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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
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R
pla supereriparciens septimas, Or Subquadrupla super-) Ference. For Wtien etie lonser Radius e l Hlacte
criparriens septimas.
Sind char the First hach as much Creatnels orhmal-
nels, in respect of ehe Second, 25 the Thira hath in f allo Will be come to 5, and will as vellas che
respect of the Fourrh; thole Four Ouantities are ortiet hare delcribed a Semi-cirele: S0 chat as the
called Proporcionals, and aue chus expretlec
8. 2 :: 10. 4
b : : c
d
hat i5, A5 S comeains 2 tour rimes, (0 16 comains
aTour rimes; and cheretore 8 is just as bis in re-
spect oF 2, 25 16 is in respect oF 4.
7. Lte Hon chese Considerations may all the se-
Fore theretore, the Rario berween the First (veral Species oF Proportion De demionstrated troL
Pair, is equal ro the Ratio betreen the ottier Pair ( the Nature oF the Thing. For if
ot Numbers; and consequenelr, chese Four haring
then ther will noc be Proportionals: AS it instead
OF 8 Vou Bould puL9 OF7, letring aIl the rest re
main as chey vere; twill chen be plain, chatc
hach more Magnitude, and 7 hath less in respect
OF 2, WHaII 1O HaLA In TEIBCCL OF 43 FOF 9 COn-
IE Wils cerrainty Pollon by Inversion, Fhat
A: Z.: B. 22.
Thac Is, I Z be a5 bis in respect oF A, 25 Z
tains 2 abore four rimes, and 7 doch not contain ic is in respect of B; then must A DC as licrle in reo
50 otren as Tour rimes; Whereas 26 contains + ex-  spect oF Z, as B is in respect ol X.
actli four cimes: Wheresore these latter NVum-
berS, 9, 2, 16, 4, Or 7, 2, 16, 4, dlC nOE Propor.
tionals. And trrould bc the Pame, it any other
Member oF ihe Arst Pour Numbers had been al
cered; For the Proporrion vould neceslarils be de
Rroyed.
Ox it +2 Contain 3 as OFren a5 B Contains 2, then
Will 3 be contained in 12 a5 oEc a5 2 is concained
in 8.
8. Since Z: A :: X: B, it will follow, by
Alternate Proportion, Chat Z : Z :: A: B3
thatis, Ancecedent is to Anrecedent, a5 Conse
quent is to Consequent: Wrhich is plain, il che
Formet Fisure De ell considered.
For suppose the ourer Cirele Z to be Double,
Triple, Guadruple, 690. oF the inner Circle X5
chen must che Ark A (or any ocher ParF OF IE) BC
Double, Triple, C9c. OF the ANK B, 2 litce ParE OF
the Cirele X. Therctore, Asche Whole is +O the
Whole, (0 che Parrs must be corhe PAHS; that is,
L: Z:: A: B. d. F. D
9. IF Vou compare che Differences (ertrich is
wrhac remains when one is subrracted trom che
orher) Detveen the Anrecedents or d cheir Conse-
quems, With thole Consequents; another Species
OF Proportion ill be found, which is called Pro-
porcion by Division, and ouxhc r0 be chus exprett,
Z = A: A:: Z - B: b.
Non undoubredlr, is trom che wwhole Circle Z.
Vou rake a OHarter, (OF anY OEHeF PATE) 2S A; and
also trom che whole Circle X rou cake a Ouarret,
Oc aur like ParE, as B; che remainine Three quar-
tersol the ourer Circle, must be to iis orher Ouar.
ter A, as theremainins Threc quarrers in the in-
nec Circle ave ro its Ouarrer B. Thatis,
mored orer the Fourch part ot ille Cicle L and
ee Lon cis comelor, chenee LBIK) al
Ldecoe c, ale dla lare soneorer a ua
atant ol its Circle Z; and when eis come tod;
Orcle Z is ro ans Parr ot its Peripherr, Or 25 ic is
cothe Ark A; (0 will che Circle X be ro a like
Parr oF its Peripherr, orto che Ark B. Thac IS,
.2.. 
Z: A:: X: B.
5. IF When Four Onantiries are considered, vou
equal Ratios, are Propornals.
But H ron encreasé or diminist any onc of thele
Four Numbers, the Ratio ill grow unequal, and
6. Elie atinexed Tisure vill serve vers Wen
explain Proportion.
Lec the Radius c C DC supposdro more quile
LOuI On ieS Centre C, rill the Poin c’Ce to
ehie Came Place ic wras ac betore it besatt i ore
etien it char Poine hare clsibeu ne Ccum
at the lame rime, any ocher Poine of che Radius.
25 supposes, Wwiil also have described che Inner
Circle fBGX. Dram che crvo Diamerers IIL,
and ea cntrins each ocher ac Righe Angles in C, guenes rogether, and chen compare the sums wict
ertrich wils diride borh Circles into Four Ouadrants. the Former Consequents; another Species ariles,
erhich che outer Circle (Z,) Bears to its Fourrh Prest,
(Or any ocher) PAIE A; IC LaM MLIC EC MICL
Coiscte C3) beal 10. D, ale vult d lo Circum
2. = A: A:: Z = B: B. Q. F. D.
10. Oris rou acld che Antecedents and Conte
ference ot a Circle, Wile set DCLa LC. eHen
Tis plain trom bence, char che came Proporrion called Proportion by composition; and ris chus ex
Y F A: A: . X. f B. B.