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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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considered.
Breadths.
M Lcienes or Mulcipliers; and cheretore must
makre ehe Products De in the lame Proporrion a5
e Mulciplicand was betore
Thus it che equal Alticude ot any evo Trian-
sles, Parallelopipeds, Cones, 690. De called a and
their unequal Bases b and d: Then by che L3Th ot
placed amons che Elements oE Geometry.
 AS F Y
oles will be to eacH other, 25 3 X 5 (= 15) 15 10 L sna lo LSht Lines, inhose sum and Difference
clans les ate voone aroitter in a llatio compoundee
OF char oF chest SIdes.
portion ro the Ratio of the Sides.
is siven, Reciprocally proportional to o siven
Lines.
Os ihe Proportion os Fieures
I. To find the Provorrion thar one Rectangle
haeti co anortier, boch Lenerh ane Breadihmulebe
For Rectansles are ro cach ocher as the Products
For ihe Bales, or Fleipts, vill severally be com-
ol cheir respective Lenertis mulciplied by their Proporcion (abore) b. d:: 4b. a d.
Thus, is rhere BC EVO RectanSles, ThC FOrMeF OF This Problem Beins OF ConSanE DSC, OupHE tO bC
ohick HaTH IES L CHOEH G InCHCS, TataS, ∞C. arid
iES Brcadch Z TncHeS, TaFaS, OC. aha che lateP
hath its Lensetr 8 Inches, Tards, (9c. and its
Breadth, 4 Tnches, Tards, (90. Thenthe Rectan-
X 8 (= 32) 1. c. 25 15IS 1O 32. So thaF aII R C-
Lec the ero siren Lines beb and c, and lecche
Sum ot the tro Lines Cought bCZ:  Tis required
t0 find a Point wvhere Z mar be (0 divided, 25 chae
 10 
2. Wrhen Rectangles have cheir Sides ProPOrri
onable, ((0 thal a b: ch: : a d : c f) then iS F
Rectangle A, 1o the Rectansu B, in a duplicate Pri
mm
First sindma inean procboat bellcen b andc
let talt m, ana uaW K: Lhen, lCay, a and e are
ine Sesents sequired: LOr a e = m m = b c.
Which ercet perpendiurasss al cicher end ot L
Ora a Parallelto Ly aie Wsere it cues the Circle
ti
FOr the LLaTIO OF A tO B, Lo COMMPOMIdCa Ot the
Ratio oF ab, t0c h, and oF the Ratio oL a d, 10
Bur in this Case a dsWeB, inthe very lame
Ratio a5 a d IS EO e F; and cheretOre che Proxorrion
et A co B beins componnded et those tvo cqual
Rarios, must be duplicare oF the Ratio oF rheir
Sides ro cach ocher; thac is, duplicare oF the Ra-
tio ot ab r0 eh, Or OE a d 10 ef. D F. D,
Flence all lriangles, Parallelograms, Prisms, Pa-
rallelopipeds, Prramids, Cones and Cxlinders are tO
one another respectirely compared, in a Proportion
compounded of that of their Fleishes and Bases.
3. AII Friansles, and Paralleloorams, Pyramids,
Prisins, and Parallelopipeds; al(0 aIl Cones, and
Cylinders, cach kind compared amons themsetres
IF cher hare equal Altitades, are in the Tame PrO.
perrion 25 cheir Bales: IEchey have equal Bales,
are as cheir LdeieHIS.
COROL. L. A R Y.