finita,
EPISTOLIS.
Zoz
evadet eadem quse prodit per Vulgarem Algebram ad Arcus **
, . ex Arcu *.
multi-
24B 5
3lr
6ir
5040B 7
‘008^7
j-7_ 2 77r
t 7 4-Unde efficietur 8=: I?-— r+ —L
7257OB 9 2 B J 2 B i
t 9 +.
r 3 _
48 Ii
r t 5 _j_ Arc. ex.
'1 ANC. LOG,
I45152B 9
, z 5- Si arcus ex secante logarithmica definiendus fit, defignante Utera z arcum, defignet litera Sfecantem lotrarithmicam; litera autem c logarithinorum 2, r differentiam deiignet ; live
^rationis '
‘ Scando Theoremate offensa sunt, haec efficietur aquatio
_ rationis logarithmum, quam secans arcus z ad radium habet. Tum ex iis quse jam 1’upra
u,
ane
‘- 2 z +
2 r
B . B
-7 Z 4 4-r
[ 2r4 45,- 6
z e + _L7A 8Z s + >
2 5207- 8
autem, ope Theorematis 2. Excerpti II. invertendo, hxc alia veniet;
**=
Exh »c deni,
3 b
7 +
JL
45^
^■3 4.
* 4 +,
que, partis utriufque radicem quadraticam extrahendo, conficietur
_ \/ 2.r
+
+
3.1/2.b|- " ' b0. V2.si 2520. V / .2.B l
defi ? Ulden i formula, e logarithmo rationis ejus quam secans ad radium habeat, arcus generaliter
nn *etur.
Arc ex.
Sec. Log.
Aliam vero arcus formulam, e logarithmo rationisquamfecansejus ad fecantem dimidii qua-
fenda' S ^ a ^ eat ’ Gregorius concinnavit. Hujus inventio nefcio an ex alio fonte promptius arcef-- a ht, quam ex tertii Theorematis Corollario.
b, X, <r, z,y eadem quse supra defignantibus, fecans logarithmica dimidii quadrantis
Pro
‘Ueris
O JTirvrl Ji o / o a.
1 0? , OQ ulo b defignetur litera s. Secantis autem dimidii quadrantis ad fecantem arcus z rationistner' k- US ’ ^oc eff logarithmorum s, X differentia, litera l defignetur: litera denique d nu-j 'narii logarithmus pro modulo illo b.a qtie cum fecans logarithmica arcus y per hanc formulam exponatur,
R+ A/+— 4 / +
rj.c . *r i 2.1 ■ 45
arefis z (§ 22. hujus)
e 6 , - 7L
S y + 2^
y* +, (§ 14. hujus) hac alia vero tangens loga-
R-
^har
sy
r
*r
6,-3
B)-9
24,
61 sy 1
,-5
5040,
,-7
N, tt r \ lrn quidem fumma conflabitur logarithmus reftanguli fuli fecante arcus^ et tangente arcus
B h 6l B45,-'
■jjy , - iiiauixict xwnuaLtii-ui iv/g«
Ulc igitur logarithmo hujus feriei,
fi i
-R - ?? +
B
B - B , ,
. , zr or 5 1 zr* z\
lte ea producatur, fumrna ultimo fit aequalis.
y$+ -^y 0 -— 3 JV / + :
J •5040^
Re ftangulu m autem fub secante arcus y et tangente arcus z dimidio quadrati ex fecante arcus>aleeft (ner Cor^Thcor. ,.)-Di«nidii igitur quadrati hujus logarithmo lenes novtffima xqualtspl,' Add hoque illi binarii logarithmo, integri quidem quadrati logarithmus vernet, hoc eft du-111 ipfius lecantis logarithmicx arcus z. Unde hxc efficitur «quatio.
£t hi.
22
D -f- 2R — — -f-V
“tarii divifione,
2 = ^d + r_ y +
2 r
qui
hi,
ffiidii
B , , B
rr.r + — 4 y6,-3 1ir*
,4_
At,
-j B a ® s , ® 6
T + JIT
6t B
4 r" i2r," 24,^ 4 8r 5 "' ‘ qor 0 ^ ioo8or 7
titas |o + r eft fecans logarithmica dimidii quadrantis. -Cum enim ille r radii fit Io-ltlr Ua ’ Cr * t 2R logarithmus quadrati e radio. Ergo cum d logarithmus fit binarii, horumj^ + D, dupli quidem quadrati e radio logarithmus erit. Sed quadratum ex fecante di-
Quadrati igitur ex dimidii qua-drantis
T^drantis duplum eft quadrati e radio (per Elem.:
’ °L. I
47-)
R r