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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 806933011:0669
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the Came Third Numbers, are in the Came PFOPOF)
And ris cerrain, ince Z: A:: X: B, bY che
Supposition, and al0Z: Z: : A: B. bY Aernate
Proxorrion: Z and A together will be i0 A, 25 X
and B cogether are tO B. That IS,
Z F A : A .. + 1 D. D. L. C. D.
:
11. le vou compare che Anrecedems vich che
Difterences betireen them and their Conse-
quents, anocher Species oE Proportion ariles
ivtrich is called Conversion of Proporrion: And is
chus exprett.
12
:: 8
L.A :: 2. 2L
Which is very plain from che Consideration oF che
Figure; for no doubr che whole Circle Z is 10 its
4 (0iZ. Z A) 25 the Wwhole lesser Cirele X is t0
(ertrichis = B.)
22 3
12: IE when Z. A:: X. B, Vou compare e
Conseguents A and B wich cvo ocher Ouantiries
(0 a5 ro make rro Rons of Proportionals, Candine
chuS. A, d : : B. Y
Then will Z be 10 d:: 25 Z: L, wtich is
anorter Species ot Proportion, called Proporrion bu
Equalisy, Ox ex aequo ordinata: And Follos from
this Figure verr plaintr, for no doube the wrtole
Circle Z is Eo its Z, Wrhich is gor d:: 28 the whole
Circle X is eO its 2 Which iS L. OF 6.
13. IFZ DC taken as Otren a5 LL, ex. 1. 3 L al
3X, vou may conclude, ThacZ: Z :: 3Z: 3X.
OF 25 10Z 10 10 Z; Or al(0 25 12 =Z, 1O 12 =Z
And (0 on in Wwhacloerer Proporrion the evo MaG
nicudes Z and X are multiplied, (0 chey are mul.
riplied equallr, ox thac rou rakce one 25 olten a5
ron take che ocher. For then there ill be che
Tame Proportion betveen the Magnicudes hus e
quallr Mulciplied, as there was berweenthesimple
Masniiudes, betore such Multiplications.
Number is just as much encreased by Mulciplicarin
on, ex diministed by Divilion, as rhie ortier is.
And chese Magnitudes thus equally mulciplied,
are called, Equi Mulciples, oF che smple Nagni-
tudes Z and X: Hlence ve Cay, thar P. qui Multi-
ples are in thelame Proporrion a5 such simple Mag-
nicudes, our of wrhich ther are compounded.
24. IF Z be divided in the lame manner 25 ZiS;
and ex. gr. Vou cake a Fourth part ot Z, and the
like os X; or he renth, or ariy ocher parr ot L
and the Pame of Z: Then will Thele PAFES DC PFO
portional ro their Wholes, Z: Z:: +Z (OF Z,Z)
 Or = X. AII which is selF evident.
15. A Proportion is Paid to be Compounded OE 0-
ther PropOrrionS, Wrhen che KXPOnenE OF THaE, IS
made b7 che Nulciplicarion oF the PXPONenES OE
Thele, one inco anocher. Thus, che Compound os
the Treble and Double, (evhole FZponenrs are z and
2) is che Treble of the Double, (rtole Exponent is
3 X 2;) chac is, eic Sexcuple (Decaule 3X 2 = 6
Which is manifestly a W ork oF Mulciplication.
16. The Products, Ox the Quorients OF any L Wvo
duacicies or Wumibers Mulciplied or Divided by
tion a5 che Numbers ere betore they vere MuIZ
uplied, et toracu.
E. or. 1. L et 8 and r2, be MpICd 68. 43
then Will 8: 12.. 32. 40.
2. Tec 8 and 12, be la by 4;  vile
8: 12 : = 2 : 3.
The reason os whieh is very plain; vecaule onc
portional.
LR OBL E M 5
Eo Euo Lines A and B, 10 find D a Thirc Pro
Make any Riohe lined Anole, 25 0 a e. Then Pet
OA in ic a d = A, and a b = B. Sec oH al(O B a-
sain fcom d ro e; then join b and d, and r0 b d
dram a Parallel chro che Poince, (0 Mall b0bertie
Line Coughic FOF, A. B: : B. D, by 2e6 Euolid.
dThrec siven Lines, AB and C; 10 find a Fourtta
Provortionat D.
aatC al) Lgle do ace3 then trom a; tatic
ab =  and b 0 = B, and a d = C, joyn b d.
and chro c dra a Paralset ro b d: (0 Mall de b0
che Line Coueht: FOr A. B: : C. D. 2 e6 FV
at