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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 806933011:0584
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t
che Onestion co hare tivo Antivers, and chC ROOrS ( peces inelined contcanely co che Fleracior
chereot ave L  P = V p P -  + PB
From Which L derire che follovine Rule.
Divide halF che Parameter by the Florizoncal
Distance, and Keep the Ouore, viZ.  chen (aY,
As Square of che Distance siven 2o che halt Pa.
ramerer, so hals Parameter .  double Z Deseene
10 che Square OF ihe Secant = P P + 4
+
b
he Fangenre ansiverins t0 chat Secant, Wvill be
l PP, F 4 P  -1 oErr: 50 chen che Sum
and Disterence oEche atorelaid Onore, and chis
Tangent will BC. the ROOES OFThe Rquation, and
the Pangents oF ehe Elerations (OngHE.
Nore here, thac in Delcents, if the TangenE
exceed the Ouore, as it does wvten ph is
more then b b, the Direction of the lorver Flera-
tion ill De belo che Hlorizon, and it p h == bb,
ic must be directed TTorizontal, and the Tan-
Sent oE che uprer Fleration will Be: Nore,
likervise, That it + b b - ] 4 p B in A(CCNES, OF
+bb = 4 p B in DesCentS, De equal EO P p, There
is but one Plerarion thac can hir the Object, and
us Fangentis; and it 4bb -F + p B in A
SCens, anil 4 bb = A p B in DesCenES, do ex
cecd pp Etic Object is Withouethereach OF a PFO-
ject calt wirh chat Velocur, and so chechinsim-
poltible.
From chis Equarion + b b -L = 4 P h = p P arC
derermined the urmost Limirs of che reach ot any
Project, and the Fisure astigned, Wherein are
all the Flcistus uxon cach Florizontal Distance
berond wrtich ic cannor pals; For by Reduction
Ot chac L. quarion, h ill be found equal a P =
in Feighes, and - - = p in DesCentS:
From Whence it sollous, That all che Poinrs B.
are in che Curre ot the Parabola, whose Focus
is the Point trom Whence the Project is cast, and
wrhole Latus Rectum, OE Paramerer ad Axem is
Filcevile From che lame Equation, m2z
ihe least Parameter or Velocier be found capable
10 reachthe Object proposed; For bb = = PP. Y
Ph beins reduced = p will be = sbb.  Bh -= h Follons tro thC L GuaLIOH, Cstat L MLaL M Cd (aY
in AScens, wtich is the FTorizontal RangC AE
Forey Are Deorees of Elerarion that vould just
reach che Objcet and the Flerarion requilire wrill
Be casily had; for diridins che (0 found Semi-
Darameter by che Hlorizoncal Dictance siren b,
The Ouore into Radius wil DC che Tangene ot
the Elevation COnoHE.
This Rule may be ot o0od rise co all Bom-
Barders and Cunners, nor only thac they may
nomore about ic.
To determine the Foree or Velocity of a Projeet in
everys Point os the urd et cferts.
TOCIHS WE HIECaHO OTHeF Praecormtaus BHIL OTI)
the Third Propontion, viz. That ehe Velocity os
ule no more Porder rhan is necessarr, ro cast Falline Bodies, is double to that mhich in the same
cheir Bombs incoche place altiend, bur charcher time vould have described the Space fallen by an e-
MaY MOOE WITH MUCH MOTE CCFFAInEY, FOK thac a
quable Motion: For the Velocier ot a Project, ic
(maIl Frror commirred in che Filerarion oF the componnded oF che constam cquas retcus ol
peice, rill produce no sensible Ditterence in the the Impressed Morion, and che Velociry ot the
Fall ot che Shor: For which Reasons ehe French Fall, under a siven Anele, viz. che Comiplemenc
tincinects in cheis lace Dieses harc uled Morras.(o rhe Elevacion.
ocas
proporcionins cheir Charse oE Porder accordins
eo theDistance of the Object cher incend ro Arike
on chetTorizon.
And ehis is all chat necd co be laid concernine
Ehis Problem, oF Strooring upon Fleighis and De-
(cents. Bur it a Geomerrical Construction there
oF be required, Pchink I have one chatis as ea
he as any thar can be expected, wrhich l deduce
Eeishe (trom  Toresoins Analycical Soluion, viz.
pP-I pB = bb
and ris chis.
a a ne C L a, Fig. 3.
makre D A, D F = p, Or grearest RanS, D
=b che Hlorizontal Distance, D B, DC=
1
the Perpendicular heighe ot the Object; and
dram GB, and matce DP. = thereto: Them
rich che Radius A C and C enere L siveep an
Arch, Wrhich if che ching be possible, will Inrer-
(ectthe Line A D in HI; andthe Line DH beins
laid boch vars trom P, will gire the points R
and L, to wrtich draw the Lines GL, OK:
lar the AIneles L.GD, K G D arethe Elerations
regue IOE MCS  OscLD. A VCIOW MC
FTorico iIs DelCenEDC =DB must be la
From A, (0 aS t0 have A C = AD-) V
Nece litevise, thac if in Descents D H BC
Sreater than F D, and (OR FaII BeloW D, thc
Ansle  CD Mall bethe Deprestion belou che
FOTIZON. Non this Construction (o naturalls
PKO P. VI