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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 343v, page id 00068196:0682
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Productum ex Xx abatac in ex +mxtan aequatii debet quadrato ad usum Tecragonisticum
Sit  Xx+bX + ac =00D et Axt mxtan  D28 tipt Lxnrburac, aermut ac = 0
facimus X= (, 2 + 1t6 + 148 + s DZ nott  +130rh6 + vosq6, + 2 C  rotg rro  go sq 16ol 4 1906
22 6och + br0 1y +63016
e O= 510 sq + fro su +. 53016
BC = 100r 2 20B +2) 6= ∞ +31 N= 400 + 4 2 =  oDV + 001
nn- h4 +26 124 (+ 29 1h5 (a2 q 146
bx = bse + b -. + b..
Habemus literas 10, 20, 30  1, 2, 31i n0, 19, 2H, 5 10, 0, 530; 40, ocv 11, 001
in summa literas  19
aquaues seop, prumal. bblu
aberuus
9paratitias ad
1 limatculi th
00D Eususq e msa eqs 13 5o. co1ro f hb sn songo h GS pra B, r0, e   10. 00d
520. 520 130 3 .. 520. S. 230 2
pro 0, 10, 20, 30; 510, 520, 530; 40, 000
325027 siaso1o
32. 530 78 Bos3o t.. 51. 530 130 8. . 530. 520. 2308..
2hamenteeste srgob. . (1510. 8o2go2, ..  2 3u po17ot . . ( pro e, 11 21, 319 610, 5B 630, 41. 001
2. s1o. Sgp. 19 l7 2. 520. sto. 1406. . 2. 520. 5301204.. 2. 50.530 10t..
2 5v sp 2e  su 7 . . 2. 810 530. 4 . . l 2. 520510 7 ..
610,620, 630.
i Ad OOG pro irrationali it 3 ob v, fit , 3s3o +2. 40 Hb =. 10. 120. 510 + 20. 128. 520 + 30.120. sy0 +2. 7021D. 510 5)at 2. 30170 520. 170 , 00B. sior eo
Eodem modo coincidentiabuatur axt HXtan, et D9G.
pro irrationali eti4 obv 120= 20 +2. ∞0+ AB 3. 20, 24g., 1. (.  . 10 510, 20 (. si0 vuip (1D aor, 5i . s3o . 7. 20. 510. 530
sin 120 = D 2. 30+ 2o
2. 10+2. 40 = 2. 10, 130, 510.520 = 10. 230.510 -20. 230.526- 30. 2385, 1 -2. 005. 530. 52,: . 10. 510. 530
 Ex amobus posterioribus valoribus insius o  130 = tE  Msso = 2 2o 3o. Aru. so +   B  asiB 3 a 138  d    0
pro irrationali 1t2 obv 1252
Seu 18. t20
a
aaoer
22. 1042. 40 + 2. 000. 570.530 (910 270. 510 + 20. 2. 12o +30230. 57D1. 2,20. 520 (579 5 110 o. u  3t  ) (  1B VaHLC530
1302 +2. 40 + 2. 40 - 2. 000. 540 530 (- 2. 20. 230 310. 52d, P210. 510626)
o l. rao F 1, 000. 520. Ggu + 19, B0. B250 nome 105IS,  10. 310t 2OSIO 3053D)Pi amas g0. 210 Sar
fiet
 t. 40 210SOZ 4 o 1 90. 520530 r
quos duos valores ipsia 130 ae quando inter se
-21 +2. 40. 2. 20s +4. 0oe 20521350 na  o  Wost dr305o +2  250. 
+2. 3052. 90. 210 sie. Ssu - 4. vo se stoisu s  946.38. 238. 513. 5,  vniresi
=1.10-290. 42 00o. 5 20. 530. 18. 5167205 5a3 +290. 
do
2oge seige - 20. 528
+4. 10. 20. 510 4 4.o. 40. 510 - 4. 00o 310. 2530, = 520, 10. 51a1 30 51du 3S
+ 2 20 +240 - R oe 10.5
 5ro-4. L 45 152P, 185320.3130
vio 2. 40 + 5. 000. 51050, 15 1, 10 s 120 5id 30yse
+2. 20 +2. 40 = 2.B00. 510. 530, - 2. 10. 510.520, 10. 510 + 10. 510 - 30. 530
-2.10 - 2. 46 + 2.000. 520. 572, = 2. 205243 p10. 51d + 20. 32 - 30 530
+2. 2 + 2. 40 = 2000. 5I0. SIB, 2. 18. 510. 530, 10. 510 - 20, 520 4 30. 54
L. 10. j19) 520, 10go (po gui o 11e
onmodi +oofeso rronrosio i
=210-2. 40 4 20000. G203 30, 1d. 5d4 40. 2. 184 538 +30 (39+ 182. 510 H 7B. 30. 5t0. 130 F. 2s1o. 20.30. 510. 520. 530
  .on0. 510. 120, a 10. 510 4 0. 310 to  . 510.
+4. 1020 520. seo,
= 4. 10. 40. 510.520,
74. 10. 000. 510. 516. 530,)
(4 10. 20. 520. 520,
+4. 20. 40. 520.5201
= 4. 20. ∞0. 528. 530)
= X 10, 30.510. 5309.
- 4. 10. 40. 510. 530
( 4. 10. 000. 510, 140, 5303)
F 2. 10
+ 2.40
 = 2. 00, 520. 530
1. 18 sie _ naste  Hosi
 trose miniotusi ex di
seubreviu
eno i B. 10. 900. 515.: 520. 530.c.
+2. 30-2. 40 + 2   13, 2. 10, 510, 520 +2. 10+2. 40 - 2000. 320.530 2. 20. 510. 520 10. 510 +20.520 -30. 53
2.30- 240 + 3 2.10. 310.530 H   210 +2 - rm. 1B,30 13413. 20 gyt 3051
8. 10,000. 510. 520.530
30. 51 2 ,6. 5 7 328. 510
d l + decies 1020.30.7M 350
in summa
aequationes
F 3. 1030. 519. 530
20.30. 5V. 530
+20. 381616. 510
130. 5d( + 18. 29. 51. 510
Crom 52o, 20. 51d -  3id, +2 10. . Su. Sod
38S B. Eiroabis reluum eon nescit
(vono ud  so o nes oron to st
(4. 1030. 220. 510. 550  (on Wex 10. 319 (130. 53d
+(.520 1840. 30. 510. 530
438. 530 4+18. 20.517.520
10. 26. 310. Se
=20.30, 526, 536
420. 30. 626. 530
+10. 510 - 18. 30. 515. 530
- 10. 30, 510.538
= 10. 510220,526
+Lecies 10. 20. 30. 510. 520. 530
uos ut his calau it bay tia h itbea si hilese odem modo
) P10. 518) - 13. 30. 510. 51 (24)
20. 5105 - 10. 36. 1d. 538 = 230