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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 806933011:0481
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buc a very (inall Distance From cach other:
To find any Number of mean Proportionals bermixt Then imagine a Curre Line deawn chrougt
any tuo Numbers.
all che Extremities oE chese parallel Lines, 25
eou deha, and chis is called the Lozarith-
Fake the Disserence oF the Locarithms OF che micat Line
trvo giren Numbers, which diride by a Tum-
IF chis Figure vere drann on a verr larse
ber more by one than che Numbex OF MeanS Table, and ith all requisire Exactnels, cactr
desired; and chis Logarichmick Ouorient added Part, AB, BC, (9c. mighe be divided nOL
torhe Locarithm of che least, gires the Locarichm
OnlY InEO An 1OO OF 1OOO, BUIE CVeN InEO 10000,
ot che first mean nexr ic; and chen added ro che  100000 equal Parts, and more. So haL AB
last Sum, Ands the nexF, (9C.
beins 10000O, AC ould bC 200000; AD
As suppose ic vere required t0 sind 3 mean 300000, 9c. as must alwars be in an Arictne.
Proxortionals berween 4 and 64; che Lozarithm rick PFOSreNION.
OF 4, 150. 602060; 0f 64, i5 1. 806180; Their
TheLine Pe beins supposed eo contain 10000
Difference, r. 204+20, dirided by 4, (1. c. 3-] 1) Parrs, lec us imagine chrough cach ot chole Di-
sires 0.301030; Which added eo che Locarithm visions a Parallel co be drann eo che Line AP
OF 4, makes 0. 903090, the Losarithm oE B, che currins che Curre in (0 many Points, v. gr. let
first mean; and again, added co rhe last Sum, the Line io be dravn chrough the Dirision 9900
Sires T. 204120, the Losarithm oF 16; and 2- oE the Line Fe, and wrhich curs che Curre in
Bain added, sires che Losarithm oF 32: Which che Point o. Let chere be allo supposed. the
are the threc Means berwixt 4 and 64.
Parallel O0, cuttins the Line A P. in che Divi-
TOGARTTEMICK-Line of Pardie, iS a Sion 399563: Then any one may Hnon thaE
Curre which discorers perfectiy all the Myste
ries of the Locarithms, wich sereral orher very
399563 is che Lozarithm oF che Number 9900.
In like manner, if S u passed chroush che Divi
excellent Properries and Vses; and is thus deli- sion 9000 oF the Line Fe, the Line Vu Were
neaced.
drann curtins AF. in 395424, then vould haE
Tet the Righr Line AP be dirided into the Line u V bC The Locarithm OF 900O, COC.
equat ParS AB, BC; CD, DF, C9C. From tnC
Sochac by chis means a Table ot Losarithms
Points A, B, C, D, P, (90. Let che Lines A a, From + t0 20000 may casili be made; and Far-
Bb, Cc, D d, and P e, be drann all perpen- cher, by producins the Line AP
dicular 10 AF, and consequemis parallel r0 onc
another:
Note, T0 obtain aIl the LOsarithusS FFOM L 1O
10000, twill be enough to seck the Locarithms
From 1000 10 10000; that is Charins drann
che Parallel d+) 10 cake ehe Lozarirhms oF all
che Dirisions From +toe; which Locarithms are
aI concaincd between F and D: For by this vou
Wvill have the Locarithms OF aII the Parrs thaL
are between s and F, and whole Locarithms lic
berreen D and A. For Fxample: Since O0 is
9900 Parrs, and ies Logarithm 399563, the Pame
Number may be caken For che Losarithm oF 990.
wrhichis NVn; 25 alto oE che Number Xy 99
chanoino onty the Ars Figure 3. Becaule, ac
cordins ro che Composicion oF chis Linc, OP
Or TY y oustc e0 bc equal 1O F D OFD C; 25
anr one mas casils prore. S0 chat O N OrN)
will contain 100000; and because A O id
399563, Tubstractins ON 100000, there wilt
rest 199563 FOr Ay. And after che same man-
ner, havins Ay 395424 For the Locarithm ol
Vu, irhich is9000; rou mar have al(0 09542
Cor che Losarithm of X x, Which is 9: O
195424 FOr thC Locarithm OF 90; OF 295424
FOT ehe Locarithm Ot900.
HI this may be reduced co Practice FOr C al
uotrac ve have here explained, is susticient ro sain
Let each oF the equal ParIS, E D, DC, CB,ihe KnoWledse oF che Nature and Composition
Tho inaced chere will noc arise Cuch Adran
between
And let them all be in a Geometrical Progrel-
FOn : 25, let A a bC L, Bb 1O, CC1OO, D d
1003, F e 20000, (90. Then Mall wre havecvo
Prosrestions oF Lines, Arichmerical and Ceome- cularion, writhout actually dramins chese Fi
in Arichmerical Progression, Ox 25 1, 2, 3, 4,5, (90. For by che Rules oF common Arichmerick, we
and (o do represent the Locarithms, to Which may find out FF, the mean Proporrional BerWeer
correspond
E9c. be dirided equally again in F, C, HI; and ot ihe Locarithms.
dec the ParallelS Ff, C 5, (c. bC drawn, and
De Mean Proxortionals Berween the Collaterat cage For makino Lorariihms by this Oblerra-
ones: chacis, EC: Ff:: Ff: Dd:: Dd: 68, (90. rion, a5 ic may ac firtt Sishr Coem 10 promile,
dramn trom che midele of each Subdirision and 10000, Whose Locarichms must be Founc
FF, FD, D6, (90. and (0 on, rill chese paral- also; and buc 900 Betreen 100 and 1000
el Lines sromine verr numerous, have al lalt aut bur 90 bereen 10 and 100, and buc
trical: For the Lines AB, AC, AD, AF, are gures, buc ontr imaginins chem to be dravn.
the Geomerrical Lines A a, Bb, Cc, (96. d0 dD and FF, Or between F f arid F c, EC. BUI
Let there allo be more Mean Proportionals because chere are 9000 Mmbers berween 100C