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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 30r, page id 00068198:0059
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in
sax or
Quaeritur sex unde pendet quade dimensio Linea conicae, et plerarumque
quad incus
hunc multarum cu
DX+C
in
10X + 12 in 50X +52, aequetur quadrato, posito x explicari rationaliter, vel saltem modo
revocabili ad rationalem. Sit  ergo 10xn B y+EE, Boyy. Similiterus
 es sit ergo X= 41y +42,: 3oyy+ y +32  qui valor est revocabilis
ad rationalem et fiat 10X + 12 = B 219+22, : 130yy+ 31GH32 _50X5 = PIIy 162,: L3oyy+319432
et (pers, D) eKCd VIX+I2, 50X152=2y+22, in, 619162, :  (30yy1 31y+32 qui
valor etiam  revocabilis et ad rationalem, et simul ad rationem cum ipsa X (aeq. 2.) correvocabilis ad rationalem
superest ergo ut tantum efficiamus aequationes 3 et 4. explicando X per aeq. 2.
Ex  Ex 3per 2 fit +10. 41 a1yy + 10. 2. 91 42y +10.92 n ( 2I 21yy + 2. 21. 29122. 2
+ 12 30 Hy + 12. 312 +12.32
i
fit 21 Si. aF13o 22= 10gr +n, Z2 et 2. Sioai+n3O, 1042+n = 2. 10. 41.42,: 12  3)
Et similiter
ex q2 61 = 150. 41152. 30 62= 150. 12 +52.32 et 2 150. 45 + 5. 30, 50.92+ 5232 =2. 50. 41. 427 : 52 = 31
Et dups ipsius _3. valores (ex 9 et 12) inter se aequando habebitur 4 (13) in qua sunt
Incognitae 41, 42, 30, 32, ex quibus tamen unam ess mmaratiam jam tum
alsumtsti
patet ex valore ipsius X. Sed et ex tribus reliquis una supl superflua est; 
ob legem homo ut eventus docet,  adeoque si ex quatuor  assumtitiis incognitis
duas faceremus impossi aequales nihilo, v. g. 32 et 41, omnes incognitae evanescerent
compandii causa fiat 0= 10. 4(2+, 12. 30, 10. 42 +12. 32 et D = 50. 41+52. 30, 50. 42 +, 52. 32 et B - 0 1 501
Ergo ex  aeq. 13 fiet , 10-, X D = Bnseu B41. 42 seu 52 O + 12D - 2, 12. 52
B41. 42 seu
52O +12   + 2. 12. 55 0D)+ B 41. 4242. 51.D B. 45. 422 4) 2. 520D. Videamus
2.
au liceat n 41 vel 42 facere = 0 ita enim plurimum contraheretur calculus. Nempesit 42 =0 et
Ex aeq. 17. fevet Gr0 = 12D seu 52. 12. 32. 10. 45 ( 52. 12. 32. 12. 39) = 12. 52. 32. 50. 41 12. f2. 52. 52. 30)
 fieret 52. 10 =12.50. Quod est contra generalitateem datorum.
superest ergo, ut si calculum contrahere volumus faciamus vel 31, vel 30, vel 32Z
Sed tentemus in d, fit 0= 16 41 43 + 10 12 2Bq sed tentemus in 32 et sit 32 0. fiet
en 
O 16, 41 42 +10. 12. 30. 42 et 3 = 50. 58. 41. 42 + 50.52. 30. 42
510 = 5i, (1091 424 2. 10312. 30. 4. 10. 12. 30. 42
1218 = 1, 156. 41 42t 2 58. 52. 30419d +50. st. 30. n
B.n=  41, 92, (10. 5224. 10. 52. 50. 124610. 52. 5012 4. 10. 52. 50. 1 + 50. 1
(4
252. B. 31 D-,- 255. 4142 (18.52. 11. 92118. 12. 52. 30. 427. 10. 1250. 52. 10. 41. 9V- 2. 10. 12. 50. 52. 10. 12 3042412, ∞. 10. 41. 4 150 10170
2M8 qnD - - 2 1 M N, (10 52. 50 11n + 10. 52. 5952301 = 2. 10, 12. 50. 52 50. 41 1 - 2. 10.125052 5052 3a 47 12 50. 50. 41. 3 10. 5 5220. 9V
2.1251O -- 2.1250,  (10. 50. 41 42 16.50.52. 30. 41- 42 + 10. 12.50. 30. 41. 927 10. 12.50. 52 30.9
Hanc ergo aequationem , ex aeq. 19 per 21, 22, 16 explicata factam, ordinando  destructis destruendis
fiet
41,  
ao. 
4. 10.12.50. 58.
4.50. 52. 10. 123.
30, 10, 12. 52
50.52. 12
=a 10.125857
-4. 50. 58. 19. 12
ro 1ese
=2. 10.50. 123.52
quae aequatio dividi potest per 1050, 12, 52, adeoque tandem fiet
30 4 41, 12501 1052 5052 125d, : 10 521501-2 1. 52
Ergo cum 32 fecerimu o, fit inde similiter 30 = d nisi f dato permittant feri 105 e
nisi data cermittant Aeri 1 1on 2 1 5o: n 2. 12. 51 = 0 se 10 - 22.52 70127:52
et ex 10x +1.: 50 152 siet 2. 12 52 - 50. 15 X + 11 52,., 5057 X +52
Sed ita evane scit 41. et fit 30 F 10. 12.52 - 50.52. 12 = 0. Ergo fit vel 30 -0 vel fit
10. 12. 52 - 50. 52. 12 =0 seu 10. 52 - 50 12 =0 quod ipsum non licet,
sed nec licet
facere 30=0. nam si simul 30 et 32  sint 0. tunc ex 9 et 10 vel 31 eliam sult 0.
contra desiderata, vel fiet  31 = - 4. 10. 41. 42: 12. = - 4. 50. 41. 42: 52 et fiet 10. 52 = 12. 50
quod nolumus.
(241
haec aequa
10. 12.52 -5051. 12
250,6.1 52
18.52-12.50-c