SE R


C 6il


Ininite     1~ . If then, 2dly, that TIermf in the
Qluotierit continually decreafe ; the Series will give a quo-
tient as near the Truth as poffible. -E. gr. If l-it
C= i and a= 2; thefe Values fubflituted in the gene-
ral Series,~ or the Divifion performed as in the general
Example;i we fhall find T=...... --4~-Y~'
-~~±rF_, ~c Suppofe then, the Series to be broke ONf in
the Fourth Term;i there will be a Deficiency : but 'twill
be lefi than    If it be. broke off in the Sixth, there will
be a Deficiency, but that lefs than T. g. The further there-~
fore the Series is continued, the nearer it approaches to
Truth, but never arrives at iti
After the like Manner we find~.. I
T ir+      E,)~c, In infinit. e  ~'_
L e~c. in Infinitum. This is a conflant Law, where-
'by all Fradfions, whore Numerator is Unity, may be ex-
preffed by inflnite Series: Thofe Series being all Geomne-
trical Progrefflonsi decreafing in fuch Manner as that the
Numerator is always Unity ; and the Denominator of
the firft Term, which is alfo the Exponent of the
.Ratio, differs by Unity from the Denominator of the
Fraafion to be refolved,
If the Terms of' the Quotient be continually increafing,
the Series recedes fo much the farther from the Quotient
as it is continued longer ;  nor does it ever became
equal to the Quotient, unlefs it be terminated ; and the
laft Remainder be added under its Sign. .Egr. Suppofe
____  5 the Ojiotient will be found £- z+4---8+
3±2
z6-64+1 28, Eec. One Term, i exceeds {t by an Ex-
cefs of 2; Two Terms come lhorr by 4 Three Terms
exceed by 9 5 Four fall flhort by Jsc.T If the Series be
fuppofed to terminate in -8;5 then will ..4.
4-8±V.But I - 2 ± 4-8- - 5 ==,-Therefore,
I  16.,.T$ ~L*Suppofete  General Sre to ter-~
i1+2                        th          ere
* inmate i    0      then will _!=-cc_


I


To find an JIfnjte Seres   (
by extraffing of Roots - - See QuAin&A-vrUrEoftdoe
To find an In~finite Series CCIRCLE.
by prefuppofed Series -- -)
To extrad the Roots of  ~  CE xTACTiON Of
an Infinite Series -  .- ' -  ie   Roots.
SERMOLOGIES, in Church IHiflory, Books of Ser-


r Homilies of P'opes and other Perfons of Emi-
nd Sanifity, read at the Feafls of the, Confef-
.- Purification, All Saints, and on every Day from
rs to the Oftave of the Epiphany. See HomILY.
4ONBS, the Title Horace give, hisSatyrs., The
are divided about the Reafon of the Name. The
of Father Bioffu feerns well grounded. A mere
tion of Feet, and Meafure, Ijich as we find in
Plautus, and in Horace's Satyrs, he thinks, is not
rto conflitute Verfe; to determine the Work to
cal ; or to diffinguiflh it from Profe : unlefs it have
,ther Air, or Chara~ter of Poetry ; fomnewhat of the
ir the Sublime. See POETRY. Hence it is, thiat
:als his Satyrs, 'Profe, Sermones. His Odes have
Dther Air, and are therefore called, Poems, Carmina.
.M, PROSE, and VERSzIFCATION~.
A'ONIUM, in Old Records, a kind of Interlude
1rical. Play, which the Inferior Orders of Cler Y.
by Bqys, Ee5k. ufed to a& in the Bady of t~e
fus table to the Solemnity of fame Feflival or high
)n Day. This is fuppofed to have been the Origin
4odern Drama. See ComEDY.
:)N OF ALMONDS, is the Quantity of Two
d Weight;5 of Anife-feeds from 3 to 4oo0 5Of Ca-
~,pfromn 200o and a Half, to 300o and 3 Quarters.
DSTin Medicine, an aqueous Liquor, mixed
e Blood and other Humours. fDegori defines it,
bilious 'uce , approaching nearly the Nature of
but which, being extravafated, does, not coagulate
Blood. See SEuM. Diforders, of the S~pleen
nded with Serofities. The Kidneys help to, purge
7(ities.
PENS, in Alironomy, a Conflellation in the
rn Hemifphere, called Serptens ,p hi ucii,


SEIR


'The 8tirs iti the 'Confiellatio  &rpOs In 'tim'
Catalogue are i -; in 7ycho's it ; in the B8ritannic Cata-
logue 59. ,TheILongitudes, Latitudesl Magnitudes, .
whereof are as follow.
Stars in the Conflelation SIZAPhNS OpPH~CjIn


