# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0684
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0684?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 806933011:0684
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=684
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000684.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
# Lines: 64 recognised, mean confidence 0.85
# 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.

adine in ihe Square A B C D, the Difference be
eweon the Sides and Diaxonal = 6, or a, t0 finc
eho Side os che squace.
Then x - a = A C the Diax Mal.
Bur(By 47 c. Y Fucl.) AC 9: = 2 A D 93 OF EO 2 X X.
That IS X =  2 X a = a a = 2 X X
PR OBL. F M IH.
and becaule ihe Angle ax the Lop is a Rigti
one, theretore p p == b x, WICH streS d-
nocher mar oF exprestins p P. S0 hal,
Cc
b x and conseguent 0s
Pransposicion.
C = XX  b x. whiich is an Adfected u2.
drarick ot che trst Form. Muscibre,
50-
i == X X - -. b X -
pleacine che Square. Mud,
a-
Caner, V cc +--
by com
. e Lvolurion.
Geometricat Construction
Foin cogerher ac RiehE. anoleS C F = = b and F A
ele B E D, and chrO thC CCnErC CMTAWIHC LMN A
Expunge chen x x on both sides, and ic wilt be
2 X a - aa = X X, and then by Transposition,
X X = 2 a X = a a. Compleat rtie Square.
aud it will bC X X = 2 a x = a a = 2 a a
WheretOrCx = a = V: 2 a e,
And consequentts X = V: 2 a a - a =
Civen one segment os the Base of a RCht- aneled Lr-
angle, as also the Side os the Trianele Adjacent to
the orher Serment os the Dase; tis required tofinc
the rest, and ro form the Triansle.
Suppose it done; and tet Me Desment b. and che Whence dra che rvo L ess B R and E A. S0 is B
Side o, be both knonn ox siren. L. et x, the orher K A che Triangle (ougHE.
Cerche Side Comehr be colled i, dud 6 = a.
C, Then ivich thelauus LMeribe the Cir-
OB, Ereet chen ac D che P’erpendicular D R,
Which Limir, by Describins a Semicircle
on BA
thar Semicirele MaII cur the Perpendicular in the
Poiur K, che Vertex oF chie Priansle required,
WVADRATRE (in Ceomet) is a Curre
Line chus generaced.
Lex there De 2 Radius OF a Cirele, a5 AD, which
imagine ro move on the Cenee A cont ie CI-
cumterence of che Ouadrane D B, and at the same
time lec the side OF the Square C D move equaliy
donnvards, Pothac che Radius A D and che side
Oche Square CD, may come tothe Line A B 1O
gecher. Or ler therighe Line D A, and che Oua
deantat Ark D B, be borh dirided ineo a lite Num-
Det oF equal ParIS, as in this Cale chez are each
into 8. And ro the Dirisions oF che Ouadrant let
25 ulans Radii be drawn trom the Cenere A, and
chrouch che Dirisions in AD a5 mans Parallels 10
CD, loe chen il a Curve Line be dcaron neactys
Hlere cherelore, lille L. 1 hupposed 10Be a 1r
Perpendicular.
connecline
Seoment oF che Bale, De Coughe; Which is all
is necessary ro solve che Problem.