Full text: A treatise of algebra

we have r+ fizrx r ■ 
— t % x r* — z' 1 ; where 
304 
THE APPLICATION OF ALGEBRA 
thus found being, in like manner, multiplied by 24 
( zz 2 \/ we shall thence get— 18,38506 for an 
other of the roots: whence the third, or remaining root 
will also be known ; for, seeing the equation wants the 
second term, the positive and negative roots do here 
mutually destroy each other; and therefore the remain 
ing root must be — 4,16756, the difference of the two 
former, with a negative sign. 
problem xxxv. 
From a. given circle ABCH it is proposed to cut off a 
segment ABC, such, that a right line DE drawn from the 
middle of the chord, AC, to make a given angle there 
with, shall dir-ide the arch BC of the semi-segment into 
two equal parts, BE and EC. 
Let the chord BC be drawn, and upon the diameter 
HDB let fall the perpendicular EF: put the radius OB 
of the circle = r, and the 
tangent of t|ip given angle 
CDE (answering to that 
radius) — t, "and let OF 
z z;> then will EF zz 
\/rr — zz, and BC ( zz 
2EF) zz 2 \/rr — zz, and 
consequently BD ( zz 
BC 1 _ 4r 5 — 4z* _ 
BH V “ 
B 
2r 
from 
T-\r 2z x r- 
wliich taking BF zzr — z, we have DF _ 
But, by trigonometry, EF : DF :: rad. : tang. DEF, 
that is, y/iFZZTz : 1+ 8 * ' f ~1 :: r : f. Whence 
tWi
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.