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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 806933011:0693
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BuriE the Number of ReRlections be even, chen
che double of che grearest Retracted Angle, Will be
che Diltance oF che Tris trom che sun himselF.
Nou ro sain chele Createst Lxcesses, havins he
Petractlon oF any Liquor, or che Rario ot che sine
oF che Angle of Incidence ro the Sine oF Retracted
Arisle, sou must obserre, thac che Excess OF ENO
Retracted Angles, abore one ot Incidence, will
BC Greatst Where ThC NIOMENLANCOUS AUBMCME OP
Filuxion of che Angle ofIncidence, is precisels dou-
ble to ee Momentaneous Auement ot che Retra-
cted ansle. And if chere be chrec Retracted An-
sles, the createst Excess, will be Wrhere the MO-
mentaneols Auement of che Ansle ot Incidence is
Friple ot heMoment of the Refracted Angle, anc
S0 on, Which is sufficieney evident.
Buc in order 10 And che Angles themselre
Eles ac the Bale, ate lo oe alotiet cucs as etie
Lecchere be anr RiphE Linc as A C, and let ir bC
10 dirided in D, FhaE C A may bC LO C D::
according ro the Rario OI LCHALHO; ThaEIS, IM
NVateF: : 25 250 i5 1O 187, OF more nicelY : : 529
i5 r0 396. Then lec ic be divided acain in P, 10
that C F Ball BC EO A F: : a5 Oniry is eo che
Number OF Reections Which chre SolaE RayS
must undergo in producins the Tris propoled: This
cular draw the Larallet F B
E
MI. Fralley premiles che Lols Lemma.
OLD
ARY.
Elence it follons, Lhacche Moes Otne AH
langenes ot chele Aneles.
Lainthe Diamerer ot any Iris, cither GeomerricallY,
Ot by Calcularion.
Du ehe help ot chis Lemma he Bewvs hon 1o ob.
done; on che Diamerer AL lecché Semicirele ABL
De described; and on the Cenere wrirh che Radius
CD, deaw the Ark B D, curring chie Semi-circle
A B F inthe PoinE B. Then drawing rhe RigHE
CS C
B, AB, ler the Perpendicular C F, be le
FaII on A B produced eO F; and to chac Perpendi-
he piocuc  c Blopel His.
Yche Ansle C B F is che Angle of Incidenice
C A B is the Retracted Angle, borh required For
at A; ies L egS B A and C A, ane ene BasC
on Which produced, let Fall che Perpendlcular AV
Chen let the Verrical Ansle B A, C bC suppo
De encreased by a Ouancier infinitely sittalI, a5 sup
pole by che Momene C Ac: LIn Cawins il
Lines B C d, and c D, chey vill de os mmagina
rils differene trom BC D and C. D.
This done, JCaY, Thac if che Lessb ite Planc
Friariele B A C, Cor any ocher) continuns ch
tame, the Verrical Ansle be imagined Wdde en
crealed by any Infinicetr (mall Moment ot LIuXior
chen will the Moments of the Anoles at the bas
reciprocally as the segments of the Base: Lhar ie
CBc, is 20 che Momenc oF che, ASC AC B, 0
ACD:: 26C D i5 10BD.
For since the extemal Angle A C D ==  A B
I- anele BAC, its Momene must allo be equat r
ere Sum ot cheir Moments, Ox to C BC = CAC.
buc non because che Frianole AC D is ris alls led
aC D A C may bc che Diameter oF a Mcle
Whose Peripherr ill pass chro A, D, C, al
and consequencly chc Angles C A0, C VC DemE
in rhe lame Seomene are equal. S0 chac ehie Sum
ot che rvo Fluxionarr Angles C Bc, andcD
(1. c. the external Angle D)cd) Will be che MO,
menic oF che Angle A CD, Or ACB. Buc chole
CBC, and Dc d, beins infinicely (mall, will bc
o each ortier, as the Sides oppolce rochem, el a5
cD Or C D isto BO: Thac is, reciprocallu ad
Scgmenes ot the Balc. D. F. D. 11
IFB and C had been boch Acure, rhe way ot
AB
Eistea BuD E MONS FR A YFO H.
istoDniey; by che Construction.
roche Moenoe e AL u ne sate Ra-
Since chec trianeles AOE, A F B are Similar
AF will bero BF e: 25 A O2OBC:: Thac is, 2d
che Numbe   s
Wherelore the MomeneoF the Anele C BF, is
rio, by che Lemma. cse hac
ProOF Bchelame, all  Coeledo
Duc chepune osche AnsleilBL, is ro the SiC
de ate And eo l dt si. Me Aeo. leauio de atere deda