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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 73r, page id 00068255:0145
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id cnfendo aequabiones 4 et s articuli 8, eum aequationibus 7 et 8 arti culi 7. habetur
quaedam depcressio. Nempe multiplicetur aequatio 7 per 4, et 8 per s, fiet ex priori
multiplicatione Sircgl. 31213. 5123,:, 7121, 3. 14213. 7,223 = 51224 (112+ S12) : 712253(32+7,2). Sed hrl: 1113 -521
et ita in pluribus. Ergo fit: Sin13: 71213 = (1mo) 11223 (112+512) : 31223 (3121712). Et ex posteriore mulbiplicatione nempe y8 per
Cq.5. fit 523131. 32313. 51223,:, 723133. 12913. 71223 = 51an 1 (123+525), : 412233 (33+723) unde factis destructionibus
fiet : 52313372313 = (2d0) 112 23 (1234523): 3129 (323+723). Eropa harum aequasionum 1 et2 articuli praesentis, Et
ex aeqque 4 et sarticuli praecedentis fiet 3ng. Im  t) li13 . 31213 = (3tio) Si2e3 (312+ 712) :72 .3 (112 + 112) et
Et eodem modo labebita
12313 = 32913 =51223 (323+713): 71223 (123+523). His igitur quatuor aequationibus continentur inventae jam
10) Tollamus jam earum opelitums  113, S1g, 213, 21B. idem Explicanto pa quae pertinent ad 113
relationes determinatarum. Comprudio pro aeq. 1. serilamus sirs  M. Explicemus
non sertinent; ex equi fiet _  st nSt, :, 3ec. 73= 313. 712
 seu 12 S3a 113 Sisa ex aeq. 1 fit H~ Seza - 13. ra  3rETIZ. NeL 213 112. 7512
Ex aq sit (200) insua- IB 503a L 313. (13.752 313. 72525. Et (x ag. 3. (C
et (3to) _2 Osa + 1c3. Sra= 312 713. 5712 + 313 712 5712 Et ex q. 4fit (4to)123 sisa tnSga 32  5xyf 313 Y. 57
F112. SB = WX3(A1I. Sez = 51223 et ita porto SuE siiis. at . m. jujis a seinvilem agg 3 et  fieta Auferatur etiam aequ. 1. ab aq. 3 fit V13 sua ( m9 (71 Y51)S3 +(BHCE 11)313. 712
s
et auteratur postremo aequ. 2 ab eg. 4 fit 2. U3 523
3 l 73  In 313 EX ex aeq. 2
t (2d0) 123. 3s. siz - 523. 3323. 118 - 303. 11237 13 713A 313. Et ex a42 ft (otro ) 1. 712. 51g + S12 mu s3 B3,2 MM2 1 X2 31, 3
e.772.535B13. Proquibus
A 7 M. VE S1  Sir. 33i2 114 reC m. 313, preoite sit bmo) 15. 13F1. 513 4 13513 + H. 713 L0,
Et ex eg 4 fit (4to) 123. 7123. 51 n a
 3F 2L53 + 13. 313 + 24. 713 =0 et tib) 31. 715 +32. 813 4 53. 313 + 34.713- 0et(4to)9 1tyr 2B3+43831 17B
 jam earum ese liter 113, 513, 313, 7 13. Et ideo in aegq.  123, 4 articuli praecedentis
Ex Ya 1Daexplicemus terminos ubi 13, compeudiole exprimemus as rubi non est 13. fit (1mo)  H12. 513 G2. 1iga =
Z 312 IN 21 M. 13I 4 1312. 312. 73 -1312. 712. 313 et Bdo 1∞ 1235Ba-523. 113a= 132932713-1325. 33. 313
et (3tio) 112. 513 a + G12. 113a =, s3I2 12 Sg. 5712. 317,71345712. 712.313. E(1) 123. 513a 4 523. 1134 =5733,323713+5723. 73,313
Ex 1 et 3 addendo fit 2. 112. 513 d= (1313+ 571 e (2 (+ 13n)7B+ (+ 512 1312)712. 313. Et subtra
fet ((10), 1a 3 fil 2512. 113a = (64) (5712- 1312) 312.713 4 (571241312)712. 313. Et ex 2 ct 4 fi( ad
2.123.513a (5723+1323) 323. 713 4 (5723 - 1323) X23. 313. Et gubtrahendo 2 a 4 fil 2. 523. Ha =(657 23-1323 )123. 713 H(51234323) 725. 313.
