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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0857
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eles are Lguaterat (bY l4C. )
prearex han 2 Lipsc AnSles, and Lels Clati 6 AIBI
Ones.
Forn_ F m X = F m n = 4 L (B7 121)
Thar is,
ther are Equiansulur, ee eus ncal Frian-
2: The Lees oE che Righr angle are or ctie same
Kind wich the opposire Anoles. So in che Triangle
BD A, bccause D A is Grearer thau a Ou2
deanc D P, che Ansle D B A is GreateE Than che
Richc-ansle D BP. And inthe Friansle BC A
becaule A C is leser than che OuadranEP C, the
Ansle C B A is lels chanthe Righr- angle C BP,
2. YF che Legs (and consequentty che Angles)
are ot che Came or disserene kinds; the TIrpOTI
nuse is accordinslr lesser or grearer than a Oua
drant: S0 in che Friangles P D A, F C A, the
IIypochenuse A P is lesser than a Ouadram, ou
in che Priansle BD A, che Fyporhenuse A B, is
Greater thanche Ouadrane B P
sles are Equilateral, (BY LAth) and cheretore Pqui
angular (by sch) and cheretore che provoled Trian
17. First, The3 Angles oF every Friangle, are
6
1. 0. 2L = D. )- 6  fl.
2ay, The Sum oF che internal Angles, is le
than ehe Sum oE the Incernal and External boch
erhrich in all, matie buc siX Righe Angles.
18. OE leveral Arks oF srear Circles Fallinsfrom
thie Pame Poine of the Spheres Surtace on another
Circle, the greacest is thac which palses chroush
che Pole ot the Circle, andche nexerothis, is grea
ter than thac ertich is Faxcher OH.
For suppose P che Pole oF che Circle C a L
and  the lole ot ll C; then iS AL
AF = AC; andche Arch B aC = BP
Jors trom che WO lall.
3. IFHC LSPOHeMUICIS LCIS Os SICateL CMAH a
Ouadrant, CiFMCL LCD WSCIE Les aacCse LInole, I5
accordinsly oE che lame ox ditterent Lind, 25 F0l-
D - C = TI
L
For che viewing che Sines, Cosines, and orter
Riohe Lines oF Arks, Wrhich are noc visible in a
common Sphere; Let the Arks ot chree orcal CH
eles oE Card Past. board be put roserter; do  al
Armillar Sptiere.
19. A great Circle pastins chrouph che Poles
anocher srear Circle, curs it ac Righe angles; at
On the contrarr, if ie curs ic at Righe-angles, i
passes chroush iis Poles. Thus the Angle P BL
-. = POD = PDB, 21(0 = 10 a AC.
20. In an oblique ansled Friangle, il che An-
eles at the BasC are like, Or of the same Kind, i. c. borH
Acure, or boch Obcule; che Perpendicular FalIS
richin che Triansle, and the Ouadrantal ArH
withoue: Bur is ches be untike, the Perpendicular
Falls withour, and che Ouadrant within. FOr che
Frianele F A F has the Angles F and F ACurC, and
the Perpendicular AC Falls victiin, and ehe Oua-
drane A  Writhour. AIO the Triangle B AC hatH
B and C obtuse; and the Perpendicular AD wvichim
and che Ouadrant A u Wwithour: Bur che Triansle
BA F haS the Angles B, L OF different Kinds, and
che l’erpendicular AC wirhour, and che Ouadrant
A a Wrichrim.
AIIO, by che Paus LISuC lsmanitere, ho ene
ambiruities ot Rishc ansed Prianples may be
Colred, viz.
AS SupPOTC ThC ENO ACRS DL, D R, and ChaL
BP II, The Plane ot the greater  WeC CIHC
round B FI, eill thac a Righe Line Fallins trom
pervendicular ro the Plane B A H, mas tall 01
Lome Poine of che line CA, suppole on ; 10
in chat Poluion L’a B WillDe aSpesek Hlal.
Righe ansled ac A, and B P chc FIyporhenule, B A
che Bale, P A rheperpendicular Arct.
And suppose PA (in thenexE Figure) BC equal PA
OE the Frianole, and sicred accordins ro irs Letrers
cherein, and dra A F, P FPerpendicular tO BC
(0 A B, P B, PD, Will bC Sines oF the ANtS B A
B P, P A, and cheir Co sines will be E C, F C
DC.
Thele