1000000031

538 / 868

E s p
.,. roTe ¡l,e .n~le B •• n.l (.lIinC pcrprnclieul,rly on 11 D .
1 hi, 1JC'lng cOIHinucd íU a bale Ime. I.~y yllur r\ll~f 00 the
lide o{ die Iqujf,re Al) and O C , and where · thc rul~r cut.
she Icrrettn ,,1 IlDc lH~kc: the pUlnll B ,I.
ThLfl Iltr:j) H ",nJ B draw lioes 10 che poiot of dirbncc:
P. anct (roOl 1 draw a IlOe 10 .he other r OlO{ of (ilft ...ncc G;
and in Ihe locecft'thon o. ,ho(, Jinc., poiots, whl~h
",di C'\'( you ,he fqi..re KLMIl .
Tu do wit huUI Ihe pl an: lel off the diamctcr e"eh way
Irom th~ micid/e pOIlH H, as 10 H anJ 1. HUI in citbcr
care no lioc is 10 be drawn to «he pui ot of Cighl Q.
'Fo diminifh • eire/e. Se< 1;'. ,. CXLIII. fiC · 13 .
Dr.\V a ('1uar. ARCD .bou. i., ond (rom lhe .ngJe.
AD and eH dnw diagonals. dlvld,og Ihe circle loto C'lght
pans,.. and Ihroagh the POiDU whert rhey Cut il OO. draw
Jlne, from ,he bale !loe ptrp~nd ,cula r lO DEF.
Then draw 'wo diagonal. Q3. SP, interfettinc .aeh ~.
ther Ole righr angles in the cenlre G.
H..iog ,ho. dlfpofed ,he pl,n. draw Jine. (rom all .h.
,erpedicu lars to Ihe: poiot of 'fight JI i and where they are
,"«rfellen by ,he doagonah AK . nd BI. puin.. ; ,he
two hU of whieh M .N ~IV' Ihe fquar•. whleh i. ' o be di·
,ided ioto (our by dugOQ1ls, imedcthng eaeh other iD ,be
poin, .P .
In the I.n . '(rom ,he ..Irrmeo o( ,hi. erof•• dra.,
cu••c lioes rhroogh rhe: raid poinu, wh¡ch WIJI give lllt! form
of rhe cirele in ,erlp~fI;o,.
1)[ ¡I" '"'"furo .pon ¡he ha[, ;n perffd/iw, PI. CXLlV.
By ,h. bar. lin••JoM .ny dep,h m'y be given, .nd in .ny
place al plcarure. withoUllhe ule of fquuu; which " a vcry
expeditluus way.
A. (or ex,mple, fuppofe ,he baf. Jine AS. (fi~ . I ) ,he
paint of view A, and lhe points of d,(bncc D E: -Ir now you
would makc a plan of a cube He, drilw ( WO nc.:clJh or dot-.
ted liocI (rom lhe cxtrcm~J Be to (he p010t oC li,:h[ : then
to gn/e fhe breadch. takc (he (.1nH~ mc;:a(ure He. and fel ir
,atf 00 (he .crrcflrialline Cf, and from F d raw a line tO tha
point of nce D; and where tbis lioe mter(c(ts the fidl
~'y C in ,he poin, G, WllJ b. ,h. dlm;nu,ion o( .he pl.n o(
,he euh. Il l/ec.
Ir yuu wCJuld h4lve an ohj.,(l (Jrthcr rowarcfs the pniddle,
1,ke ,he bl • •d ,h. ,nd ,h. d, n.oce ~f .he I,ne••• IK ;
'Ind ro 11",'C lhe d( plh, {el it as you would httl'C u on Ihe
("me: b.. (e :n LM. anct iu wid.h bOl h on LM . Thcn ((om
L and M d~ ..w oc,·uh linea to Ihe puin( uf dtlhn,c D. and
'rom lhe: pOI OIJ NO, where thofe "nes inlerfd} Ihe rav K,
.dril"' par:tllcls 10 lhe lerrcflre. 1 Jlne:, 4lnd you wllI lu vc lhe
fqu .rc QPON.
A(ler lhe: I:\me ,"anner you may r.:t uff Ihe Olhr.r firt e of
1he IquArc ",hieh n,uu l,1 be on che b.. re , d' HII CC IJ hcre
tumft rre:d 10 V. l ·hc pcunl5 ,.., and , .... whu'lt H e only
two (eer f(om Ihe pOlot S, .:frurd a '.'f.:.ry nHrow ficurc In
X, as bClng nCoIr.
O[ ¡h. b"¡e 111,'" . " .1 a jin¿'I, 1'.;,,/ of d,J1,U/«.
Sine!: lh(' tlcplh, "nrt wit.hhs m<Jy Lt had uy the nI ':,n, of
thi, hale line, Ihtre i. no nt'cfl uf ~ny (untwr 1I0II\llc iD
m,¡l.:il"lg (I( '(lu~rCJ; .15 01..11 be." flH~\1 n in tllis cxa1Ilpl,.
slIrJ'IIIrC a roUl of If,.,., Of el,!lIOl'" 15 10 he III ~ dc e'n eael'
fide : on Ihe h .fe lim' IAy c!tLWn ,h II~ (, ;;and tllC cldl.lnre
k'.w( t"n Ihe"" wllh Ihei r url!,cJt h Or J iJnlctcr,. as J\L;C -
VOL. 111. N". 68. ~
e T v R.