ubi unde ex aequis et 7 fit (5712+ 1312). 123. 312. 713 4 (5712- 1312) 123.712. 313 = (9no) 5723 + 1323) 112.323.713+ (5725.1324)112.723. 313
Unde fiet (1b ino) (1323 - 5723) 112. 723  - (1312∞ 5712) 123. 712( 6., ((13224, 5723) 42. 323 - (1312157 12) 123 31 = 713: 313
Et ex ggg.  et 8 6 et 8 fit (712 - 13n) 523. 312. 7(34 (5712F1312) 523.71. 315 (5725, 1323)512. 323. 71345723+ 123)512.723.313
se unde fie (12mo)  (1323+9723) 512. 723 -(1312+5712)523. I,: (1323-5723) e2 313 - (13. 2 5 n2)523312 = 713: 313
iea unde semiliter pro 1312 et semilibus ponendo i habetur 513. 313. Et notaridum ut ex duobus valoribu ipsi rviin
513: 313 fieri novam Ane 2. 13 
1+ sed fortusse brevique propedilicebit, refinendo H3I et similes, nempe ex articuli 9 aequat nbus 1,23, 4
sis set 13a i fima) 1 Et B1. S et S23Ca = r 1325. 113B et tu) Mra = 571 3113 et dem
Ato) 1231hA  5729. 32313. E 9. sed ex articuli 10 aequatio 1,r 3, 4 alies fabrica vimus vable
D  et d destructis jam irrationalibus in Aquatione articuli restat sequeas aequatio
12 2. smepsues Gt4
mm
, 1323. 11213 -51223. 512B3 - (a + b( lan)(a- lisl- n
123. S12. IIZ. 1121y12313. - 123. 322. L12a. 12313. 123137
Btam abL bm = Lametbl = (M2. 523+ 13, 4)  (In 527 11 4. 51) (1. - insns
2 112. 512. 118. 529 4 2. H2. 512. 173. 513 == 2. 112.512. 12313. Ergo coefficiens ipsiu ev
est - 112. SiZ. 11213, 12313 et coefficiens ipsius ZZ est - 125. 5233 12313. 11213
ipsius vZ duo quae per L conpanximus, sunt 10213o 12313. 11225
jam in coefficiente
Ex reliquis tubus nemeris
doefficientis il si22(II2. 512. S1323I + 123. 523: 512131 + 113. 513 512281). quae explicando
de bos ae dad
pro quibus substituendo valores, ex aequationibus 4 et S articuli 6, et aeque 1. et 2 articulia 7, prodibit aequatio (M. 51, S1223. W SEC. SIB231 = u2 H 2h. 5+32(+13. 
ubi interpretanda 3, B. t per a9. 4. 5.6 et quide
+123 52L5I231923, 1133372
L123. 512) 1272515
8. 512. l1213. I122Z V = 523, lgg3. 71223 Z = 312. 3121B. Suues V. + 31. 32313. Si23 Z =)- 112. 1.213 fin2, Vel13. 12sis. In23Z + 3ahug siu, . 79tus. Sicese) et edem modys 123. 523. 51227. (2 131 9
plura inveniamus.
71223 (G SI2) N3. s 3B. 712
 512Vyt _. SBPH + a3. 513 VZ + 100p50ot-er mon =6
=112. S12. H1223,. Iu5. 1113 (B. 1p112. 513. I12rZ. 112. 12313.
+ Ig. S13. 1123. 51213. 31123.
por coefficiente ipsius yv. vel Z
obso vetur infra artia
S12 23 (912(712) Ar. 523, 327 a siZ,
aequationes per A2B et Aimilibus Nam addendo E et 3 fit SiB.
 (1t0) W1 tsyn in (aF
f112. 512. 5123. 11212. 5213VB + 112. 512. 31223. 11323,5B23V.
+n3. 523. 51n3. 1117 51213.
= ab+ am +blm
G(Sie 75IB23.7 4 (5, 23F1325) 313 723
Hini ex aequ. I. fit (imo) nc. 3312. Sih- Si. 3312. 13
pro quibus breviter scribama
13= l p. 113+1V.
ysPh
valorem Y) sic scribertuus, 114(3. 5121) v 4 11323. 5143Z,:, 81223. 5I223. Inde fint
ft 123 hg3mi=Ds
u2. 522 3.. 723 = 13 sn. nq addantur aequ, h et 4 fiet 2. 12 5a = (6to) (572317525) 3C3. 713 + (3, 23, 15 a1) 313 223. Aeferantur etiam
 ex a
Andantur aegu. 1 et 3. firt L. iZ sca (to) (S +Y51) M sA ((5)(2 7612) 313 n Semiliter
Qfiet 17.S1  Ec, Se, ., SIE h segit= 5ri.  lt ex aq. + fiit 1 sp 113. 5e5, , 32g H3. D
= Hll bitur ∞, D- 0, tantum pra 1 vet 5) et compendiose scribe
s
63523. 52312. 513171
(uddatur 11213. 1233. 1225 ot1 12. 92 I4123. 513 f,112. 525
113. 512) VIB. 523129. 51
 i
51223. 112. Si2. 51323I = 112. 517+ 12 5_)NZ. 523
1 ssu). 125. 51 lu e
Su. S12. p2. 52Z. 115. 52t X
12. 5Ic112. 529. 17551
ur. st2. 127. 512. 17
(+ 123. 523. 129. 312. 113. 51
(∞IL. 523. 123. 512. II2. 51
172 . . S2MB. Se
4 123. 52. 112. 58. 115.51
B.Z. 123 513. 525 (112. 175. 5. 513 + AE 13 512 siz s
ot pS. 113. 513. 233  12. 117. 125. 512. 513. 523 eU9  
.f 115.13. 123. 512. 513. 35  113. 125(. 31B. 113 2. 112. 11) 14. 5 512. 57  
127 12. 1132. 512. 523363. 125.113. 532 in 113(123. 512.52
idat msu
an  fi  sii in in sr hnuns ns ffshtun ns saisis
(VS1  1123. 5253, H3 Se5IUI3. s13 L 2 1ssi (L113 +2 1. n3. 523 513
ues su t E r.tet ( 
s i
seu Bsmontus  A3 3t +
is
est aest r
11235
Slohis 1 127