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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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R
3. Fle sewstheNPature, ILe a
Morrar.peices, Wich cheir Complications and
Relarions.
4. FIe considers the Method OF Shoorins Cre-
nadoes out ot Lons Cuns, wirh cheir Manitold.
Dles, (9C.
And nou, verr larely, chac Fxcellent Work
Man NIr. Zohn Romley, Mathemarical Instru
ment Maker under Sc. Dunstans Church in Flcet-
street, hach contrired a Method ot purtins an
dersonsTables uxon a Scale; irhere bnomins
only che urmost Random oF any Cun, rou have
byInspection the upper and lover Flerarions thac
are necessary to chro the Shor to any altigned
Dictance Wirhin che Reach of chePeice, and vicc
versa.
In che Zear 1690, Anderson Publisec ano-
cher BoOK, enticuled, T0 hit a Mark as mell upon
Ascenes and Descents as upon the Plane of the FIo-
rizon: And in che Pretace he cakres norice oF Arch B F, and A the Cenire: Dram the Radir
WhatMIT. BCondell, Mariorre, Perault, and FaL AB, A F, A C, andche Chord B D C, and let
ley trare done in this Matter; and agrees wich Fall B P. Perpenatcular 10 A C, and the Angle
Cavallerius, to besin eo acconne the Curre oF) BC F, will be equal ro che Ansle ABD, and
the Shor ro be a Parabola, just then wtere the the Triansle BC li, will be like co the Trian-
Force leavesthe Thins projected; and the Line sle BD A: WAcretore ic will bC aS ABEOAD,
OF Stior ro that place, he CallS, The Line of Im-
pulse of the Fire, and for easc ot Calculation,
takces ic for a Righe Line: Onty he Cays, That Areh. And 25 A B+0 BD, Potvice BD OFBC
the more irregular the Fipure ot the projected E0 E C, that is as Radiusto Sine, (o trvice thar
Body is, che longer che Line will be, betore il
Passes into its ParabOla.
Fe Laith, ater 15 Tears Experience (in which
are hie Propolicions corcamed in ihe Lemma 10
time hemade lome Thoulands oF Shors) heknousbe proved.
hour ro Aind che Line et Impulse ot Fire, and
HO EO CarEY etre NTatrer on, on che Principles
oF Galilaeus, and can hic a Mark noc only on che
Plane ot ihc Horizon, BUE uxon AICenIS and (The Roromal Distances os Projections made wich
Delcents, accordins to Machemarical Princi-
ples: The Mechod ot which rou hare in tiis
B0Ch.
The Fearned Mr. Talley, in Philoso.
phical Transactions, Number 179
havinz proved the Motion of all Pro
jectiles, 50 be in the Curve of a Para
Bola, Cwhich jou will find under Pro-
jectile) Premises this Lemma.
That the Sine of the Double os ant
Archu is equat to tvice the Sine )
that Arch into its Co sne, divided
by Radius; and the Versed Sine o)
the Double of any Arch is equal to
the Square ofthe Sine thereos, divi
ea by Racire.
Tex the Arch B C (in Fis. Y.) Be double roche
(o BC or trice B DIOBF, thac is ds Radiusto
Cosine, 10 ev, 10 Sine ot the double
Sine to the Versed Sine ot the double Arch;
wrhich trvo Analosies resolred into Equarions.
PROPOSTTTONL
the same Velocity et several Elevations of the
Line of Direction, are as the Sines os the double
Ansles os Flevation.
Let OB (Fis. 2.) che FTorizonial Distance be
che Sine oF cheAnole oF Eleration, FOB
S, IES C0- sinC = c, Radius = r, and chc
Parameret = p, ic will be 250105: 50 Z10
=FB =CC, aul by renten et ie Par.
b0l2