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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 806933011:0442
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In oire Cale Cheretore Ille Laprecion is Pohrire
in ehe octier Negatire. Buc a5 the Potns SO L
apprOaCk1O L, The Cmanciries B F and B F de.
Crease continually, and at the Point F are equal 10
norhins.
Sochac ie is plain, Thac chere is no parting From
a Positire toa Negarire Exprection, inthis Calc ot
Y. In chose Curres thac tave a Point OF IH
Rection, har the Abscista A P encrealerh conrin
ally; and, chac the Patr A T, oF ihe Diamerer, in-
tercepred berween A ehe Orixinal oF a, and Y che
concourse of the Pangent and che Are, enereasert
till such rime as the Poine P Fall upon F, and asier
thac it again begins eo diminist: From wvhence ic
2 Ouantier continually decreasine, Withour pastins is apPareNE, ChaEA T must become che Maximuni
chro noching. FOrrhe otheF pATE.
Let us consider the TAnGeHES (aS D A OF FTI)
curoH by Lirres continually dracon trom L rhe Poin
ot the Cireles coritact. IF, C B; OF C F, DC DUF
equal roy; che Exprection of ans suchi Tangene,
will bc = , BE
AL, utien che PoinE P FalIS uxon che Poisc F re-
quired.
2. In thole Curres thac have a POInE OF Retro
pression, ris evidene, MaE THC PArE A T CnCrCasech
continually; and chiar che Abscirta encreaseth (0
 accordins as we rake lons, eilletie Poine T FalI uxon L, ascer whichi ic 2
it on che one or on the orter side oF the PoinEF;
ir ore ense cheretore tis Politire, in ehe orher Ne-
satire. Buc as the Points B or F approach 1o F,
he Targents D A and EP P enCrease ContinualIY,
and ac the Poine P chey become Infinice. There.
Tore a Guanvies chac contininally encreasech, cannor
pals trom a Posirire 20 à Nepatire Exprestion,
vithoui Decomine Infinice.
AII ehis is Oniversally erue, Whecher ic be a Fi-
nice Ouantier or a Fluxion chiar ve consider. Phere
eain diminisech: From whence ic is clear, Thac
A P must become a Maximum, When the Point Y
FalIS upon L.
Nou is A E BE pUE = X, EF = y, ehen vill
ALBC = 7= = s, whose Fluxion, Wotictae i5
=à (suxposine i invariable) beine
is no chansins From Positire ro Nesarire, withour dirided by X, che Fluxion oF A F must become
pastins chro Nochins or Insinice.
Applyins ehis cheresore to Fluxions, ic will Fol. Nochins or Insinice; chat is - = Norhing e
Jon trom hence, Tharche Pluxion oF a Ouancier
thac expresses a Maximum, Or a Minimum, must
be equal ro Noching or rointinite. And upon this
Foundation re may no casily procecdiothe spe
culacion oE chie Poines ot inptection and Retro
cression.
Insitile: S0 chac mulcipivins by j, and divi-
dins by = y, y willbe = co Nochins or Intinice
Which in the Sequel will Serre For a general Form
t0 sind F che Point or InRection or Rerrogrestion.
In order ro sind a General TheoteM to altist us FOF Mhe NatuTC OF ihC Curre A F H beins Birem
che Value oC y may be sound in x; and catine che
Fluxion oF chis Value, and supposine x inrariable;
he Vatue oF y will be Found in X, Which beins
Duc equal eo Wochins, or Intnier, serres in cicher ot
thele Suppohtions eo And sucti a Value ot A P, 25
char che Ordinare P F Mall intersect che Curve
A PKL in P che Point oF InRection or Rerroprectiori
OEchis Y Mall orils no trom che Analyse des insic
niment Petits, sive one
ENampte
Wvhose Diaheter is che Righe Line AB; andits
thro che Point l’be dramn che Catnace applicate
in ehis Matrer, ler us consider che Curre AFH,
Ordinares PMI, cF, Patallel 10 onc anocher. II
E F, cogecher wich che Tansene P. L; and trom
any ortiex Poine a5 MI, on che lame side wich A P
be dravn ette Ordinare pae M P, 25 litrerise
che Tangenr H P: Mis evidem.
Lec AF K, be a prorracted Semi cyeloid, whor
Base is lonper chan ehe Circumterence oF che gene
rarins Cirele ADB, Wvhose Centre is C. Tisre
quired ro sind P in ehe Diamerer A B, PO thac lC
Ordinace Applicare B F, Mallcur che Semi crciot
ot. ce ceonre es cenuaes tileacon
ot