1 ~7(
D :, rG ; ,hen J.ying a rulcr (roOl Úl. poin, of d O
to c,",eh o( lhe poinl!! A BCDEFG , ,he inter(l'éllon. ir m;,ke.
on 'he vifu.1 ..y AH .wil! b. ,h. bounJ. o( .be , <k.
lúcd, .I-'Ig. 'l .
T o (el ,hCnl 0JI' on ,h·e olher ~de .pon ,h. ray GH. f.t
one (OOt of th<: eu",pltres IIpon the point o( fhe eye H , an.!
Wilh the other (lrike ;;an areh; Ihe pojO( whercjn Ihll cut,
,he "y GH, wil! b. ,h. eorrefpondlng bound .
Thu. M will b. ,he (ame Wllh N . and fo o( ,he rell;
throuxh whieh urawing pardlich, yvú will h~ve Ihe br~adth••
And as (or ,he lengfh, yoü may m;rke il al pl "';¡(ure :
fet l1ng it off (rol11 A , as (or inll"nee, to p, ano tuen (rofll
P J rawing a line 10 H; and ",here ,his cu. Ihe other
pi4ralldi, b..: formed the pi.n rcquireJ¡ whlch you m Iy
mólkc ei lhcr round or (qude .
r ojind ¡h, heigh¡ and p"pu/ion o[ an) o'id/J, ,Ir ¡h<J AP–
,(ar ah"fu ih, hDrizon ." 11 fupp"frd plan~. See
CXL IV. fig . 3.
F"lt rule your horizon'al line NO. and hX you r poin, of
frghl, ~, al M ; Ihen m~rk. the plf\ce o( your ne.aren PIU",.
by m~ki ng a düt for Ihe b..re or b OllO,". as at A; :lnd aro–
thcr for the rummit or top, ,.. al B : rule a Jine (rom A to
tht pOlot of {ight M, f\nd an'olher from D 10 M, ;tnd 1hefe
two lines will give the height of an, oumbcr of pil"Hs, As
fo«xam ple : Suppof. yuu would h.... ~ plll..., C. ti",
yoor dOl for Ihe b.are, f\nd r:ule ((onl theAee a parJlld Ijn~
'o mee< ,he d•• gon, 1AM .. 1) : ,h.n rule th. pe"l'endleulor
DE '0 ,he dl. gon,l BM: whieh p.rpendleul" i•• he heiglot
of your ligur< reql1ired a' C. Or, if you would pl,ce pIl:
Jaro •• F .nd l . obf.... ,h. m«hod. rulong Ihe p""
ulleJ. FG . nd IK, and .h. ptrpendleul". GH and KL wiU
give thei r heights al the d,llance:s requi(cd,.
' ·0 find ,he di .. metcr or lhicknefs of pdl.. rs ~t any pRni–
e\llar difhnce5, you are O\lro to be guidc..:d by th"l nca rd!
,he . For in(hnee : S uppore your nC'arell pollar All,o
bt..' ten (eet high, and one loot in dl~n\etcr : divide:: it from
top lO uotlom InlO ICA equa', pa'ru . and (ct off one of them
upon .he b.afe of the pillar : then rule a line (ro01 the POi r. l
o( figh, M ' o ,he di.mela P , .nd you ,",11 I..ye ,he Ih ick·
n.r. of .11 you·,. pill". on ,heir .efpcllive p.r,lIel. or •.
Tlu /11",r rul, 1'(fllJpliJ~d ;" ,,"jrrll ,htlfYW the I:or:z,n.
Seo 1'1.1< CXLlV. fiC· 4.
I( you ,"ould know ,he heigh" o( a nll mhrr of fi ~"reo
bclow Ihe rule you r horizontal line QE. , a011 b!'(
your poinl or light, as ,H P : Ihen pl.tce yüur Ill "le: ll tlgure.
or m..,k lhe" dUts (or (he:: he~d ~nd (tef. by Ihe poinu ,\ 2nd
H. ""hieh anfwer. (he fame purpt.f,. ; ~nd rll le (I(,.n Ihefe
ctou tu th e I'0lll( of figlH the JIOC:' AP ind SP : and i( yon
wou lJ hnd (he height of li Jigu re to be dr awn :u t, rule flt m
tlu n('l' ,he par.. llrl ((1 fO Ihe ola,~on4l1 UP. ;nd che: p: rrcn–
de w.J1 gife Ihe hrlght rcquited. The 1.01111:: tllfe~~
tlnns wi ll nh:W Ihe heighl o( • figure at any olher ~hli ,lnce
y" u hHC .. mind tO rl~ee il , aS .H f. ;, ",nJ JII, t-.y
rhe p.fralld~ fJ.', ;1, und mn ; ::tnu (rom eH'h f)( ,hc!t Ihelr
rcfpf'fllve pcrpenJiculu . Xl,. l/, and no : whlch p('rrtn~
o lLul.tf5 \Vdl (h~w th~ ht:ighu of , he: figlll U al / : i, "lid fU .
4. 'Fo drn.u.1 di,.dl vi.",. Se< P CX L 1V. li:: 4.
'ro " 1¡I U(;'! le rhis eX:lOlr1t", furrore \,0L1 \\ ( 1 C' 0 ,fr,,\\' Ihe
¡n(jdc tll .t chu reh, na rcprcrcn1t·" in 1111$ fi~lIle : F"rl t ,¡ ~e
}'OU( J1" ti" n OH lhe poiot A. in lhe centre of lhe h.1r~, l'lle
6 I.;:t l 'e,