aa = 
Sd 
14 
fo, that Dr. Waring abiainee the profef- 
for fhip,becaufe his competitor aid not know 
enouzh about Nothing ! 
Tf I was a friend to perfecution, where 
perions differed from me, in either reli- 
gious or mathematical fubjeéts, I fhould 
not hold out to them,. that they might 
“< Repent of their wicked errors,”’ aficr 
doing penance for “ an z#fite number of 
years; for in fuch cafe IE do not fee of 
what aval! their repentance would be : but 
perhaps No Conjurer withes us to under- 
fiand the term /zfimite, in the fame man- 
ner as the Univerfalifis do the terms ever- 
dafing ‘and eternal; fhould this be his 
meaning, — fhall, in deference to his fupe- 
rior ji udement, farrender the point, and 
regueft him to afcertain the precife dura- 
tion of an ifmiie number of years, that 
thofe who are to do penance, may be made 
acquainted with the exact period when 
they are to begin repenting. 
Before I conclude, I muf add, that if 
Mr. Search fhould, on reconfidering the 
nature of equations, ftill find reafon to 
maintain the opinions he has advanced 1n 
his former letter, I fhall efteem it asa 
favour, if he will prefent us, through the 
medium of the Monthly Magarine, with 
a farther explanation of his ideas : for if 
he be able to demonfirate the fallacy of the 
mede of reafoning now in ufe, and fubtti- 
tute fomething preferable, I fhail with 
alacrity embrace the earlieft opportunity of 
thanking him for his endeavours to ferve 
the {ciences; as fuch conduét will merit 
the acknowledgments of all who are en- 
lifted in the fervice of truth, as well asof, 
fir, Your’s refpecfully, 
O. G. GREGORY, 
Yaxley, Hunts, April 12. 

To the Editor of the Monibly Magazine. 
STR, 
i SEND you inclofed fome papers in the 
Mathematics, which I hope you will 
infert, if confitent with your plan, or 
fufficiently important. Should this De- 
partment be continued, you will proba- 
bly have many communications on the 
fame fubjeét, from 
— £ondon, April, 1796. Bp. CYGNI. 
‘The following problem was propo‘ed in the 
Eady*s Diary for 1758, and two fluxionary 
folutions given to it in the fucceeding Diary. It 
is faid that Mr. O’Cavannah (Mr. Simpfon) 
had given a conftruétion and demonitration from 
geometrical principles, independent of fluxions, 
which was omitted on account cf its length: 
pevhaps his fclution did not‘differ’much from 
the following, which I hope you will infert as 
fon as poffible. 
Mathematical Quefitions. 
[April 
PRosLeEM. 
To draw a light line from the vertex of an _ 
if fofccles, triangular to the bafe, fo that the folid 
under it, and the two fegments, may be the 
greatett poffible. 
Analyfis. Let ABC 
be the CAE D triangle, 
ACBF a circle de- 4 
fcribed round it, and CD 
a perpendicular on the 
baie. Suppofe the line 
SE drawn as required in 
he queftion, fo that CE 
2 AE xX BE is a maxi- 
mum ; and produce CE to meet the circle in F. 
whchi as AEX BE is==CE x EF, CE*x EF 
is a maximum, but EF==CF—CE, therefore 
CH (CE CF—CE?) is likewife a maxi- 
mum ; ands by the property of the circle AC2 
is=CEX CF, CE (AC2—-CE ) is a maxi- 
mum. Upon AC deferibe a femicircle, and 
apply the chord CE equalto CE; join AE. 
and draw EH perpendicular to AC, Thea 
AE? being =AC2—CEz2, CE Xx AE* is a 
maximum, and confequently by Simpion’s Geo. 
metiy, page 208, AH is=2 CH. Hence the 
conttrudtion is manifett. 

Cor.1. The fquare of AC is equal to 3 
CEz. 
Cor. 2. When the f{quare of AC is to the 
{quare of AB as 3 to 8, or in any greater ratio, 
the line required is the eal dicular on AB. 
Cor, 3. If the equal fides be conftant, and 
the bafe vary, the locus-of the pot E wiil be a 
circle, whoie centre is C: alfo the folid under 
AE, BE, and CE, will be conftant. 
B Cyent. 
ene a 
ANSWERS TO THE QUESTIONS PROPOSED 
in No. I. : 
Question L—Anfwered by Mr. Olinthus 
Culbert Gregory. 
The method moft frequently aie for res 
folving queftions of this nature, is.derived from 
confidering the fpecific gravity of air m a me- 
dium fiate, and thence deducing, agreeably to 
the laws of fluids in motion, the force of the 
wind on affumed furfaces, correfponding to dif- - 
ferent velocities. Or, when the force is deter-~ 
mined accurately to any velocity, we may, by 
means of the law given for {mall velocities 
(namely, that the force is as the fquare of the 
velocity, determine the force correfponding to 
ad other: and, by comparing the velocities 
hus determined, with thofe determined by ex- 
aes the general law has been found to 
hold very nearly in all velocities under that of 
50 miles per hour. Whether it holds in cafes 
where the wind is in fwifter motion, is a que 
tion which has not till lately been decifively 
anfwered, viz. in Dr. HuTToN’s Mathematical 
and Philufophical Didtionary :. fee the articles 
WInp, and RESISTANCE of the Ar. 
In a table conftrnéted by Mr. Roufe, and 
communicated to the late Mr. Smeaton, the per~ 
pendicular force on a {guare foot, when the ve+ 
: locity , 
