# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0306
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0306?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 806933011:0306
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=306
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000306.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 122 lines, status machine
# Lines: 122 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.

tet oF ihc Lpieycle 10 che Centers oF the Worta,
and orhe Lccentricke
2. When chere is an intermixture oF Ouantile.
EOVA TIONosthe Orbit, is che Came wich the knovn and untenonn, in anr Equation, let all ehe
Total Prostapheresis Ox Lquation Total.
EODALION, in Alscbra, is a murual com
Parins oF evo equal Thinss oFditterent denomina
riOnS; 2535. = 36 d. 10 CFOWNS = 2 l. 105. =
505. = 600 d. = 2400 FarhineS, (9c. a = b-
du 36 =
50c.
The Ferms os an Equarion, are che severat Onan
riries ox Parrs of wtich any lquarion is composed
untnovn Ouanciries (bY Transpolicion) Oc Made
1o possels ony one side ot rhe Equarion, and all the
Knorn ones another.
Transposirion is alvays done by purtine cheduan-
tiey over roche ocher side wich a concrary sien ce
wtrat ic had betore. The Demonstrarion ot whict
Rule dexends on charAxiom, Thac il to or trom
Equals vou add or lubrract Equal, he SumS Ox
connected roserher by the Sions-I and - A5Remainders willbe equal.
in ehis Equation a = b ) c. The TermS are
2, b, and c, where ris suppoled chat some Ouan-
Thus, suppose a = 34 = 60, Then a = 34- 1.
60
94. Or it a -1 b
ciry reprelenced by a, is equal 10 che summ oF b (chen a = e = c - 1 d. IF 4 a = 300 = 3bb. ]
and c, or ro b andc addedtosether.
4c - 4 5, chen 4 a = 300 -] 3bb-)
Wtienerer any Ouection or Problem is proxosed IF36- 44 = 4 = 60, then a = 140.
in Alsebra, e alvays suppole the chins soughr or
requirea, r0 be bnonn or done: And then by put
ting ehe Letter a, or some other Vovel (manv use
phe last Lecters oF the AIphabet Z, X, 3) FOr thC un
Z. FEThC hiphest Pover Ox Species ot che n-
Hnonn Ouantier be mulciplied into any known
Ouancier or Ouanciries, ler che wrhole be dirided
knon Cuantiir, or For che Thins Couche, and by such knoun Ouanciis or Ouanrities.
Consonants for wharever is Knomn ox siven, in Or
der ro distinguiss one trom che orher. The Oue-
Rion or Problem is first chrouxhly considered, and
Thus, Is 5 a a = 30000, a a = 30000
then duls staced, and aster this JudicionAr com- (IFb a -)  d a = 100, then a =, 100
pared, transformed and raried, by Addition, Sub.
40- 48
sraction, Mulciplication, Division, Fxiraction oF IE d ee = a de = Z, chene c- F de = 3
ROOrS, (90. accotdins a5 che narure sF che Thins.
and the Rules oF Art direct; eill ae last che Ouan
ciry sovelt, Or at least seme Porver ot il, becomes
equal eo lome knonn or siven Ouancier, and s0 is
it seltos consequence discorered.
Afcer a Ouection is duly Cared, tis proper t0
consider arhecher it De subject ro any Limitations
OrnOL. Towhich end, the Wricers oF AIgCBE
Bire chesc general Rules.
Y. HEthe Onantiries (Oughr Or requir d are more
than the number otrhe siren Equations, the due.
stion is capable of innumerable AnSIVerS. SeC R er
ser S Algebra, P. 301. Vol. 1.
2. Dur il che siron quarions, independane one
upon anocher, are just as mans as the uanciries
Souste, chenchie Ouection hach onty onc certain ane
determinable nUIBCTOF ANLNCTS.
IFche Duanciries Soushe er required, are less in
number chan the siron Rguations, che Orection
=6000
This is called Lometimes Depression, aud by Vieca
Parabolismus.
4. TE 2I che knoun Onanrities happen 10 be
mulciplied into any desree of the untnovn onc;
ler ali be brouphe down (by Dirision) cothe lowest
degree chereot char can bC.
AS Il aaaa=  baca = ZZaa chen by Dirision
OF all by aa, aa - b
IE aa =)  ab = ac = ad  fa, then a -  - b - c
d - Fby Division; and a = d - b-
by Fransposirion.
c.
IF ea ] - 90 - - 70 = 13 c- 1 - 34 0 = 10 e, ther
vist c -  9 - 7 = 15 - 1 34 = 10 by Divi
SiOn.
And e - 2 = 39, theretore by Transpolion.
 = 37. This Rule is chac wrhich Vieta CallS Hy-
pobibasmus.
5. IF anY One Member OF the Lquation bC 2
is perimore limited, and is fometimes discorerable lSurd RoOr, aH must be raised up co char Pover
tobe impossiblero be resolved, by reason oF such) and thenche Equation continued.
Equarions beins inconsistene wwich each orher.
Equations, in order to be Resolved, must Airst
be prepared and reduced; which may be done by
chefollonins Rules.
T. IF the OVaHEIEY COUGHE, OE aNY PANE OF DC-
srec oFic be in Fractions, let all De reduced to one
common Denominarion, and then omirting the
Denominators, let che Equarion be continued in
Thus, iE V: b a  - b = c, chen bY Transpo.
sition V: a b = c = b, and by chis Rule C0-
2 b0 -]  b b = a b; and by Ruse the 3d, a =
C c = 2 bc - b
EOTATTON (Annuat) oE ehe mean Morion ot
chesun and MOOn, and oF the MoonS Aposce and
Nodes.
The annual Equation OF che meau Morion ol
the Numerators oniy. v. 8r.   d = 100 chc Sun, dexends uxon che Fccentricier oF che
= B. Then siA a 1 b. 1 cd
D VDGA PAE Y =
1b L cd = cB. Oeit a = b = 2 a c
L B, mulciply all by d, and it ilt Atand ehus a d
 aB = d b. Or it a
25 = 3 bb 1 c = 5. mulcipis all by 4. etien 4 a
Farchs Orbit roundhim; and i5 16 E= such parts
Ot which rhe mean Distance becreen ehe Sun and
the Farch is 1000: From Whence, by some, tis
called che
Equation oF the Cenrer; and ehis when greareA,
1 deg. 56, 2011. Thesrearest Aniual
Equation oF che MoOnS mean Notion iS FYI
401 OFIES ApOgCe 20 and OF its FTode 9. 301
300 = 3bb- 4c- 48. This is called by And chese + Arnual F. quations are alvars murual
Vieca, isomeria, anid b7 oihiers conversion.
Is proporrienable c0 ore arocher. 30 chac vetaen