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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 806933011:0160
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3 6 b :  66 0 6d0
14 0d.
and cd.
For il y0
che ( a e d (I 0b.
1
(Decaule the Radius IS =r) and conHo L 25 ehe
Aris ot a Conick Section, che Part a c in che Fi
eure will be che Abscissa Or incer ceplC AX pOPer
co che Ordinare be; Wheretore call8, a5 is ulu-
alu che Abscissa x and che Ordinace y, chis gene
ral Properey oF che Cirole will be chus expressed
2. yX- X X=y y; FOr a e Deins X, a d n
2r-x, and chac mulciplied by x SH 2r X XX
extrich must bc equal 10 D b a= y y
e be
It ervo Lines (25 a f and a c) trom a Poine (a)
Wvithour a Cirole be dravn ro ies Circumferende
wichin (a5 e0 C and f,) the Rectangles made by
hose Lines and cheir Fxternal Parrs Malt Be equali
Thac iS, II cab== If a c. Or thole Lines are
to each orher in a Reciprocal Proporrion ot their
Exrermal Pacto, i. c. ac: a5: a0: ab.
Demonstration.
E. Fhe Frianples a eb and ced are similar;
Becaule the Anples ac e are equal, and ac, bc-
cause in che lame Segmene; cheretore che sides
about che equal Hnsles are Proporrional, ul lon
4C: cb: : e0: cd. D. F D.
Sorol. 1. Fencer i ruo Chords eut each ocher,
the Produet made by che mulciplicarion ot lu
Paris ot one Chord, is alvars equalro che
Produe ot rhe Parrs ostheocher:
Phac is, che lP ot chefxireans a 
mean Lerms b cc.
Corolt. II. IF one Chord (a d) be a Diameter,
and the orher (b0) cur ic perpendicularty;
then is be or irs equal ec, a mean Proporii-
onal bermeen che Parrs of rhe Diamerer ae
magine che Lines a b and b d 10
bc drawn, he Triangles x end y will be similar.
and theretore a e: cb:: 0b: c d. And cher
Dravo bs and eo: Then are che Trianples eac
and abf equiangulat, or rhe (f = Lc, being in
ehe lame Scxmene, and a is common
Lheresele a e: ac:: a f: a b, and then al
retharely. a c . af:: ac: ab
Mereto  e X ab (=e ab)) d   C
fac.) R. F. D.
Problem I.
Fo divide he Circumterence oF a Circle inro a.
Ay RAMBeF OE PAFES ROE abOVC 1O.
Suppose che Cirele, A B C D WerE 10 bC di-
The Diamerer AC divides che Circle, inTB
20 L Radius AF being made the Chord.
AB, is the side oF rhe Isexacon inseribed by 15 e4.
Lhe Line B D is the side ot an Equilarerat
Prianple.
ad.
And A F the side oF a Square interi
vided
tvo equal PaPES.
Euclo Theretore
80 ob atao d A dd AA d  C A L AEC
Xo 2 33. L. Heto 1152C
and chis mar be called ihe Generat Propertu et) P. L:, ihc Rietr Line F L, 15 che side ot a Pentai.
he Circle, arisine fron he ate o) the lurve
edl it you cate a hoiarnert  tat Crecte 3t Glndt ad vis uti