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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 806933011:0501
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MEAN Morion of the Sun, in che OId AArO. ( he CtC oF a Semi cirele, ard then erect rhe
nomr, is che Distance (accounced on in che F. Line P perpendicular co che Fwo siren Lines,
eliprick, trom che Beginnins oF Aries) oFche sun ac eler Point os Onion: L Cay, che line L iS che
Fron che Line oF his Mean Motion. Sec Line Mean Proportional (OusA.
of the suns Mean Motion.
MEAN Or Midale Proportional, between any
cvo Lines or Numbers, is chac wtrich hach che
Came Proportion eo a chird Term char che firA
Lhus B is a mean Proporrional becween 2 and
32, Decause 2: 8:: 8 32. And the chree Num- extract che Square RoOr oF che Product: OE
bees in ehis Case are rhns expressed 2. 8. 32:: Wvtrich see more under Lorarithms, and che r se
Thac is, Tvo, Fishr, and Thiry cwo, are in of Losarichms, Numb. 1L aFid 12.
Continual Proportion; For the lame Proportion is
conctiued from che Midele or Second Perm 10
ehe Lhird, 25 was becveen che First and Se-
cond. Pheretore ris the very Came chins a5 it
che middle Term had Been pur donn ewice. This Famous Problem (Which is the same 2e
NTon because when Four Numbers are Propor- the Duplication of ihe Cube) may be relolvec
rional che Rectangle oF rhe midale Ferms is and demonstrared by means of the Conchoid ot
equal to chac oE rhe Exrreams, ic must be (0 Nicomedes; and vould be Geometrical, it chab
here: Buc here che rvo midale Terims beins rvere a Geomerrical Curre.
che lame Number, cher will makce a Square;
(0 Thac wrhen Phrec Numbers arc in continuat
Proxortion, the Square ot che midale Term is
equal ro the Rectangle of the ExrreamS; and
Etiac midele Term is called a Mean Proportionat
becwech the ocher tvo.
EROPOSFZFON.
The Perpendicular (a d ) is a Mean Propor.
sional betuveen the Scements oF che Hyporhe-
Bears 1O ic
nute (b d and c d.
For 3. L.. L.  8) e Last Proposiion.
Lo find a Mean PFOPOral betmeen any
Mascipir che Numbers ineo one anocher, and
Fo find Lvo Mean Proporrionals betmeen
Evo Civen Lines, AB and BC.
Lno Lrumborsus
Join ehe siren Lines AB and BC rogettret
ac Rishr Aneles, and bissect cach in chie Poines
D and R: Complear che Rectansle A L B C
and atair L. D eill ic meer wich C B produceo
10 S. Then Wwill S B = A L OE r0 BC
From P. let Fall a Perpendiculat, Wrtich produce
EIIL
F be coual ro A B, WCM will cuc oA
ThC PATE PF. Dat ce LO, ale PataI
1O ic CFI. Then (by Cor. 2. Prop. 2. OF ch
Cmmus chroushiche Legs oF the Angle R C L
ataW che Lichr Linc LHIE, (0 chac LTK b0
escat ittad ae it e  it
TR
dc; and chere
Fore che Square oF a d is equal ro cheRectans
betireen b d and d c.
For the Frianeles c d a and a d b, beins sim
Tat, CWs bC 25
da: db, and co
ceues D d a = D b de
PROBL F H.
Io find a Mean Proporrional to Tno Civen
Lines, A and B.
Le ic cill ic meec wica B A allo producec
in M. S0 wil C K and A ML bC thC ZWO
Mean Proportionals CougHE.
DF. 1 1L(- LL11
L. ec M A bC calld b. LC Or AB = eb anc
BC = c. Then because ot che Similar Pri-
ansleS M AL. and L CR
AM. L C Oc AB.: AL eBC.K
cb
c.
COr CC
Wherctore Cc =CKE. AIIOM A. AD:: SC. CK
.- :: 2C. Cc.
(Because it rou halre one Consequent, rou
must double che ocher Antecedent.) And
SC. CR:: FHI. HK (because C HI is pa
rallel cOSF) Wheretore MA. AD:: LHI. HIK
EL L 1 equat 1O AD OF Z Cb (25 Was taker
chac conore Lle; ate hC Poinc et Bcetion l or b. And conseguemiy MD = FH (Eor bort
Put A and B both into onc Linc, thenbissect abore) Wrheretore FHI must be equal to MI L