# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0340
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0340?run=74
# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0340
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=340
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000340.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
# Lines: 86 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

2
Suxpole Xy = 20 any R ectanole made Ox encrea.
Sed br a Perpetual Morion ox Fluxions ot cichet O
che Sides _ Or y, along the otter, and let tHC MIO-
menis, ox Fluxions of che Sides, Be x and y. By
I. From ihe Flovinz Ouantity siven, 10 finct
the Fluxion.
II. From the Pluxion, to find the Flomins
duantity.
AS torhe Formet oF these, the L eared Dr. W al- wrhrich e undersland che Velociry wich wtiich ei-
lis, in che place abore mentioned, (romM. Nem. xher Side mores r0 Tocus ine Meclalis C.
tons Papers) sires this general Rule,
Pet each Ferm of the Lquation be Multiplied sepa-
rately by theseverat Indexes of the Povers of all
the Flomine Ouantities contain d in that Term:
And in every such Mulciplication let one ROOt or
Letter of the Pover be chanced into its proper
Fluxion: Sostall the Aegrezate of al the Pro-
ducts connected rozether bytheir proper Siens be
ehe Fluxion os the L. quation destred.
And aII ehie Cases oF ir are demonstrated by
MIF. Tsaac Nemton in the Lemmata abore deliver-
ed, Wotrich L Mall exemplisie by parricular In-
Rances.
T. In che General, 10 express the Eluxions oF
Simple rariable Ouanciries, as was laid betore,
vou necd only use the Letter or Lerrers Which ex
prels them, wich a mall Poine over their Fleads,
chus: The Fluxion OE x is i, and the Fluxion oF
yisy, and che Fluxion OF x ] - y - v -) Z i5
L
v
2 8C
And (Inversely) ehe Flomine Ouantities in chis
cale will bc casly had From the Pluxions, by on
ly uvririne che Lerters withoue che POints Over
chem.
N. B. FOr the Fluxion OF Permanent Onanti
cies, wohen any such are in the Equation,
Vou must imaeine o or a Crpher; For Cuch
Ouantities ean have no Pluxions, propert
speatins, because they are wichout Morion,
or Inrariable.
TI. T0 And the Fluxions oF the Products ol
evO Or more Variable Or Flovins Ouantiries:
Multiply the Fluxion of each simple Duantity, bs
the Factors of the Products, or ibe Product os a
the rest, and connect the last Products by theit
proper Siens, the sum or Asgresate is the Fluxion
Soueht.
Thus che Fluxion OE X y is x y - X y, andche
Fluxion OF X y Z, i5 x y Z - ] = X y Z F X. y Z, ane
the Fluxion OF x V y Z is x V yZ - F X V7Z=
X Vy Z-= X V y Z, and che Fluxion OF a - X X
By b = y (ihe common Product beins a b -) - b X
) a = X 7) wvill beb it - ) a = v y = x 3
Erom che Sides subduet the hale Fluxions of
chose Sides, anel it will Mand chus; x - = anel
Mulipir chese onc ino amorher; and che PrO.
duet wilt BC r y - 7 X - X 7  X 1
Thencoche Sides add che hals Moments Or FIuX.
ions, and ic will be thus; X ]- =, and y-]- 7:
Wtich mulciplied also inco onc anortier, will pro-
duce x y -- 7 X  X y  x y
Atcer which, Suberact ihc former Product trom
this last, and che Difference will beonty x g  X Y,
the Fluxion oF. x y, accordins co the Rule.
The Inverse oErhis Rule finds also (in chis case)
the Flomins. Ouantiry From the Fluxion, viz. IF cach
Member oE che Flixion be. dirided by che Fluxi-
onary Ouaniey Or Letrer, or by changins the
Fluxionarr Letrer into chac proxer Elovvine Ouan
ruy oF wvhich ic is che Fluxion. For chen ihe
Ouores connected by cheir proper Siens will be the
the Florvine Ouantities CougtE. Ontr il che Ler-
ters aIl be exactly the Pame, che Flovine Ouan-
tiey will be a Simple onc, Wwhole parrsare noc tobe
connected rogether by che Signs  and -, a5 in
che tirt chree Examples oF chis Rule.
III. Fo Hnd che Fluxion ol any Fraction. Mut.
tiplus the Fluxion of the Numerator by the Denomina-
tor, and aster it place (with the Sien -) the Fluxion
of the Denominator into the Numerator; and Divide
the whole by the Square os the Denominator.
Thus che Fluxion OE = ; x y = = 7, (0r
Cuppole 4 = 2. Then Will r = 7 2: ntiea e