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# Title: Leibniz-Handschriften zur Jurisprudenz LH 2, 5, 2
# Folio 4v, page id 00068407:0008
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datio tum per anticipationem
n
n
primi an aun componitur ex omnibus illis summis et praeterea
ipsa pensione eo anno de 1000 nummis caedua seu perteptibili seu 50
quae est 50. itaque tota prima pensio erit.
50 + scx 50 (3 s0o:os: P, = ( 1100. 125 = 50 (2100. 105 : 1 - (C2. lio0. 105. 3C + 50 ser 6 o8. 105. 1 - p. (100. 105
1- ((21) (100: 105 erit 50+ 500)
t ergo opus est inveniri quantitatem  seu summam terminorum numero
finitorum progressionis Geometricae, quorum primus est 13)100: 105, secundus
vero est 14) 105: 105, ultimus denique (2+ (6)(100: c05. quod semper fieri
(2. 3) 100: 105 -  (2 + 4 + (6))100:105
135100: 105 - (4 100-105
B) 100: 105 - (3 + (5](100: 105
 5: 105 aequ 1 : 21
Ergo tota prima pensio tandem erit
c
a lequ. c+ 5 +g.
Et secunda pensio erit e 21100
50 + 1050 (2+ C 100 : 105 = (2 + (6) 4(7) 1100: 105
Et tertia pensio erit 50 +
aibrc: ersig:: a. P.
Quas aequationes ut resolvamus ideo compendis lausa, seribam
(pro 1050, c. pro (3) 100: 105, d. pro (3+6) 100: 1 0s, e. pro B3 + (6B 100 0r f
Unde patet P et q ers non quidem omnino pro arbitrio posse assumi
alioqui enim et pensio de mille annis solvi posset quantacunque
triennio extinguibilis, sed tamen admodum et infinitis quidem
(2+(6) +)1 100: 105
1 81 eM ess1ovitos 1-. (E) r7) H8) r0B.:105 1- ((8) 16) H 8 sicv. 105
B ((7) (100:105
aequaegu
aqu
G+D
 Ergo ) (6) (100: 105 aequ AFE, seu (5) log. 100 - log. 105 aequ log. A +E
seu (6) aequ log. A+E B: 1og. 100 - log. 105 v
et (7)  qu. log. AFE+F : log. 100 - log. 105
et (8) aequ. log. AEHFAG : log. 100 - log. 105
Est aulam A aequ 13 1002ros aego A- A (5, H
Aaequ. C: 1- g rursus AF aequ Cg   1-g - E- FG
Ergo C aqu cg - E+F1G. 1- g seu CC FFGd
nempe vel erit Caequ = E+ F+G. umque c. sit quantitas positiva
debebrit E+ F + G esse contra hypothesin, ponimus enim p esse
affirmativam et majorem quam 50. Ergo erq erit affirmativa
a multo major quam 50 et, s affirmativa adhuc multo
major superef erpo at Aciamus 129 qu. 0. seu d equ. 1
Auqu. A +E iis Ergo
Unde alterntium faciendum est,
seu C_=9 aequ - E +F+G 1-9 vel erit 1-g equ. 00
modis posse variari. Notandum autem si p. q.r crescant, debere
necessario etiam crescere ipsas qua numeros 6.7. 8. Patet
esse differentias seriei
12+(6))100: 105
A(C6) 108: 105
 raG+e
aequari ptar sive)
cf - ce9
etiam quantitates p- 50: f1050, et 4.50; 1050, et s- 50: 1050
vel potepit scuibi
EFF+Ged
aqor bo Ast daequ
-Br nC: 1-D
1050 (2+ C1 + (7) (100. 105 - (2 + (51 + (7) + (3)) 100. 105 quae debet
aureis asignam
et ita porro, (si plures reperiantur,
cujus termini sunt: (3(100:105
et ita porro.
A.
aequ
dd et arhrcedaequ. aalatare
a   jam eaqu.
Ero atb
ontp Za r eca B , rm  - (61 +C7I H8) ( 100. 105
vot e+ que equ.  
.
a.
( + 1050 B) 100. 105 - (2t C)I1VO,1Oqu debet aequari. p
1(5) Hr ,8100. 10s
1 - (10. ( +) (200: 105
5 1. ( (1
pro ((6) + (71 4(8) (100: 10), g. et
-d
vel ex, 50,  1100. 105 , B 1n0: 1v5 + 5 1100. 005 HC + 12+ (0) 100: 105 -. seu 50 + 50C = seu quia (21 aequ. (1) () )
1 - ((2 11) 100: 105
potest eritque 0 aequ
en O aequ.
2a, 105a
5
u
nempe (3 (100: 105