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The doctrine of projectiles demonstrated and apply'd to all the most useful problems in practical gunnery : to which is added, the description and use of a new mathematical instrument, together with serveral curious properties of projectiles never before publish'd / by William Starrat
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of ProjeBilesi 79

Vitiate, the Sum of the T angents of theAngles at the Base, will still be equalthe Tangent of the Angle ffllAt ,made by the Tangent to the Point Aand its Ordinate, -

| DEMON St RAT ION. '

Let 2 =A Yy and L, r and T, as! before: then, ( per Lemma i.) L: 2 ::

b - z : Y x, = AiT, and {per %)

L i

b Z~- ZZ ^ , ,

2 :- - -. : r : Tj Y A k , equal

y fp _ y 2

-j ; but, because b -2 = Y M ,

7 bz zz ^ ,

o 2 : ----:: r : 7 , Y Mx } equal

j but the Sum of these Tangents; r J> rz rz

I L~ +

1 ) t he Tangent of the Angle M At.

&E.D.COR

r b

T '

equal [per Lem.

L