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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 806933011:0093
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Cipte oE cheir Genetis las beine Tormed trom lc. ( trich it allo, and cBCrCe F F is nOt an Asym-
ciprocas selses) dle calisy prored cohare cuo A- ptote.
symprotes. And ot che larter lorr we have che
Conchoid, che Cissoid, and che Locarithmick Curve
V. Bur à Kiphe Line may de an somptote 10 à
mixe Curre thac is parrly Concave and parcly
The Nacure oF which considered, as clearly Mens Conrex rowards thar lame Linc. an Instance ot
thac cher hare one and no more.
TII. A5 a Righr Line and a Curre may be A.
simpeotical 10 one anocher, (0 allo may Curves
and Curres: And here are rvo or chree Varieries
to be considered.
ehis ve have in che Conchoid ot Mcomedes, Which
is Concave (for lome parr OF it) eO its Normal,
and chen atter the Punctum Flexus, in Which rie
neithet Concave nOT Convex, ic is FOr ever Con
vex cowards che lame. Concernine etich Pun-
I. Any OE chese Curres, that hare trom cheir ctum Flexus, see Schoten. Comment upon Cart. Ceo.
ouon Nature and Construction an Asymptote, are
capable ot beine Alymprorical eo one anocher.
metry, L. Ib. 2
VI. AII Curres thac have one and che same
Thus in Conick Sections ris demonstrared, thac Common Asymprote, are allo Alymprorical c0 one
Fyperbolas chat have the lame common asimptote
are allo themlelres Asimptores ro cach orher; and
ehis Mall atterwards be Menn univerlally ot alt
Tuch Curres.
Wich an Asympeote; buc even such as in cheir own
nature admir ot no luch ching, may also have chis
aftection. Tie Parabola (For instance) ve know
has no Rectilineal asimpeote belongins ro ic; and
Tame Rishr Linc, will bc ACymiprorical to cach
other; as De la Fire has demonstrared, Sect. C0-
nic. LIb. 6.
anocher.
.Noc only chole Curres, Wrhich are endowed
vec cvo Parabolas, Wu est aes placed in ehe
3. Buc no Curre chat has any asimptote De
longins e HE, Can ever be A(ymprorical EO ano-
chier whose Narure retules a nur mp
for it ic wesc supposed co be lo, then chis lalter
Curre vould hare che Lympon et cn sertet
Cuere For its onn Asymptote coo, wtrich is concra-
ey eo cuc Lypochesis oF ies having none ac all.
can neret be Alymprorical to one anocher; for
ere IE (0, the Asimptote ot che LIyperbola woulo
bc allo an Asimptore co che Parabola; which is
imponBe, since chac Curre can have no A.
V. Ho Riphe Line can ever possibly be an A
simptote to a Curve, chat is every wvhere concave
corvards chac Righr Rinc: Thisis very clear Fror
che bare Consideration ot the Curvarure and rh
Demonstrarion.
Thus, for instance, a Parabola and an Hlyperbola
Simptote.
Tendeney of ic; and may be thus broughe inte
Let the Curre ADC (vtole AX iS AF) bc
concare in all ies parrs comards cheRiphr Linc
F E; this Linc chen F P MaII never bc an A-
L et the Curres FGH, O F R, have che com
mon Alymprore AD P; thenchey MalI be AIym
protical ro cach orher. Fir oE all ic is evidem
thar chey continually approacti ro one anochex
for instance, drawine ihc Line FD a TangenEr
the Curve OR in F, r0 meer wich che Alympo
in D, and producins B F rOC in the Curve L. L
deaw CF a Subrense in char Curve paranel t
FD, and then From HY, the Line HIKC PatallC
simprote 1o che Curre AD G. Lec A B couchche, toGB; ris clear that FG =FT, andHIL IIN
Curre in che Verrex A, and be imagined parallel because FD couches in F; cheretore FO L Hs
hac is, the Curves are nearer to one another it
EO FF; then any Ocher TaMBeNE, 25 CD sup.
Pole, all, it ic be produced, meet wirh F F in che Poines FT, K, chan in F, G; and che Pame
lome Poine or orher; bur because C D is a Tan- may be Mevn ot any ocher Poines taken from rhe
ParES OF B, C, rowards P. Buc chen again, chet
Benc, cheretore rhe Curve Line ic selF Falls be-
cveen che Tangent and che Line F E; bur ir is by Curres can never postibly meer wich, or euc one
che Fypochelis alto concare 10 F P in aIl its ParIS; anocher. For Imagine chey could and did in-
cheretore if the TanGenE C D produced inter. cerlect cach orher, ar the Poine  suppole, anid
secto FF, afortiari, ihc Curre Cm sat L L, R Y bc pacallet 10 B8, HC. Hte
Sorve