C 88.1 ) 
points P, Q,; draw PS, QR,' parallel to the Cylinders 
Axe, till they meet with the aforefaid Circle IKLM in 
the points R, S, and draw the Lines RTS, QVP bifefted 
in T and V. I fay again, that the Curve Surface RMS- 
QDP is equal to the Rediangle of BL or MD and RS r 
or of 2 BL or AD and ST or VP • and the Curve Sur- 
face QNPD is equal to RS x MD— the Arch RMS#. 
SP, .or the Arch MS x z SP: or it is equal to the Sur- 
face RMSQDP, fubtra&ing the SurfacellMSQNP. So 
likewife the Curve Surface Q3PO is equal to the fum of 
the Surface RMSQDP or RS x MD, and of the Sur- 
face RLSQGP or the Arch LS x % SP. 
This is mod eafily deaionftrated from the confidera- 
tion, That the Cylindrick Surface 1KLB is to the inferr- 
ed Spherical Surface IKLE, either in the whole or in its 
Analogous Parts, as the tangent BL is to the Arch EL, 
and from the Demonftrations of Archimedes d$ Sphara 
& Cylindro^ Lih. i. prop, xxx, and xxxvi i. kxxiix. 
which 1 (hall not repeat here, but leave the Reader the 
pleafure of examining it himfelf; nor will it be amifs to 
confolt Dr. Barrows s Learned Lectures on that Book, 
Publilhed at London , An. 1684, viz. Probl. ix. and the 
Corollaries thereof. 
Now to reduce our Cafe of the Sum of all the Sine* 
of the Suns Altitude in a given Declination and Latitude 
to the aforefaid Problem 3 let us confider Fig. 10. which is 
the Analemma projected on the Plain of the Meridian 
Z the Zenith, P the Pole, HH the Horizon, x x the E- 
quinodlial, s s, vr the two Tropicks, si the Sine 
of the Meridian Altitude in s ; and equal thereto, but 
perpendicular to the Tropick, eredfc si, and draw the 
Line T 1 interfering x\y6 Horizon in T, and the hour 
Circle of 6, in the Point 4, and 6 4 lhall be equal to 
<5R,or to th^JSiite of the Altitude at 6 : and the like for any- 
other Point in the Tropick, eredting a Perpen Jicular 
thereat, terminated by the Line T 1 :Through the Point 4 
