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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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carries a Flair, and Mens by Inspection, che sun s) sular Section by che Axis, ehen he Wvilt be ma-
Meridian, Alticude, Riche Ascension, amplitude.
nifest, thaF che Fyperbolick L ine C. LFI is cistan
Oeclination; time os his Risine and Setring, _cc. Cach way trom the Asymprores BC, B A, by etie
to oreater nicety chan the larpest Globes non
made.
lenorh ot che verred Sines of the Rqual ATHS BC
and e A in the Circumterence ot ehe Circua
ASFRONOMTCAL Numbers: See Sexagesimal BasC OF the COnC; and THAE ZE ThC late FitC sl
Fractions.
ASTRONOMTCAL Place of a Star or Planet,
is IES Lonenac ot Llac IH che CCMprick, reckon
ed from CC DCGHIIS Ot Ares, in Consequentia,
OF ACCOTAIIIZ IO LRC MaLUIEAL Ordet OF the SienS.
comes, it produced, stiII BeRTer ANC RCATEF d
chem. And consequeher, Tlar
F. RG and FFS, Or AC and IY C BCmZ adW2Y
equal eo one anorher; 25 are al(0 EhC OrdinaLES
G F and FTI, _C. ThC RectanBles RGS ana
ASTRONOMIOAL Ouadrant, Is an InAru- SFTR; AGC and C EP G Wriil alivays be resve
mene curtoun tramed, and the Degrees exactlr)
Ctively equal to one anocher.
and minurely divided by che help ot a Screw on 2. Thé Curve and che Asymptotes can nevet
the Fdse ot the Limb, ficred ich Telelcopes, meet, because the Circles generared by LQ anc
and cirhex apply d ro a Nall in che Meridian on che Rines Benerared by RS, H C, ecc. (irtiict
a Arone Axis ox Pedestal, wich evo Semicircles vill arise trom theP.
placed ac Riyhe Angles on co endless Screns, maginary Rerolurion ot
Whicti readily direct or guide the Instrument ro chewhole Figure round
FaKC OBICLVaLIOIIS OF FhC SUn, MOOH, OF STaES.
ASFHONOML, IS a MatheMatical Science,
the Axis F B) WvilI 21.
vays be equal 10 onc
reactiins IHC Knowledee ot the scars or Fleavensy anocher and eo the Cir
Bodies, and cheir Maenicudes, Mltances, Felip.
cle made by the Rero.
Ses, Order, and Morions: By some ris caten in lurion OF che Radius
10 larse a sente, a5 FO COnLAIM In IE alsO the DO-
etrine ot ihe Mundane System, the Lawus ot the
Planecary Morions, (90. Which ochers reckon a5 a
rable.
F 9, 25 is plain b
comparine chis laAFi
Bure wich che Former,
n N.
For che Spaces gene-
rared by the Lines F. 9.
FC, _c. will Be a5 the Squares oF cheir Diameters.
or ofche Generarins Lines. Buc ris cerrain, châc
the Square oF F h Or OF F C exceeds the siguare
approach nearer ro cach orter, bur ino Locinued OF FFI, by the Square ot h FI Or f F; chac is, by
the Square oF P. Q, by che Suppolicion abore;
ny kincs, as the Curve ot the Conchoid, _cc. bur it Wheretore the Circle generared by che Morien ot
may beenouss lele lo mention che lamous
ASTMPTOTESInCO-
F C Will exceed thar generaced by FLB, by tB~I
Circle generated by L O: Bur the Space genera-
nick sections, Which are red by F C exceeds thac generared by FHI, by
che Lines O5 and OR:
wvhich are thus dravn
imasine in the Fyperbo.
la, che Second Or Conju-
jusate Axis P Q r0 de
Scend, AiI Keexins P2-
rallet eo che Ordinates,
till ic couch cheVertex ot
the Ring generated by FTC; Wheretore chacline
made by FC must be equal co che C ircle made
by F Q, DF D. And chis will alvrays be 10
and cheretore the Line TTC can never gro oF nO
lenerh, and consequenely che Curre and the A-
Symptore can never meet.
There are orher Asymptotes ro other Curves, ans
thoueh che Parabola hath no AsimptotC, yeE LS
the Section E, For then, Parabolas may be dravn Asumpeorically ro cacte
if chroueh the C entre O Other.
The Followins general Obserrations abonc A
Linc p 9. These are che famous Asymproles men- symptores and asimpeoricke Curves, Lhad Commeni
cared Trom ME. Trumphrey Dicton, a perlon Decu.
liarly stiltul in chese Marrers, and are as tollons.
Some General Observations about Alymptotes,
and ACymprorical Curres.
PaEE OF PHyHCKS Or Lracural Philo(ophy.
bility: Which lec
ASVMMETRAT, IC LaLR M Incommensu
ASTMETOTES, are Lines WwhiCM comcinual
Intincely can never meet. Ot iele rhere are ma-
ASYNMETRY, eie Came wich Incommensura
rou dram Lines chroush ine enus oF ehis Tangent
tioned by Apollonius, Lib. 2. Prop. L. and ot whicti
he demonstraces, char chough insess produced,
and chough the Curre come connually near-
et and nearer ro chem, ver can ley never be
Coincidene wich che Sides oF che Fyperbola, nOr
ever meer ic, or touch ic; whence comehthele
lame OE Asymptotes: And by lome LACM MLIIErS
chey are called Intactae, For the lame realon. Lhis
Non-Co-incidence appears very plasus, wtiere the
Triangular Section ot a Cone Dy FhC AZ.
Supeose aloHS cC LIne
L. Lhousa uE be cercam chac all Tucti L urres as
have Alymprores, De ot che Number oE chole
wtrict (rumnins on in Infinitum) do noc include a
Space; ver ic is nor rrue, on the orher hand, chac
where erer ve hare a Curre of thac Nature anet
Properey, ve find an Asymptore aI(O. For this
ef Parallel co B F. For infinire Continuarion of che Curve is visible in al
thole oF che Parabolick Family, and ver none ot
perbola seh, to bemored all chese ean hare an asymptote; chac is, noc any
oFWata PaFAHeL 1O sE seIF
Righe Line placed in any position co the Curve
as fac as the lenort ot the can infinicely approach eO it and peF HOE CUE iF, 25
Liqual and Parallel Lines.
CoMLC COOC Ia ClL LC
is noc hard eo be demonstrated.
TI. OF those Curves rhat have an Asymptote
Tome chere arethac havetwo, orhers chac haveon-
On GF FY, Or 10 be co- ly one. Instances of the former Kind are all che
merdems vuict _e Luia.) Corio ot Hyperbolick Cueres, uhich tom be ci
Section of the Fyperbola is madte parallel, 10 che
it you imagine che LIy.
C, fF, E 4, BFF, riIl ir