3 o6

Excerptum

Quartum.

Arc. bx.Si.C. Log..

Arcus »js*x A-rcu «.

EXCERPTA EXmultiplicandum datum angulum per illum numerum n ( ! ) .

Si

drantis fecante ille 2R + d logarithmus erit.. Quare Hlius femiflis, nimirum r + |d, dimidii q u3 'drantis ipfa fecans erit logarithmica, five logarithmo s aequalis. Ex aquatione igitur novi# 013 ’demptis hinc inde aequalibus, s, r + |d, efficietur

Ergo Iz

B

E

B

-t- _ y* — - y 3 _ y 4 _— __y 5 ' 4 - - __

+ ^ ,. ri y + 00 ,.6> >

4 r

V

zr

zr 4 r z ^ + I2r 3 ^ 24^^ "** 48, 3 ^ 90 r u

Hujus autem inversio, ope Theorematis 1. Excerpt. II. perficienda, hanc aliam excitabit

1 zr 3

B- - B B B

—y 4 -3 y^ — —u/H-- v5 -

A.r y 1 zr iJ

90 r

B

j 5 /+.

nr/ 4 + ^ /5 _,

3 B>

r 2r j 2r ;2, &r n

five 22, “ — /-i / + —r / 3 -

B E 3B 3 3 B 4

_ zr zr ,

Ergo 2Z~q -/ + —J- / —,

B B

Ex hac vero,.per binarii divifionem, exfiftet tandem generalis arefio formula-

Z = iq- —1 +

lr-

./ 4 -

I 4 r

' 5 + ,

3B J ZB'» ZB

ex ejus nimirum rationis.conflata logarithmo, quam secans arcus z ad fccantem dimidii qua<habet.

dran tlJ ’

('). Cum a* chorda Ut arcus dati, arcus datus erit

• v + b¥ + ^ + 77 ^ +

d«'

(per §1.hujus Excerpti) nam arcus circularis per eandem formulam ex chorda cum diametrofinitur, atque ex finu redo cum radio.

Q, , «.r 3 . 3 >av 5 r *7

uare arcus exquirendus — nx-\ -- 4 - --p _ 2 —, -p

bd z 40</4 11 3/fi

Subftituatur haec feries pro a in formulam chordx ex arcu dato, & proveniet formula -chordi*cus exquirendi e data*. Nempe hoc modo. Defignet z arcum exquirendum ; chorda igit^ 3

+ (§ 2. hujus Excerpti)

it'

z 3 z^

cus exquirendi =z- ^ ^

SedErgo -

et +et —

«* 3 ZJtX$

z. =»*+—---p 2 --p

bif 40-^

M 3 * 3 « 2 jr 5

bd z

n 3 x 3

~bd*

z 3

I 20i/ 4

z^

5.04 OtP

5040 tp

_

11 2

720 ct *5 a 3 * 71 zodB ■ ' yzoiB

I 2 -/4

» 5*5

+ -^ +

Quare hujus feriei, infiniti quidem P ^dudhe, fumma chorda; arcis exquirenditimo aequalis erit. Atque haec feries, fiefficientium poteftatis cujufque fumm*colligantur, formam induet Nevi'toniaobili»

5040^

ALIT E R

2. Sit * chorda arcus dati,^ chordaarcus exquirendi ;

. , a: 3 3* 5 . _

Ent arcus datus =*+ — 2 + + II2 >.

+

Arcus autem exquirendus —y + ^ -p -E- q-

bd z ' 401/4

„ 3 '

1121/°

Hinc rurfum arcus datus = 2L + J-. -p , -p. — Q —- -p

6W 40«^ lizna'

rrgo*-P —J

* J

Jfl + Jf!

40 l /4 1 1 2 ^'

b +

l_ , 2L + 3 / _

6 « i / 2 40»</4 1 11 2»</ 6

S^ 7

Et radice y infinite affeda per formulam generalem Moivrasanam extrada