o.6o MifceUanea Curiofa. 



face RMSQDP, or RS x MD, and of the Sur- 

 face RLSQOP, or the Arch LS * x SP. 



This is the moil eafily demonftrated from the 

 Confederation , That the Cylindrick Surface 

 1KLB is to the infcnb'd Spherical Surface 1KLE, 

 either in the whole, or in its Analogous Parts, 

 as the tangent BL is to the Arch EL, and from 

 the Demonftrations of Archimedes de Sphara & 

 Cylindro,Lib.\. Prop. XXX, and XXXVII, XXXI IX. 

 which I mail not repeat here, but leave the Rea- 

 der the pleafure of examining it himfelf , nor 

 will it be amils to confult Dr. Barrows Learned 

 Le&ures on that Book, Publifh'd at London, Anno 

 1684, vi%. Brobl. ix. and the Corollaries thereof. 



Now to reduce our Cafe of the Sum of all the 

 Sines of the Sun's Altitude in a given Declina- 

 tion and Latitude to the aforefaid Problem, let 

 us confider (Tab. 4. Fig. '4.) which is the Ana* 

 lemma projected on the Plain of the Meridian, 

 Z the Zenith, P the Pole, HH the Horizon, 

 x x the ^Equinoctial, £ S, v? v? the two 

 Tropicks, © I the Sine of the Meridian Altitude 

 in S ; and equal thereto, but perpendicular to 

 the Tropick, ere<5t, S 1, and draw the Line 

 T 1 interfering the Horizon in T, and the 

 Hour Circle of 6, in the Point 4, and 6 4 (hall 

 be equal to 6R, or to the Sine of the Altitude at 6 : 

 And the like for any other Point in the Tropick, 

 ere&ing a Perpendicular thereat, terminated by the 

 Line T 1 : Through the Point 4 draw the Line 

 4, 7 p aran, el to the Tropick, and reprefenting 

 a Circle equal thereto; then (hall the Tropick 

 S S in Fig. 4. anlwer to the Circle NOPQ, 

 in F/g.g. the Circle 4, 5", 7, (hall anfwer the Circle 

 1KLM, T 4 1 (hall anfwer to the Elliptick 

 Segment QIBKP, 6 R or 6 4 (hall anfwer to 



