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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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Rerolurion eo be made ot the Line CarFMIHS HeCircle lO deteribed, 25 1 10273 10 a AFh, 2S L EO
Poine, (0 EHac ther MaII enA THCIE MLOTIOM ac lasE
rogether; there wvill be Formed a Double Spiral
Line, and ruo Spiral Spaces as vou sec in chié fii
sure. From the Cenesis oF which may casily be
drawnchese Corollaries.
kins equal Angles wich the first and second Spiral
(25 2I(0B +2, B 10, B8, (95,) dre in Arichmeticat
Proporrion.
the Circle incercepred berwire B A and those Lines.
Because Wvhacerer parts oF the Circumterence che
Point A describes, a5 suppose 7, che Poine B wil
al(o hare run over 7 Parts oF che Line A B.
3. Ans Les uaem B coe lecond Spiral,
a5 B 18, B22, 690. are r0 each other, a5 che
atorelaid Artes, rogecher wich che whole Peri-
48, 69c.
ervo, enouxh on this Subject, ro sire cheReader
1
phery added on boch sides: For ac che lame cime dian, must also (as ive Mewr in Prop. 7. OE Sphe-
Thac che Point A runs over 12, Or the Whole Peri-
pherr, and perhaps 7 pares more, Mall chac Poine
B hare run over r2 anid7 parts oE che Line A B,
extrichis nom suppoled eo be dirided into 24 equa
PAFIS.
med che Circle; and il thien rou imagine a new j ehie second Cirele will be 25 1 10r2: and r0 a 3 d
F. That the Lines B +2, B FN, B 1O, (50. Ma
2. The Lines B7, B 1O, CdC. drawn any hoW 1O
I. The first Spirat Line is equat eo hals ehre Deri-
Phery of the first Cirele; for the Radii os the Se-
Etors, and consequently rhe Arches are in simple
Arithmeticte Prorression, vhile the Periphery of
the Chiele contains as many arches equat to the
Greatest; wherefore the Periphery to all those
Arches, is to the Spiral- line a5 2 t0 L (b7 LI. 6. 0f
Llum. ProgreHtiOn.)
PehOPHE OnE ProxOsition, Wwich 2 Corollary Ox
The Rel SpitaI, aEC Ed One anocher as the ArKS Ot
Specimen oE thie Genest, a nd Properries, ard
PROPOSTTTONS.
L. IBc first Spirat Space A D CB is 10 the first
Circte:: 45 L +0 3
ar ot Demonitrarion uled abour spirat Lines.
Thole chac vould see more, may consule Archime-
des, Dr. WVallis S Arithmetick of Infinires, Ox Stur-
minss Math. Fnucleat. lib. 2. Chap. 4.
Proportional Spirals, are Cuch Spiral Lines as che
Phumb Lnes on the Perrestrial Clobe, which be-
cause thes makce equal Angles wich every Meri-
rick Ceometer, Which scc) make equal Angles
wich ehe Meridians in the Stereographick Projecti
on the Plane ot the EquatOr; and cheretore wili
ve, 25 the Learned C apr. Palley obserres, Propor-
tional Spirals abour che Polar Point. From Whence
that excellent Machemaricran aBIMOMNITateS, LHaE
che Meridian Linc 1. a Scalc e L05. TangenEs
Sec Meriatan L.M.
ot che: Meridian complemenes ot elie Lacicudes.
Diride itic Circumterence oF the C HCtC ITO:
=ParES, by Lines drawn From the Ceniter B, bC
Sinmins from ehe first Line B A; chen Wil (BY
Cor. F.) BcbC == T, B D = 2, ana
and he Sectors circumseribe d aboue the Spiral will
be 25 The Squares oF che Radii, viz. C BC=
DBd == 4. and AB a == 9; and (0 ir will bC a1.
vays, il rou makce nerer so manx bissections ot che
3 first Dirisions ofche Circle. Phac is, che Lines
drawn trom Bco rhe Spiral, Wvill bC 25 1, 2, 3, 4,5, 6.
5c. and the Sectors circumleribed, a5 X, 4, 25, 36
Coc. alivars soins on in ehe order of Squares
or in a duplicare Rario. Buc 2 Rank of Cuct
PerIS, arc t0 a R ank of a5 many, equal ro che
Greatest, aS L +0 3 (bY N, 7. OF Arithm. Progression.
TVheretore che wwhole Spiral Space (Wrhich is Com
In Proportional Spirals; the Angles B P D, BPd.
(90. Or The Arches BD, B d, E3C. are Exponents
OF Ehe Rarios OF B P EO P C. FOF FOr IE the ArCh
BD De divided into innumerable equal ParES, ristE
Lines dracon from them ro che Center P, MalI di-
vide the Curre B cc C inco an infinier oF PFODOT-
tionals; and all che Lines PC, P c, C9c. Tall BC
an Intinier oF Proporrionals berween P B and BC
vhose Number is equal eo all che Points d d, in
the Arch B D: Buc ar intinire NumbeF OF PFOPOF-
tionals becween the rvo terms ot the Rario, is eo
Poled ot such Sectors) is ro che Whole Circle:: 25 chac infinice Number oF equal parrs between any
2103. L F. D.
IE anoctier Circle be dravn wich a Radius dou
Ble coche former, ies Area Wwill DC (aS eHe Square
eF IES DLAMCECY) 4 rimeS aS GFCAE AS CHaE OF FhE FOF.
Mer. Lheretore the Arst Cirele corhe second wil
be 25 Y 10 4, OF 45 3lB +2. And since the Spira
Orher Lvo TerMS : : 25 the Logarirtim ot che one
Racio is co rhe Logarichm oFche ocher; theretore,
25 BD eO B d, Or a5 The Argle B PD tO thC AN
Sle BP c; (0 isthe Logarictum ot the R ario OF P B
E0PC, coche Locarictm oF che Rario OF P B 10
Pc.
e
F. D.
SPIRET, Which che Chrmists call Mercury,
Is ore oF the s Principles separable From a MixI,
by Fire; eis subeit, listr, penecrarine, and actire,
F
doaec id eo rhe hek Citede ad 1 10 3, phac done  aee hacia 1e Paeveleo i a vers epiet Mogesii
Etiis