Nipher—Graphical Algebra. 199 
The difference between these areas y® and 2° or 
y*—«°® may be expressed by dividing by y— 4, and 
multiplying this factor into the terms of the quotient. 
y — 2 =y* (y—a2)+y' a (y—2) 
+ y’ a (y— a2) +y' a (y—2z) 
oe (y—a) +y' a (y—a) 
+ y’ a (y— ax) + ya" (y—z) 
(G2 )e iia iw (4) 
swuet Ge0es sedsaeneEe ings 
—e ar-us S2S8 SESE eueensenee: Sanus eeu reese seuss Eases seaseseees sees seses tore? sapeuvenss sazess 
fesenersee 3 gases seeee ee seezs a bnass sqnesenesa sesesesessssases = 
idue au’? seuuae Sauna Suaes SSGSaSSEES 
$900 S0ucd ESRUs FERe Rees ooeee ee 
2E5 TRCRS RGGE: SEES ceRee Ceeed seas 
tae eee sane! GSGHE SGuas souneeeuns ou 
Sus Suan Guany seses saned seeee coeee 
iss Fors Zou susesasant sosavisees Severs 
Le a tases Srnec aseseseses aoeaen ‘sane, 
Seresses sess iegessnews sass sssts sosssssses ppsssaait tants 
Poot tases cease cases tH oe -- 
'SO4 REUEVGeEes Seeetrenge 
tre 
ee pane lent 3 ooo 
oH mes ses rasenceses 
ES oA We, mer eens wereyes a eras 
pe raeee codes = waese 
‘Ste lawesahens weeen cena 
ett 4 
NSS GSOue Seems aus ueEeS erry 
Poa Poot 
io "ae,* Ass sauee noses fanena gaze sgazesesst Peo 
ae Es ee eee ane: Ee ee moun esess: 
Ee, SSSSSER sozwasccescevaznans tanesanes tones sodas oes Sep eeeeseeeeere serra iis uuysen gets 
Pt titre anes a Sasnecursss ne. sevens Seuneunnna scene Suane © senceseaue rit 
eth ‘Guage sues ni awea: essestensvatsses a daeed conenoas =< 
ges aneuacarst inawe sewes on ieee To SERIE SS wasue 
See seee Ff taae raaws tases cuaees: agnas ree a sasan sisessssase mates 
— ———, SRE RS Foses Geeks Bees oneTS rr iineee 
[Se sedeaaeaaaszeez a 
a degen suns sdsesseess cases ditiiniassnssansstise atts razah 
Sis tunenauast runs Seess Seees ssces seees eases cecee seers seceesesst oH 
ane QUSSUERM Seder tawes ene en eeeee raene w Seaee suues seuss sues 2 ceauue 
‘See sened susas Suounuanns sadae canes Sasee coon case eeeeee ceeeaaeeet sua —= 
gan 00Gen naam cedee sanes geass REERS TESS Bees Sees sees ow 
‘SES GRRE SERE! ceees cee a Tite2 Cee Boe 
S86 Gewee seem eewwe s FESRS Ce we SSee6 oe 
ane 22998 Sena: BeEaE Sena cones SeSes anesa are 
Sag TESOR Gteer seacecaans sues SaMas Sones a: 
Bas SASSUNGGE CO200 Rogue seaee aeens arene e a 
tr om oe SSSee Sees = a cusenagase & 
So S0Rne aeeut: Sunes Canes SESEeSeeee seeee eee Seuss cases sane eee 
ORS cheGe wuee: spanen oH sense seeee races tot SSnGtegane basse eaeuens H 
Sau seeSSSS00( sa0uS guess reuse cnawa cae . i 4 
ame anBN seases aves Sasacecesua sunes — 5 seuee = 1sese8 
(S28 ewnes ewan, seers: S ase? Seas iam owes suseeasges taeuce 
Sasssssssese: sesssewes S inass jones Soenoteess fesse 
Set sense ene sauusse sue HF 2 
eeuvc sums: es: 
Saccuusnsecey 
Sori 
oeumea: 
‘85 Gagan 
ene Mes 
me 
~ a 
sereery 
Scccacuwns eucsdcceus suena saaee sieeyesees ss 
The first four terms may be written 
yxy (y—a) or x (ys —y) 
y X ya (y—x) or y (ya—y sole 
y Xyx(y—a) or y' (ya—y a’) 
y Xa (y—a) or y’ (yv—2") 
These terms represent the areas of four rectangles, 
marked a, b, c and d in Fig. 5. They have a common 
y° 
length 
