Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 10r
Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.89.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.
The machine reads it as
- (e (6) 10 = -0
- Nam r qu e0 +0 + 0 = 0 (per 1141) jam 0= 0- (per 2. hujas)
- (6be ait +c =
- (6) si a + c = b+ c erit a = b
- (6) Si a = b erit a - c = b -c. s
- Nam a = c = a - C (per 1,2) in qua aequationis
- latere posteriore si pro a, ponas aequalem (ex hyp.) b
- quod licet (per 1, 1) fiet a - c = b = c Z. E. d
- in Lineis si ab aequalibus AC, Bd, subtrahas
- eandem BC, residuae erunt aequales AB, et CD
- (7) si a + C = b + C erit a = b
- Nami quia a + B = b +C (ex hyp) erit (per 6 hujus)
- a + C - C = b + c - c, id est (per 2 hujus) a = b L. E. D
- in Lineis si AB+ BC seu AC aequ. D C+ CB seu DB
- DC 1+ m et sit b= m erit a = l
- panquid al b= aolus ltin C ex hyp, erit a
- 8). +0 = = 0 seu nihil rejert quod nam ipsi o praefigatur signum
- Nam . :0 + 0 = 0 (per I. ) et 0 = 0-0 (per 2 huius)
- ergo fit 0+0 = 0-0. Unde abjiciendo utrobique o
- quod licet per 7. hujus) fiet +0 = -0
- a = 0 = a. seu nihilum nihil subtrahit
- Nam a = 0 = a + 0 (per 8 hujus) et a +0 = a
- Aliter a = 0 = a = 0 + 0 (per 1, 4
- jam -0 +0 = 0 (per Z hujus) ergo a - 0 = a +0
- seu (per 1, 4) a -0 = a
- et b = m erit a - b = (-m
- seu si ab aequalibus afea A) auferas aequalia (b et m) residna (aab, et lum ) erunt aequaliu
- (10) si
- demonstratur eodem modo ut artic. 6. capitis ujui
- praecedentis jam et sit a = l erit b = m
- ( sam ab aequalibus; at
- inferas se
- et
- ualieastm et p= s enit B2 = 61
- ei erit e a = b
- Nam quia a - c = b - c erit (per 2,5)
- 1 ec4
- a - C + C = b - c + C, id est (per 2 hujus) a = b, Z. E. c
- in lineis si EG = FG = HF - FG (id es si EF = HG) erit EG = HF
- (12) Si a - b = L m et sit a = l, erit et b = m
- (12) Si a - b = l - m et sit b = m erit a = l
- Nam quia a b = L m erit (per 2,6)
- (per 2 hujus) a = l. 9Ed
- i Leneis si EG - FG= HK - 1K (id est Et EF = Hi) sitque FG = iK erit EG = HK
- a - b + b = l - m + m Ergo
- (13) e Si a = b erit - a - b
- Nam - a = - a (per 1, 4) Ergo in posteriore
- latere hujus aequationis pro a substituendo aequalem (ex hyp.) b
- quod licet (per 1, 1) fior ex = a = - a fiet - a = - b Q. E. D
- (13) Si a = b - l m et sit a = l erit b = m
- (13) - a = - b erit a = b
- Nam a a = b - b (per 2 hujus) ergo
- 13) Si a = b = l - m et sit d = l erit b = m
- Q. E. d
- ne snsic (per 1, 4) ergo a = 0 = a Q. E. d
- Nam cauferendo utrobique aequalia (per 10 hujus) et
- ex a - b = l- m,
- a et l’ex hyp)
- fist a - b - a = l - m - l id est (per 2 huius)
- sit = b = _ -m. unde (per 5 hujus) fit b = m. Q. E. D
- in Lineis EG- FG = HK - IK (id est EF = HI) et F5 = IK
- et EG = HK ent FG- 1K
- si at b = l+ et b = m
- erit a = l
- = a = - b Ergo + a = + b
- Nam a - a = b - b ergo utrob.que
- anferendo re qualia za et = N
- in Lineis si Ny = RT, et NP =R5
- erit NL - N P = AT - A5, seu pq = 5F
- =a = b - b Ergo +at b
- Nam quia - a = - b ergo addendo
- ntrobique b, fiet b a = -b + b
- (per 2,5) a =b
- =a + b = b + b id est (per 2 hujus
- ergo -g + b = 0 Erge (per 5hujus)
- eris a = b
- X. Ed.
- a = - b. Ergo b - - a
- a a = -b ergo at a - a =
- a + b = 0. Ergo
- d + b( a = (0) - a
Cite
Leibniz-Handschriften zur Mathematik LH 35, 4, 13, fol. 10r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068010:0019?run=73