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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 806933011:0671
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CASF HI.
Ds che Proporcion of Solids.
Wrhere che Difterence = X is oiven, And n 25
betore, Wrhich erect perpendicularty ac cicter end
OE Z: Then draw R trom che midale Poinc OF X,
and with ic, 25 a Radius, describe a Semicircle on
the Centre d: SoTall a =I X be che greater Linc
anda che lesser Coush: FOr a  X, mulcipliedby
a= m m = bc. R. C. D.
Fhat is, in otter words, il pon tave THE FX
creams, and che Sum and Difterence oF + PFOPOF.
cionals, sou mas sind che Lerms severally.
PROBL F M H.
To findtvo squares, mhose sum or Difference is sid
Reciprocally proportional to evo siven Squares.
C ASF
8  1. 1 dO lite latile Dale adtel Lte BC, do 310F.
Every Parallelopiped, as a 5, is 10 a Prramid;
Let b ane c DC ie sides ot the Squares siren
and let Sbe equal rorhe sum ot che squares re
quired.
Find a Courct proportional toSB ande; wotrich
suxpose ro be d: Then, by che former Problem
sind 2 Lines reciprocally proporrionable ro b and c,
otose Sum is S: AS suppose che Segmenes s andh,
and draw the Lines a and e, wrhich Mall be the
Sides of the Squares Tought. For sincc S. b: : c. d.
(Or m): Theretore by Similar Frianglcs, 5. a: : c. m.
Wheretore ex equo reciprocally b. a:: e. c. WVhere.
Core cheir Sguares uill be also in che lame Ratio.
P. E. F.
For il von suppole the Alcitude b e, co be divis
ded into any Humber ot equal parts, by Plains
parallel rothe Bale; then because oF the Prramido
bn ekm b, bF DBHIb, _c. beine similar, eH
Balesm n E R and IIBD F, will be in 2 Dupli
care Ratio ot their AItirudes b 8, Db. Llal l
Thele Bales diminist cowards the Veriex l che
Proporrion oF the syuales oF Numbers in Arirhime-
E d che side ot a Square, wotich ie che Disse-
rence ot the Squares required, vere siven; make
25 d. V. : c. f. a Fourch proporrional; and, by che
Former Poblem, Aind 2 Fines reciprocally proporti-
onal tob andc; wrhich suppole ro be s and d -] 5,
Whose Dinterence is d: Then crect fac Righe An
Bles, and on v.) 5, describe a Semi cirele: AIL
tical Progrestion.
Buc ic was proved abore in Numb. 7. OE arith.
merical Proeression, Thar a Rank oF Tuch Ouanci-
cies are Subxriple ro as any, equal rothe prearel
i. e. 10 Tuch as compole, or are the Flements oF the
Parallelopiped: Wheretore che Parallelopipel te
the Prramid, 15 253 101, C ene oet IS LP1
OE che latrer.
And chiis must holc in all Pritms Ot Wolat PiBure
Toever, in P
vich chem.
And (0 allo in che Proporrion oF Cones ro Cylin.
ders; For a Cone being composed ot Ciicles nnole
Peripheries decrease Arichmerically, che Llabes 0
those Circles must be a Ranke ot Secundans, (Ec
cher are asthe Squares oF cheir R acuS) and conte
quey che whole Rank, or che Cone, vllb
Subrriple oF che Cylinder, wtich is d lank Ot a5
mans Ceems equal io the greatcll.
A Cylinder–
Sp.
idu and Cont
and Heiphe, are 253, 2, and T.
xence ro a Pyramid ot the lame Bale
os chetame Bale
chesquares reguiteu.
ahict dravins a and e, cher Mals be the Sides ot