1000000030

710

n v

" e,l in.! tI,c

"i,,"e'~,

o: che

f,~ ,,,n

a' ,I,e m

.hll~

"~,e.1S

nf ei,des are

e1,c

r~ " lrcs

of Ihei,

;j' c~mfe.

" cite!!

/ruj/I,III

;

thi.'lh':C:

tt)

CIInllHilt:

die c.,.tl tot of

!!4ch, ..

rt'nce~,

" as if

W.IS

C)'I",Jer uf ch.•"" " " e1"",,,,e'" ; anJ 'u

"11," che rommlln IY.'y ufe,1

,,, ir,"cr! f..,

me.fu

" glVt'

thtir

('1111

as Ih

cOr!rf\t

ul Ihe:

\'C.'lIeJ . From

Ihe

"rin}~

IlIund lIIll1H'r,

clllr~ls

II1l1cil

flUI"

dll

rulr Th.

101.\1 CunlCIH,

l llllpllrd

¡n

11m

01.1011" ',

I h~y IlIh!l r,,~t

c,dl

nn'

(0111111

pHI

uf lht

cm~\lllIlacnl'e

lhe

X"I•

•• luetdl,vcly Ihc

oll",l)Lr~

.hid,

e~~ftl,

eh<CIr( ul" a· .. whirl, " hy che", reek ..o.d ,he li.leof a f'l'lHe, wh le

r.:.s

tll ..

cund pllIlJ tv IUlJ(c

nll,.m

dlAilICltlS,

r.¡ch:u

are..

I.'q".4¡ !eI,lhe

.Ilt',(

die

lefliun

lI¡e

tiC' ;

ol'l.:n as

there~rl! in"¡lt's

it\ lhl·"lwudc u!

t'le

/,,,}fulJI

IhC'C!prl' they

Iqll;\1('

dH~p'1I 11

itnd

tlu:r¡

mlllflrly hy

,. to which

l>c1unc~51

bt'J!inning with

tllI:

uPl'crnluft ;

ti ..:

It'Il~l h

(Ir

rll~

Irc!,·.

'(or.llII~

thcl r

mClhilJ•

~o.I",

ellIS '" IIIOl '

t.,k"I.IIc a e.l,je 1,,,

eI,~

ven·:I. by .. Ihe

c;,~

of ,he 1,II,·x.'OIl'lc ,"ould lIe(oo'p'IIcd

'5'1.

wl,ieh ie rr .,.ldy

31'1'"lrS

hOI&l n"" h I'qll'"

.oy

r."hic; ll~te

001)'.

einl< eooe"i"cd 'o ie. uy I.,k'ng e,eher ,h" d, Y o, wce

' 11,,.. f" ""e ei",he, is OI·!,f"rrd. will bee,lily 110,1"

" ;oehe,:

h~\'

,e)! Ir.1

che ",.(,.Ial,,,n or dllp of .. 11""d f",n , ",e p,.e·.I'''g 1" "1,,,10'",,"

1'11"

(,,1,,11,"\

Ihe

vcn~ l,

\\ 111'11 it h.l!'

.Iny

(.I(

hcwo tl",h" r, an·1

IUI1)'

(lf

rOIl,!h

tillllll'r.

m ..

T his ft'eeh"u of

co~'rullo~

eI,e eOOI' 01 of

"jiu",

"1".111

f,om che d, IIlIt'" of ch. klll',n., e e ,,"dd'"

;,!

.. >'1

Tu (,,,.1 e,e Iourocn "f ,n,ip. "'

el"

n"",h "

" heighl . is ex,{t 'o Ih" c,1e ollly \&Ih. n "

I! •

1'"11'00 "of 10los ie w.1I

''''y.

,he 1,,11., \

io~

rul. ,/ e,ulI""""1

•. of a para',ol,( con.l,J;

UJ'

111

fu;hvrlrds ',s,,, '" e",,,· .. given.

