6 
| 1794. ] Mathematical Queftions and Anfwers. 2, 
In that cafe are given, SF=95 millions of miles, the femidiameter of the earth’s orbit, the angle 
SFC=48°, the greateft elongation, and SCF=2g0°; one fide and the angles of .a right-angled 
plane triangle, to find SC another fide: this is readily difcovered by the well-known theorem, 
that the fides are proportional to the fines of the oppofite angles; for this proportion, when 
wrought, gives rather more than 70 millions of miles for SC, the femidiameter of Venus’s orbit, 
which is very nearly the fame as the diftance of Venus from the fun, determined by Dr. 
Herfchel. 
N.B. The greateft elongation of Venus is, by fome aftronomers, fet down at 47° 48’: if 
this were ufed in the proportion, the difference would not be confiderable, ' 
_ This Queftion was alfo anfwered by Mr. Sohn Haycock. 

The Refalution of an Equation of the Third Order, tranfmitted by Mr, FREND, in his Letter : fee 
: : page 880 of No. XI. 
Let y3--rsy=4; 0. yXy+15==4. Dividers, e -; Copartsy rs, 16. _yis lefs than 
si but greater than a ; let it therefore be uh, 
I 16° - I 
— — 
ft toa pce td 
. ale ie a = 4 nearly. 
4—I5% 
° cee 21.¢¢3,4 nearly, jg Sea 26843-3347 6.K= 3423.0. 0. 4268 1,422 _ 
3-4 p59. early fe 4,269 43-13 375.xX—=3423 aoe ae 
__)001246 
== ) true to fix places. 
9265420 
9001246 From ae 5266668 take x 
The reader, by raifing 15 to the third power, and adding to it 48; then dividing 1,422222 by 
1141, will fee the number of fteps taken to come to this folution, with which he may compare the 
number of fteps taken, according to Cardan’s method, to come to the fame conclufion. 
eS 
Erratum —In Mr. FREN»D’s Letter in No. XI, page 880, for a—d==1 read a—b—=4. 
— EEE 
New MATHEMATICAL QUESTIONS. 

QuEsTION XXV.—By Mr. B. W. 
To find the point P in the circumference of a circle, to which a body would defcend on an in- 
clined plane, from a given point A, in the leaft time poffible. 

aD 
Question XXVI.—By Pf. Cygni. 
Problema ad quod evolvendum Geometre invitantur. 
Invenire lineam curvam CC’C”, in cujus axe ¢ 
AB detur ejufmodi pun¢ctum A, ut, fi ducatur 
inde AC perpendicularis, ad axera, & CA/ tan- 
gens ad C, axtoccurrens in A’, etiamque A’C’ 
perpendicularis ad axem, & C‘A” tangens ad C’, 
axi occurrens in A”, et ita norro, fumma om- 
nium triangulocum ACA’, A’C/A", &c. fit ad 
aream curve ut @ ad f3. 


ERRATA in the SUPPLEMENTARY NuMBER. 
P.gs5, firft line of 3d par. whatever for whenewer. 
957, fourth line, frarticipate for anticipate. 
ibid. laft line of fecond par. dy for to. 
ibid. Jatt line of fourth par. non-refidencies for nonrefitents, 
959, fafth line down fecond column, motions for motives. 
_toid, fame par. four lines from the bottom, s4is for rhe, 
