n6

Liek. I. Sect. III.

711

= (/-

smre

cos 2 n

-) + 2 (l — ■

smre

cos 2 re

M'

3 | tang 2 re

cos 2 re

i

Z

T . r . sin 72* 7 / r . sin 71

11= (L + -) +2(L + -)

~ ~ ' cos 2 n '

COS 2 77

cos 2 re

atque sic, neglecta z, statim valor yerus ipsius n erui.

■ log liyp tang ( 45 ° + ti)

tang 2 n

tang 2 re „ „ ^

• log hyp tang (45 + re) *

tang 2 /i 3

io 4 .

Superest, vt exz, n vel c elementa ipsa determinemns. Statuendo a\/(ee —i)=( 3 , habebitur ex aequatione 6 art. 99sin f v/ rr'

[18] 8 = .; ~ -

L J e' tang 2 77

Combinando hanc formulam cum 12, 12* art. 99, eruitur

tang/tang 2 re

2(1 —z)

, ^ . tang/tang2re

[19*] taug^= —--

ynde excentricitas commode atque exacte computatur; ex /9 et \k ( ee — 1 ) prodibitper diuisionem a, per multiplicationem p, ita vt sit

2 (l — z) cos f \/ rr' 2 mni cos f. \/ rr kklt

[19] y/ (ee— x) =tangy/

«;

tang 2 re

jy tang 2 ji 2 4 YYrr cosf 2 tang 2 re a

2 ( L + z ) cos /! \/ rr — 2 illilf cos/! s/ rr kkit

tang 2 re

rr tang 2 re a

4 yy rr' cos f 2 tang 2 n 2_ sm/! ta n g/. y/ rr _ yy sin/, tang/ y/ rr / y rr sin 2/ \ a

^ 2(1 - Z ) 2 111771 \ kt J

— sin/! tang f y' rr — YY sin f. tang/! \/ rr / Y rrs in 2 f V

= /(/ 7 + 7 ) ~ 2 illd/ = V ~ki /

Expressio tertia et sexta pro p } quae omnino identicae sunt cum formulis 18, 18*art. g 5 , ostendunt, ea quae illic de significatione quantitatum y, Y tradita sunt,etiam pro liyperbola valere.

E combinatione aequationum 6, 9 art. 98 deducitur (r —r)\/'

e e

rr

e sin/! ( C-^r) j introducendo itaque ip et co , statuendoque C = tang( 45 ° + iV), fit