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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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bola 2 = 10 che Square OE CB, Or C F.
PTo aSCtOr, (OIS ZEO = = G F, and ils
Squate 2 E  Woist Be erelore = 10 
irtich Eguarion seducect, will bC    = 2
Buc by che former Lemma= is equal 10 etic
Sinc oF che double Angle, WHCTeOE S is the
Sinc: Wherefore till be a5 Radius to Sine of
double the Angle F CB, P0 is half the Parame-
tet, co che Llorizontal Ranse or Distance Cought;
and at the sereral Elerarions, the Ranges are 25
the Sines ot che double Angles oE Elevation.
2. L. D.
COROL L. A R Y
Hence il FOIIOMS, That hals ihe Parameter is
ibe ereatest Random; and that happens at
ibe Flevation of 45 Decrees tbe Sine o)
Wwhose double is Radius: Fitenvise that the
Rances equally distant above and belorv 4.
are equalus as are ihe sines of all double Ar-
ches 10 the Sines of their double comple
ments
P R OP. II.
The Altitudes of Projections made with ihe same
Velocity, at several Elevations, are as the Ver
Sed dines os che double aneles os Elevation.
15 c 1s 10 5:: 5013  = 6 B 10
Proposirion 10 = C F; chat is, 25 Radius
iealiotus attet ell eulleo ate Aopocat 10
Clee Lco. Wheccioe inc limes aee aS EnC
dineset ThC Eteration: tirso constat propositro.
 PROP. IV.
Problem. A Projection beins made as pou please.
Bavins the Distance and Altirude, or Descent of
an Object throurh which the Project passes, to
sether with the Ansle os Elevation, mith the
Line of Directien; 10 find the Parameter and
Velocitus that 15 (in L.18. 2.) Bavins ihe Ansll
FG B, GM, and M X.
catice siven, 10L; and as Radiusto l’alt
sent ot L CB, l0 6Ml 1o L. M. Lhen LM
M X in FleigHIS, OF -] MI X in De(CeHES
Ox else MX MI, il the Direction be bc
= BF, andVK = RV = = ihie AIi-
Jour the Florizontal Line, is the Fall in che Time
that the direet linpulse siren in G, ould have
carried che Project frOm C LOL = L Z = CY
Then by realon oF. che Parabola, 25 L X 0
C Y IS 1O C F OF Y X, :: (0 is C L. 10 che
Parameter (OugHE.
Prop: 2. and 4, tind the Lime in Scconds chat=
Bodr Wvould Falt che Space L X, and By thar
diridins che Line CL, che Ouore will be che
Velocitr, or Space mored in a Second (ought,
uotich is alvays a Mean Proporrional between
che Parameter, and 16 Fcer r Inch.
PROP. V.
L. Y. No by che Problem 2. Favins che Parameter, Hlorizoncal
Corexoins Lemma  = r0che Versed Sine ol
che double Angle, and theretore it wilt Be a5 Ra
dius ro Versed Sine ot double che Angle F C B,
(0 an 8th oF the Parameter 1o the heighe or che
Projection WK; and lo chese Hleiglus ac se-
veral Eleracions, are as che laid Versed Sines,
L. D.
COROL L A R Y.
Distance, and Fleisht or Descent os an Object, te
vine CML, M X, and the greatest Random
equat to hals the Parameter; to find the An-
the Horizontal Distance GM = b, the AIII
cude ot che Object M X = h, the Parameter
=P. and Radius = r, and ic Will be 25r 10
in Ascerts
From bence it is plain, ehat ehe preatest AIi- C0 b c0 = = H L, and F BZ in DesCerT
rude of the Perpendieul er Projection is a Ath
os a earameter, or halt ihe greatest Florizon- = L. X, and  = F= pB = C L. 1 = X Z R
tat Ranse; ihe Versed Sine of 130 Degrees,
beins = 2r.
P ROP. HII.
br reaton os che Parab. buc b b- 2
= 61
1. 47. T. Euclid. Wheretore  =  pB =
The Lines C F, or Times os the Flipht of n Pro- b b- - trich Equation rranspoled, is
ject cast vith the same dezree of Velocity at dif-
ferent Elevations, are as the Sines os the Fle-
vations.
b
r,
DF B F pB - bb, dividedt b7 bB
r
Aoci vor: : (015 l.  = C B by che cl (i  - g F p
2. Fhis Liquacion Mews
oa eeleracion, so che Pacanteu le lle
Line C FS Toche Lines eL arc a5 che Sines oF
SOLVT1ON
AS RadtiuS EO SCCaNE OF F CE B, (O CFMI the
20 fuid che reibens et c spulle, by
find the Flevations of the Line of Directions ne-
cessary to hit the siven Objeet; that is, TTa-
Sles FC B.
Texthe FanGeNE OF che Angle CouBHE BC == F