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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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conlequently, rhe Space described by che Fall, i5
hals ivhar vould have been deseribed by an es
qual Morion wich che Velocier BC, in che lame
time; Wheretore ehe Velociry BC ac the end ot
ihe Fall, is doublo ro char Velocity, wrtrich in ehe
Time AB, vould hare described che space fat
len reprelenced by che Triangle A BC, ivich an
equable Morion. d. F. D.
Proposition IV.
Al Bodies on or near the Surface of ihe F arcts
in their fall, descend so, as at the end of the
first Second of Time cheyhave described 16 Feet
one Tnch London Mleasure, and acquired the
Velocitr of 32 Feet 2 Tnohes in a Second.
This is made out from the 25cH Prop. OF rHC 2a
pare OF ME. TIugenius de Porologio Osoillatoria
Wherein he demonstrares che Time ot rhe leaAVI
brations oF a Pendulum, r0 beto the Time oF che
Fall oF a Body, From rhe Fleighe oF halF che lenect
OF che Pendulum, 25 che Circumference oF a Circle
ro ies Diameter: Whence, 25 a Corollary, ic Fol
IOWS, chac as the squares OE The Diameter EO chC
Sgnare oF che Circumference, Po Hals che leneth ot
he Pendulum vibracins Scconds, ro che space de-
Seribed by che fall ot a Body in 2 Second oi Time;
LeF AB reprelent che Time oF the Fall Ot 2 and che lenech oF a Pendulum vibrarins Seconds,
Body, BC pervendicular ro AB the Velocity dc- beins Found 39, 125, Or 8 Inches, the descent in 2
quired ac the end oF rhe lan, aba arau che Line Second will be found by che atorelaid Analoei 16
4 C, ehien diride che Line A Sepleleneins Boor and ore Tnch, and by che lact Prop. ihe Ve-
the Time into 25 masss Cesuas Pales a5 vou locity will be double cherero; and near eo chis ic
pleale, 25 b bbb, MC. a m chele Poinsdram hach been found by several Experiments, wtich
ihe Lines bc, bc, _c. Parallet c0 BC; ris ma- by realon of ihe Sivifeness ot he Fall, cannOE (0
nifest, thac ehe Wrtat Lines b0 reprelent che
several Velociries et che talline Body, in Puch
exactly decermine ies Ouantity.
From chese tour Propositions, all Ouestions con
dene likemise, chac e sre bC is che summ cernins che perpendicular descent of Bodies, arc
OF all ehic Lines b0 catren rogether, wtrich aCCOr-
many; (o chac che drea BC reprelents che
casily Polred, and cither Time, Height, Or Veloci
cies beins attrened, one may readily sind che o.
TheF EIVO.
From them litcewise is che Doctrine oE Projects
suppoled infinicely many; W Su is the deducible, astumins che cuo follovins axioms,
viZ.
P. Thac a Body sec a movins, will move on
continually in a Rishe Line wvich an equable Mori
on, untels lome ocher Force er Impedimene in-
cerrene, Whereby it is accelerated, or retarded,
or deRected.
2. Thac a Body beins agitaced by cuo Motions
ae a time, does by cheir compounded Forces pale
chrough che Came Points, as ic vould do, vere
thetuo Notions divided and acted suecessivelr.
The Learned Mathemarician, MIr. Reil, in his
Examinarion oF Dr. Thomas Burnet S Theory of ehe
Carth, P. 124. proves, Thac che Direction ot
Hleary Bodies is noc tomards rhe Cenere oE the
Parch any evhere, bur ac FhC RGUAEOK. OP ac the
Poles: Flovever chey will be all Perpendicular co
cheir FTorizons, and (o chere can be no Prror in
DESCLLIDLHT, a Term in Geomerry, expres
the torceoine Proposion. Lton u Ln s some Line or Surtace, which by ies Mocion
2DC is hate Mhe. Lacaltelobram ABC ti, aud produces a Planc Ribule, oi a dolid. Dec Dirisenc.
DESICCA.
Proposicion ut
The Spaces described by ihe Fall of a Body, ar
a ibe equares os ehe Times from che besinni
be Fall.
Demonstrarion.
parts OF che Time a5 Ab is ot AB; ic is evi
ding ro che Mechod ot indivisibles, are intinicely
Summ oF all che Velociries, becoeen none and BC
Space descended in chie Time represenced by
; lo char che Spaces delcenceu in ne limes
2B, 1, arc 25 che AreasoF che Linss BC
06, Wie) ec LBTh oE the oco Lna arc
25 IC Squares oF rheir Homolozous sides AD, Ab
chac 1s lolas, ete Les; Whieretore le Delcenes
A B. And by che lame realon the Areas Ab C
will reprelent che Spaces descended in che Times
oE Fallins Bodies are as l o guars et l LC
OE cheir Fall. Q. F. D.
Proposition l.
The Velociey mhich a Descendins Body acquires
in ans space of Time, is double to that, where
nith it vould have moved the Space descendec
s un equable Mocion in chesame time.
Dmonsration.
to BC, and complear che Parallelorram AB C P, Fallings ot che Cround: And trom hense (as he
AL Bevidene chac che Area chereot may reprelent (MheWs, p. 128.) ris plain, che Surtace ot che Larrt
BC vould describe in che Time AB, and che corial Diameter ro is Polar 15 2569210689.
hansle ABC reprelents the Space described by
LHe Fai ot a Body, in che lame rime 10,107
Dram EC parallet t0 A B and AF Parallel levelline oF Lines, and in Andine che risines and
the Space, a Body mored equally wich che Velocity, cannor De exactly Spherical, buc the Parchs liqua-