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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 113r, page id 00068194:0225
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+
1
d
b. + c+ d+
+c + d+
1c+
d b. +c + d + f
6- 6. + c. F d +
b -b +c + a+
Hypoth. b,c, d, f. sue areth. Proport,
b +c. + d + f
b. +c  d +f,
+c
: + bed + bc f. + bdfir cdf.
D+C + d Ff
6. +c + d+)
b. + c + d+ f
Ad propos. 19. C AP. V. Alg.. Herig..
quadrato rectangali sub lateribus. Ht... Aggrequ
trem quadrato- quadratorum duorum laterum, excedit
Quadratum aggregati laterum excedit quadratum quadratum differentiae quadratorum eorundem lat erum,
differentiae eorundem laterum, quadraeplo rectangulo
sceb lateribus. St... Aggregatum quadratorum la,
terum excedit quadratum differentice corcndem la
teram, duplo rectangulo sub lateribus.
daplo quadrato rectangali sab lateribus.
Vel.. Qvadratum aggregati laterum excedit qua
draplum rectangulum sub lateribus, quadrato differen
tiae eorundem laterum. It... Aggregatum quadrato
bbbb + 2bbcC L CCCC = = H. bb. FCC
2bbcc
bbbb + CCCC . - - - est aggr. quadr. quadr- b et c
2bbcc
bblb  ZbbCC- L cCcC = = 1. bb a CC
Idem theorema generalius sec concipi potest..- Qva.
rum laterum excedit duplum rectangulum sub latedrutum aggregati duarum similicom potestatum, exce,
ribus, quadrato defferentiae eorundem latercin.
bb + 2bc + CC = - H. b. +C
2bc
bb + CC.. - - - - - est aggreg. quadr.. b es c
22bc
bb 2 2bc + cC = =H. b 2c
Idem theorema generalius sic concipi potest.. Qua
dratcem aggregati duarum quavuncunque homogenea
rum magnetudinuem, excedit quadratum differentice
carundem magnitudinum, quadruplo vectangulo sub
dietis magnitudinibus contento. H... Aggregatum
qua dratoram ducarum quarumvis homogenearum.
magnitudinum excedit quadratum differentiae ea
rendem magnitudinum, duplo vectangclo sub dictis
magnitudinibus contento.
bbdd + 2b cdd + cedd  H. bd + cd
n2bcdd
bbdd + ccdd . . . - . est aggreg. quadr. bd dt cd
2 bcdd
bbddo 2bcdd. + ccdd = H. bd - cd
b4. + 2b2 cd. L c2d2 - -H. b2 + cd
2b2cd
b4 -+ c2d2 .. - . -. est aggr. quadr. b2. es cd
 2 b2cd
b4 = 2b2cd + c2d2 - - B. b2 2 cd
vadratum aggregati duorum quadratorum ex
cedit quadratum differentiae eorcendem quadratori
quadrup
dit quadratum differentiae earandem potestatum, qua
druplâ simili potestate rectangali sub lateribus. Ht
..Aggregatum similicem potestatum duorum laterum
quoramcunque, quarum exponens, est par, excedit quadra
tum differentiae potestatum itidem seinilium eorundem
laterum, quarum exponens est scebduplus exponentis
prioram potestatum, dupla potestate rectunguli sub
lateribus exponentem subduplum exponentis friorum
potestatum vel posteriorum exponenti aequalem habente.
bb + 263C3 + cb = =H. b3 + c3
~2b3C3
b6 + C6.. .. . . - - est aggr. Cc. b esc
2263c3
b6 - 2b3c3 + c6 =  = B. b3- c3
b3c3 =  Cub.. bc
expo- b3 et c3-- est subdupl.. expon - bb es c6
vel.- expo.. Cceb.- est subdufl.. expo.. Cab. Cub.
b8. + 2b4c2 d2 + c4 d 4 - - H. b4 F CZ d2
68-F C4 d 4 -n est aggreg.. quadr.- quadr. b2 e cd
64c2d2 = =H. b2cd
exg0.. b4 e c2 d2.- est subdupl.. ex5o..-
..- - - b8 8 C4a4
264c2d2
26gc2d2
b82 2b4c2d2 + c4d4 = - H. b 4 2 c2d2
vel. =FxPC
quadr.. est subdapl.. expo.. quadr- quadr.