# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0809
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0809?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 806933011:0809
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=809
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000809.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 101 lines, status machine
# Lines: 101 recognised, mean confidence 0.87
# 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.

tion che
villin che Denominaror, a Wvill vanist in
io nothins: And consequentr cither AD ic selF is
che l’ansent, or else lA; or ar least, a Line Pa.
On che Rishr Side, lex chere De Presixr to cach
Member, the Lixponent of che Poer wrhich a hach
chere: Or Wrhich is allone, Let rhaE Exponent be
mulriplied inco all ihe MemberS.
R V L F HI.
Terthe Came be done also on che Lelt Side, mul
riplrins cach Memberthere by che fxponent ot che
Pover oF y.
Adding thismoreorer, That one y mult (in cactu
Mlember) be alvars chansed inco a.
This done, TCay, that che Equation thuS reTOF-
med, will seu che Mechod of draing che requi
red Tangent ro ehe Point D; and wtien FhaE iS
siven, 25 allo y, u, and che ocher Ouanticies ex
Pressed by Consonanes, a cannor be unknown.
Tex there Be this Fignation by = y y = V V, in
Wxhich F B is b, B A = y, D A = V, and let a
OF A C be required eo sind che Point C, From
itence CD bemp drawt, Mall be a true Pansent
10 thac Curre D, in D.
In this Fxample nochire is to be ejected our ot
he Eguation, Because y or V, are in each Mem-
ber: Tis also (o dispoled as required BY Rulc L. I0
each pare cherelore chere must be prelixed che lx-
ponent of the Povers oF y and V, a5 in Rule 2 5
and on ehe Letr Side let oney be chansed into a.
And then che P. quation will be in this Form, b a-
27 a =2 V V, wohicti Equarior reduced, sives
easily che Value oF, a = p = - y = AC. Ane
Torhe Point C is toune, tcom whencethe Pangent
DC may be drawn.
Fo determine wohicti way etie Fangent is 10 be
deaWi, Wrhethex covards B Ox F, he directs to con-
sider ehe Numetator and Denominaror ot the Fra
aion, wohiich ac lastis tound egual coa. FOr,
2. HF in Borh pares oF che Fraction, cicher all ehe
Signs are Asirmatire, or it the Afirmatire ones
are more in Number, chenthe TanSCMEISEO EUT
rorards B.
2. IEThe Asirmarire Ouantiries are Greaterchan
the Nesatire in the Numerator, bur equal eo them
in the Denominator, the Righe Line dravn chro D
aud rouchins che Curre in chatPoine, will be Pa
rallel ro AB: For in chis Cale, a is oF an Intinite
Leneth.
Data.
in thelA; 20, and Ach kules.
3. IFin BOTH ParES OFIhC Fraction, thC AHirma- Or at SeatE, L. B voula DC II, IF N B had BCCA l a
tire Ouantiries are lels than the Negatire, chansins
allthe Signs, the Tansenr must be dravn nou allo
romards B: For this Calc, atcer the change, comes
ro be che lame Wvirh rhetirst.
the Negatire in che Denominator, bue in che Nume
rator are le(s, Ot vice versa; then changins che
Signs inthat part ot the Fraction where itiey atc
less, che Pansene must be drann a corierary vas;
3. C. A C must be taken romards F.
5. Buc Whenerer the Astirmatire and Nesatire
Duanricies axe equal inche Numerator, let chem be
keti equal r0 rhe Diameter.
rallel 20 L I3 do vont Cas de ount 6) ne
This he pires plain Examples OS, in ReserenCe
ro che Circle, chus.
Pet
t
cle, Wrtiole Diamerer is
e is siren any POInE; aSD, D, D
80. trom which chie P’expendicular D A, is lec Fail
DC
A:
AC
y, DF = B: Then chc
7 = V V, axd draroine
OF a
Non is b bE GreateF Fhan 2 y, the Fangene must
be dravn comards B, it lels rowards L, il ic bc
Fi B, in ~
co the Diameter
Equarion vill
The Tat
equal c0 ic, ic wilt be P’arallel 10E B, 25 Was laic
Letthere De anocher Semicircle inverred; as
ND D; che Poines oF whole Periphery are reter.
red ro che Riste Line BB, parallet and = e0 etie
Diameret
Let NV BbC called d; and all chings elle as be-
I VD - 2a V, Wrhich beins managed accord.
ins ro his Rules, vou will tavea=
2a
Nou since V here is supposedro be always less
thian d; iF b be preater Fhan 2 y, then the TanGeHE
mule de ca cowaras P; il equal, ll b ve
lleItOBB; is less, changino iIl etie Siens, CHB
Tangent must be dravn rowards B, a5by Rule 4.
Fore; then ene LGuaton WIH d
A. Hche A Airmative Ouaticilies are Breatex Chat
5, and 3. Buc there could be no Tangene dravn,