ipaces intercepted between two inclined planes 
infinitely extended 5 the fpace intercepted by the furface of a cone, 
or the fides of a pyramid, likewife infinitely continued, i^c. of 
all which notwithftanding, the ratio's to each other, and to the 
^o TcLv or vaft abyfs of infinite fpace (wherein is the Locus of all 
things that are, or can bcj or to the folid of infinite length, 
breadth and thicknefs taken all manner of ways) are eafily afiign- 
ablej for the fpace between two planes is to the whole, as the 
angle of thofe planes to the ^60 degrees of the circle: As for 
cones and pyramids, they are as the fpherical furface, intercepted 
by them, is to the furface of the fphere, and therefore cones are 
as the verfed fines of half their, angles to the diameter of the 
circle : Thefe three fpecies of infinite quantities are analogous to 
a line, furface, and lolid, and after the fame manner cannot be 
compared, nor have any ratio the one to the other : Befides 
theie, there are feveral other Ipecies of infinite quantities, arifing 
from the contemplation of curves and their afymptotes. 
"ithe "Defers of the Trumpet and Trumpet-iMarine 5 hy 
J/r. Fran. Roberts. Phil. Tranf N° 195. p. 559. 
THE extent of the trumpet cannot be ftri6ily determined, \t 
reaches as high a« the ftrength of the breath can force it y 
tut by confidering its notes within the ordinary compals of the 
fcale 