~1 "llIpli

Ihr

1",~e1, ."I,he

e l 1.,1., n wIII""

•• 0100 ufe. che Clf·,r i$ nOI ((Iulidt, .,ble. \\' h"o Ihe .. h",·d. b) ch. h,t,,, I'h ,1 e1'e IIt,I' ""1""

'JI.I. IJl o

veflel is

pon ion of

r":te o, hype,b,oI,c elln ,id. e1,e .. f"III' d,e ",,,ill,, p I'e'", ' Ir,III rl" 'k 10 loI,lIIk. a1111 eI,e

" eoneeol by chis

m~e ho.J

is founrl 1& ,hJO che "ulh; .. p",.I"llloy ehe'!'I',IIoIIJIIII',ld. I.,k· n I' JII' e!t< rIJl.! .

•' but "hen it is. ro, eioo uf a fl'here 01' II,heIOIII, the •. bclo'N che k«II.." e" 'he 11,,,1<-,

1'.111

of elo. IIpper d"k

.. eooeen! eon'rueed io eh" maone' excccus the lI u,h . "pl",k , aod u" iJe ,he 1'",d",'I I.y 9'1. ,h_ 'I"""coe

" The dilf.rente o, error is .Iw, y! che f,m,. ;11 Ihe d,f· .. Ih": r',lIIeOl of che

e,,,'oJ~C

,rq"""!.

'1'""

,ule

hll~'

" ferene pares of che f.tnte o, of limilar "n,¡s, wh.n che .. riel' e,nnOl ue aeCllfJ 't . n",

f,"

"ne ,,,l · I,r IIIp,IIIlul

" ahitude of

Ihefrujlum

is r." . o. And wh, o che al,i· ,. eo lerve f"r Ihe o,« I"" "g

e~.!tly

,h.' 1"".1"0 ," 11, r",f

.. elleles

~re

d,lferenl, che elfo' is i" Ihe cril'llCale

ro/,o

,JI (",,,.

Of ehi\ er"

"·.,,1,, \V,II ',lid ",·., c ,n d,c

of che ahieuele. Jf ex.flnefs be ,equirrd, che elfo, ill

"~I e",oi"

uf che I(IIy.,1 A•• I.,"y 111

!i.."""

1'... ,

me~(u,i og

eh:

[rlljlU/ll

of a eonie,1 veffci. "' chis Old"

fll' Ihe )e."

' )/ 1

.. ne" i!

of che eonlcne of aeonefio,ila, 111 Ihe , eO, I,

.. 0 11r allel,o, h..

i,,~

f.,,1 ouel,illp, ..f

\v,:~I" s,

il nlly

.. of ao ahieuue equal eo the height of the

ujl,"..

Jn .' be of ufe '" auJ bri,Oy, eh¡1 ch. l· nl:hlh J",0Y'P"'" ,1

fphe,e. ie is

eylillde, of aui,mele, "od

hei~he

"conlAio! 11 oon,,,,. ,1" ounee

pCllny · \y,i~h, .

an,l

.. equJ leo che

[,,,jiu,,,.

Jo che fphe,olCl and hype,holie .. che penn)' lY,ighl

I:wlIs; d,<I eI,e AvtrJllpn"

~ I

conLid , it is dle Clme

C1S

in a

COne

CtneliucJ

lhe

poulIll

COfllJlr.s

UlIII~e"

tlle

1JI1I.l;c!

!lr,lIm.

and

" nglll.angled t, iangle, contaioeu by che 111'11 Ii:OIiaxes of ..

el", ' "

pouncl, is "fuall)'

r.JI

,,,

el,.

hlln,llCd

.',i~itI.

.. che r,gllre, re, oh'iog about th.Hlide ..I"eh is the le· .. h

comlllollly lupV"fed, ellJl

pouo,¡' .\ v".lul"'"

.. mi.xis of

the(rujlll"'.

.1'e equ,leo 17 pllllllll! Troy . iI'llllll,og e"

~I ,

l·

. .. JoIhe ufu,1 meehodof eompuling a !Ji,le fur

vrf. "'emd'! eXpetlllleOIS, I p,untl AVCIIllli"III'! e'lu,1 e"

.. fel, by fubdufliog f,om che .llOle Cllnleoe d,e numbe, " 14 oUllees Il penny

w,,~III

alltl , (,

~"ins

Trll)'. el""

.. chal . xprelfts che uppe'OIull a,e"

of,eo

tl"',e

~re

.' is. eo 70(0() g,,,ns; alld "" A" "IIII'UII IIuoee;s

17:

inehes in che "PPC'OIOllfrujI,"•• aod af,trw"d! che "gwlIs.

he StOIS T, "y 1'11111,,1 (1I'I,ilh. hy Ihe

fI"""

.. numhers f", ch. ollte'

are~s

f"eeeflively; iel! olll'ioll! .' 1]18. ..

he Ihe f.o,e ,,"1, che

rf<",. h)

(0111

eh~e

Ihe

eOolenl~

alr.gneu Gy lhe "ule, \\ heo

fel\' of ,. ",uoly fupl'"f.J ('10,1 cu , 5

j ,..