FQames and Situation;o
Inform, preceding the Neck
and Head of the Serpent
5~~~~~~~
Firit of Three unider the Jaw
That in firft Bend of theNeck
Freced. in ad Bend of Neck
Middle under the jaw
Third and Subfequent
s ft from the Root of theNeck
20
Preced. in the 0 of theHead,
or in Extrem. of the Cheek
Preced. of z bef. the ad Bend
The lucid one of the Neck
Pofter, in the id Bend
IF
That follow. theLucida,toN.
by Tycho reckon, the 6 Opb.
S. of 0 in Root of the Neck
A finall one under that
30
Behind 2dBend bef.Oph.Hand
Subfeq. before the '2d Bend
In Mouth, in mid. of 0 Head
Subfeq. behind the ad Bend
That fo. theLucida to the S.
North againtl the Noftrils in
the L3 of the Head
In Temples, I fubfeq. of 0
That without the Head to N.
40
'That follo-preced. oph.Hand
45'


xI f of ;,beh. Opb. hind Thigh
Tbefe ; Tycho ranks am. Ophi.
South of z following this
50
North of thefe
InlaftBend, behind Opb. Hand
Laft but one of the Tail,  yj
Of Three fmnall ones North
following that   Sou.th
Middl'eand fubfequent


In Extremity of the Tail
Small one adjacent to, this


".Longitude
IP, 0 2 I
It 7 ;84f
8 42 07
10 33 35
12 04 08
it z 00


'3
10
14
k14
I I
14
17
12
53
II,
1±
13
IS
17
20
14
i8
i6
21
19
'9
17
23
23
II
22
:29
2S
TI T


15,
20


21
25
I
3
3
4


I I
I I


1 7 04
01 04
i6 37
57 20
45' IS
49 M7
29 35
00 35
53 15
36 4Z
00 57
40 02
57 54
12 31
13 17
42 5'0
43 22
19 46
36 34
04  6
;7 03
31 46
21 66
37 08
27 05
26 47
57 13
59 22
i6 18
Ts is
23 04
48 23
1 2. 27
45 S8
2330O
29 5'9
15- 54
II 31
07 23
5-7 39
12 46
13 23


07
47
31
o6


05
32
03
ft
38


19 15,
3~1 8
a630
31 ~48


Latitude.
0 1 it
j621 30
22 010 00
17 50 2;
19 27 c6
is 3± o6
±9 59 I11
17 OX 48
3± r8 fy
20 07 02
17 27 r4
23 4 oi
18 1
35 4834
33 24 ;8
34 23 iS
34 ;6 1 2
31 34 09
36519 54
21 45' 01
25 31 T6
17 39 25,
,602o
26 34 S;
34 21 30
15' f1 00
~3 09 36
s6 !6 in
21 47 38
37 o8 s'o
i6 414
40 0of3
3S5 4t
35 19 31
42 28 f2
aS 58 33
37 I$ oS8
37 03333
22 16 02
28 07 517
9 44 45
10 is I i
10 32 I±
19 47 r2
120 3I f6
23 29Y3-
21 17 24
22 14 64'
29 19 27
26 54 41


_,1 - , _'J


7
6 1
6
6
7
7
7
6
6
7
6'
6
7
6 1
6
6
5.
6
6
6
6
4
6
4.
6
4
3
7
4
6
7
4
S.
6
6
4
4
3
6
6
6
6
3


SERPENT, a Mufical Infirument, ferving As A B&a1Vd
to the Cornet, or Smtall Shawm, ,to fuflain a Chorus of
Sinersin  lrgeVefel.Ithas its Name Serpent, from
its igue; a  cofiflng  f everal Folds or Wreaths1
and confiffs of Three Parts ; aMuhpee       ek   n
a Tail. It has Six Holes, by easwrofthygv
it the Compafs of Two Oaaves.
SERPENTARIUsj in Affronomy, a Conflellitiott ot
the' Northern Hemnifphere, called alfo Ophiuchus, and an-
ciently ]Efculapi us.~ See CONSITELLATIOtC1
The 'Stars in the' Coniflellation Serpentarius in Polomy'
Catalogue are 29; inYy'ycho's 2s'; in the Bliann Cata-
logue 69. The Longitudes, Latitud'es, Magntude,.~c
whereof, are as follow..






. I   1. .






I +cc-+c--t-c--c -C-+C-