fHlLOSOPHICAL TRANSACTIONS. 



235 



0,0029019589 



VOL. II.] 



Therefore 4- of any number of A, or terms, is less than their so many respec- 

 tive B, that is, than twice so many of the next terms Q. E. D. 



By any one of which three series, it is not hard to calculate as near as you 

 please, these and the like hyperbolic spaces, whatever be the rational propor- 

 tion oi ji E to B C. As for example, when j4 E is to B C, as 5 to 4, (where- 

 of the calculation follows after that where the proportion is, as 2 to 1 , and both 

 by the third series.) 



First then when (in fig. l) A E : B C : *. 2:1. 

 2X3X4) 1. (0,0416666666-] o,04i6666666 



4X5X6) 1. (0,0083333333-. 



6x7X8) 1. (0,0029761904-/ ^'"^^^^y^^^7 



8X 9X10) 1.(0,0013888888 — 



10x11x12) 1.(0,0007575757 — 



12X13X14) 1.(0,0004578754 — 



14X15X16) 1.(0,0002976190 — 



16x17x18) 1 . (0,0002042484 — 



18X19X20) 1.(0,0001461988 — 



20X21X22) 1.(0,0001082251 — 



22X23X24) 1. (0,0000823452- >o 0007306482 

 24X25X26) 1. (0,0000641026- ^0,0007300482 



26 X 27 X 28) 1 . (0,00005087 5 1 — 

 28X29X30) 1. (0,0000410509 — 

 30X31X32) 1.(0,0000336021 — 

 32X33X34) 1. (0,0000278520— 

 34X35X36) 1. (0,0000233426 — 

 36X37X38) 1. (0,0000197566— 

 38X39X40) 1. (0,0000168691 — 

 40X41X42) 1.(0,0000145180— 

 42X43X44) 1. (0,0000125843 — 

 44X45X46) 1. (0,0000109793 — 

 46X47X48) 1. (0,0000096361 — 

 48X49X50) 1.(0,0000085034 — 

 50X51X52) 1.(0,0000075415- 

 52X53X54) 1. (0,0000067193 — 

 54X55X56) 1. (0,0000060125 — 

 56X57X58) 1. (0,0000054014 — 

 58X59x60) 1. (0,0000048704 — 

 60 X 6 1 X 62) 1 . (0,0000044068 — 

 62x63x64) 1. (0,0000040002— J 



0,0416666666 

 0,0113095237 

 0,0029019589 

 0,0007306482 



3) 0,000 1 829939 (0,0000609980 



0,05679179 

 -f- 0,00006 100 



^0,0001829939 0,05685279" <EdCy 



But 0,00073064821 



0,000 1 829939 [-H- 

 0,00004583153 



Therefore 0,05679179 

 -1-0,00004583 

 -1-0,00001528 



0,05685290 >- E d C y. 



Royal Society; particularly, experiments concerning the recoiling of guns ; also the series for the qua- 

 drature of the hyperbola, in tlie article above, being the first invented series of the kind on that subject, 

 besides some papers not printed. Several of his letters to Archbishop Usher were also printed in 

 Usher's Letters; as well as some to Dr. Wallis, in his Commercium Epistolicum, before mentioned. 



G G 2 



