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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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jected by ehe directione
lven in Spherical Geometry; che Angles may be
likevise tound, wichour Calculation, and cviit
Nand chus. LhC Friansse Will BC C Z. D. Wotere
In a Spherick Priangle, thar is Righr angled or
Onadrancal, the eruo pares vrhich are adiacenE +O
che Rishr angle or Ouadrant, cogether wich che
Complemenes ot che orher chree, are called, by my
Lord Neper, The Five Circular Parrs. And if ihc
chrec pares wrhich enter the Ouestion, (viZ. 2 giren-
and i’required) have no incerruprion, (no cho a
Rishe ansle or Ouadrant come betveen, ris nOt
connced an Incerruprion) chac parc irtrich is be-
cveen che orherrvo, is called The midale part, and
then the orter rvo are called Extreams adjacent, Ox
conjunet. Buc il chere be an Incerruption, rhac
parr which is separared trom the ortier tvo, is
Called The midale part, and the Other LWO aVC FX
treams opposite, or dispunct. This beine premisd
Neper, alcer a diligene vie oFthe Solurions oF aII
the Cales of Rishr angled and Ouadrancal Prian-
Eles, has obserred, Thac chey all agree in onc OF
ro Proposcions, viz. Thar the Radius multiplied
by the Sine os the midale Part, is equal to the Rect-
ansle or Product made of the Tansents of the FX
creams conjunct, or to the Rectansle of the C.0. fines s
the Extreams disjunct.
is Propolition was Invented by che Lord Ne-
per, purely For eale oF Memory, and has been ap.
lied in aIl ies Cales by most Authors; as palucu
arlY, by AIT. Nemton, Normodu, Al f. Moor, WV ard.
dec.
Some more F.xamples os Oblique Spherick Triatus
in Numbers.
In che oblique Frianele BP D, ((ee ihe Fipure
Collomins. )
I5 et
C 1 0L L+lL.
he chrec anxles beine piven, 10 find a Side.
The Aneles adjacent ro che Side requir d, cali
Tegs; and che Angle oprolre, cal Basc: Then
Work as in the rrch Case.
For, such is che Operation in che Suxplemental
Friangle, whole Angles and Sides are equal toche
Supplemenes ot che Sides and Anples ot ihe Trian-
ele propoled: Bur Arts and cheir SupplementS
have che lame Sines and Pangenes.
Fxample in Numbers.
Inche Frianele BDP, chere is given che
P = 143. 0, the SunsAzimuth fromthe NortI
AneleZ B = 15. 04, the Ansle os the Suns Posirion.
CD = 30.00, the Nour from Noon.
Required che SideP D, wtichis rhe Complemenc os
ibe latirnde.
Comp. Ansle P = 370 0012 Ar. C0, OF 50 220537
Ansle D = 30 00 5theSines 20 302030
Ansle B = 13 04 = Ansle op.
Sum = 82 04
Sum == 4+ 02
=Sum = Angle op. 25 585
dines L9 817233
9641323
The sum oE che + Logarichms equat 19 980113
Iis haltis ihe CO sinC OL 13 13 9 990056
Which doubled, sires 24 261 equat P D equat
Complement os Lacitude: Wrheretore che Laricude
mult be 65 dez. 34 min.
PD = 24 d. 28. Z Laloraat.
dd. E a sai nio fiomctoe tonto esre e
dC D. 2 iue taritier
Suppose chere be piren the Sides
Ethe Complement os ihe Suris De
BD == 73 d. 004 clination, or his distancefront
B=
52 d. 34
the North Pole.
Complement of ehe SurS
altitude.
Fis required 1o find che Anele.
2 che