Mifcellanea Curio fa. 15 



33. Then is, > R :: R.f That is, s) R* 

 /c— ~ the Secant, . 



34. And 2. S :: R.T. That U£) 3 R (T=- 

 the Tangent. 



35. Now, if we fuppofe the Radius C P, Fig. 

 7. divided into equal Parts, fandeach of them 

 — o'o ) an ^ on tne fe> t0 De ereeled the Co- 

 Sines of Latitude L A : 



35. Then are the Sines of Latitude in Arith- 

 metic^ Prpgre flio n . 



37. And the Secants anfwering thereunto, 



38. But thefe Secants, (anfwering to right 

 Sines in Arithmetical ProgrefTionJ are not thole 

 that, Hand at equal diitance on the Quadran- 

 tal Arch extended, Fig. 6. 



39. But Handing at unequal diftances (on 

 the fame extended Arch * ) Namely, on thofe 

 points thereof, whofe right Sines fwhilft it was 

 a Curve ) are in Arithmetical Progreflion. As 

 Fig. 8. 



40. To find therefore the magnitude of RE 

 Fig. 6. Which is the fame with that of 



Fig. 8. (fuppoiing EL of the fame length in 

 both \ however the number of Secants therein 

 may be unequal : ) we are to confider the Se- 

 cants, tho 5 at unequal diftances: Fig. 8. to be 

 the fame with thofe at equal diftances in Fig; 

 7. anfwering to Sines in Arithmetical Progref- 

 lion. 



41. Now thefe Intervals, (or portions of the 

 bafej in Fig. 8. are the fame with the inter- 

 cepted Arches (or portions of the Arch ) "in Fig* 

 7 4 Tor this bafe is but tbat Arch extended. . 



42, And 