'o, , \

~.n~I,'l,

TrIlY. ,,'

.. che oppermofi ind"s are drr. are flJe (u a lillle wo " 75ÓJ g..;IIs.

By , OI 'dO 01 IIJ"'¡,,J, k, r' by Il.e

.. IlIgh, if che .,lfel

n.nd!

on 'u Iclfcr h,f•• b", 100 lo", .' De.n uf (; "t1J

I~u,nuo,~h.

111'1,'. u, 76, ,

" " heoi, n,otls uo

liS

Credle r bafe ; bec.IOI" .heo 0"•• ' g"illl. T I,,'y \&11", hAY. nll'.,III,.,llh. wt'ghes

~1"c,1

•• iod,

,Ir)', fll'

ullple. ieis n"e che

~ 'C; ~t

the IIuJ· .. "'ere feol ' ro," I.oool"n, aft.. eh" 1101011 uf ,he kili,"

" die

,,1'

e!,. "ppcntl,,!I

["jlu""

bm ",he, Ihe .,ea ae "tlOlO',

be ,he lI.o,l"oIs h) "Iuch ,he "'''1:1111 ,n

.. che mi,

I.II

. 01 che "1'1' ,01011 ioeh, Iha! 011 hl

I.c .. Seull.nol Ilu,ul.1 t,e

", ,,Ir.

h", I'''''hllhe I·.ngl,'h .\

' . fllhJu,l ..oI f,olO che 10,,1conecoe. in orJcr

fi uu cI,e .. YerJupoi! p"u"t1 (I'U", .I"'1'.li"", uf 11" 1.'·e,,1

",,~hh)

"untent

111

11115

e.,fe.

wCI~11

it):>o

.IOS,

the

1:101":

l. ,.

rtrJIII:

¡l.

" XIII. Tu

",,,filrt

rouod eimber:

I.el

¡he IOe,o ,i, · ..

c",d,n~

t , wllld,. the S(oe.

I'JIt"

u, Antr.e,.I,,,,·

.. l'"tlllIente h. fouod 'o

f.ce

aod

d.~"tI.l!

of. fooe; .. p"ulI,l. 11,11 he to che ru"ool :\ " .lul""\ as lq

111

H·

" l'l"ue

11 ;

",,,Iuplye1m 1'10". by

ehed~ci",.rI

.07'),577, " The S,,,u T, o)' Jluoc ,0Ul d"I)

1/'

poun.I" ch. p"o,, 1

od ,he

",I",q 1,), che leoceh.

1.<1

Ihe

" 'tAlI .. 2 "",

ls or I

(¡

0'"1"

S, ,,,

' 1101(

, {¡

,11111'<,

"'r ; \

.. (ucum(,",.:nlC:

,llree

3 rc:ec,

JnL!

lhe

It n~lh

1.1

1:,.lId5.

Twcnly

SCulS

uun, , ' m ..

Le . Tu,u

pl.IUh

l ,

.. (tel.

heo 'o ;

X, ?

l X07'),177 X 2.1=101J"

S' ..

h", b, '.,ufe

ufu,1 '" JII.", "n. eo eht f. n" . tI,e

llu.~

llht

II~)U.,II

It el

lhe

Ircc.

1')¡e

IIHln

"I'mn

puunll ls cOOlnll1nl\'

I OUIl\ t'S.

Sir

Jllhn

d.&lutn uf

tI!"

rult

,1',

tll.U

\\licn

lhe

CUCUlllrt:lt:nU'

uf "

IIIH\lHr.

nlJk

t111':

r h'l1

Ilunl"

lU (IJUl.tlO

old 1 :

11';:: IS 1, lhe

,i1 ..

15,O, ; 'J 5,j

11 71),

,UlJ Ihlll

111'=

IHIIII"ls,"