# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068255:0164 # Permalink to this reading: https://leibnizlegible.com/page/00068255:0164?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5 # Folio 82v, page id 00068255:0164 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 83r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=164 # Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000164.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine # Lines: 86 recognised, mean confidence 0.81 # Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. # Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text. # Wording rule: say "the machine reads it as …", never "Leibniz wrote". # After the first blank line: the recognised lines in reading order, one per line. q +- V.2 3. 2 = 1 + si 9 parfit 0) par D j impar Kpar, 0 impar 0 par 0 impar jan se ex priori prima regula sugulatim in quaque sede locum constimente erat 9+ = si 4 par tit locus 0, si impar fit 1. ose et di quod cosent it secanda Ex eadem prima rogula fiet = (4) + . Ergo si (4) est par deb ef etiam K siiorum comprobari v st fieri potest a- st l’esse par et contra, quod exdeinium ubi quam tam s quam t, sunt potestates binarii. jau 1- + = ( 2) 9 + 1 v: 2q +Y = 6. 2 (4) + (Y) eC St, et g = S. EHF C + 1 fiit eo stiK + St: 25 + fit. 2 Y r = 5. 2(9))() jam r et ss sunt impares ergo r.() por est par ergo SC. 2K + At: 2p + St. 2- S. 2(4) est par, adeoque totum divisum per st: 2 est par nempe st: 2X + C + 1 - 19). sed P est impar, ut et 1 ergo e+1 est par ergo (et: D) K (9) est par. Ergu vel mbo Y jam esse pares C. 1 divide prius per 5:2 post a t provemens per t perinde est ac si 1-1 divisisses per a jam l- 1 divis. per 5: 2 dat (9) + () sit (9) divis. per + = (X) + B) et fit (X) H(8) + (V) = 4 + = e seu X+ 416 o 410 =. 9 . = H Y K 5: 2 +5 - 1 l - 1 = a q + Y = sA) + no Xk q. () - a5 + C + () r. - 1s) r1 1) it q= K s _ P + 1 et fiet _ KS + o p + ~ + Y = 5 (41) + (1) 2(4) = (Y) = Y ergo (Y) Y necessario est par, divisibilis per 2 2. inde (Y) et Y sunt ejusdem paritatis, id est ambo impares vel ambo pares it fi et sit (Y) Y =f, fiet Entn + 2e A 2n - (9) = f pantas prior hine ejusdem paritatis 29 f1 si parem abjicias vel ad picias, manet formulae X. (9) s 25 + 2 hinc (9) et f sunt s 62. 5f2 quia in venumus pro quaque sde loctu cujusque sedis dete implere possumus hac regula generalt, quod fit locus 14, sin. Impar 1. l: 5 faciendo in integuis 9+ 7 si q sit par Hinc si duae sint sedes 2 25 et 2l, et sit = g+ et L = (9) + . hinc si q et (9) sint ejusdem paritatis consentiant locu, si aubo paria in nihilo; si ambo imparia in unitate; si sint diversae pautalis, ubi tunc ubi pautas L = g+ . 4 4 = K + B, debent K et (9) e jusdem esse paritatis 10, ubi impantas est 25 sit l = 25 25f1+ 37f19+ q = sK F 5 sit vsK + Vp = 5 (9) HY) 25f12+2 7+3. sed hic non 18 seu q) et 7 seu X jusdem paritatis. Ioaque verocrne erratum sit in ratiocinatione quae ejusdem seneroliter etiam additio omnis sic enuntiari posset rgo S puanter pras pro ipsis s, h, K, l n, est pouatura ita loco s erit oc loco est 2hs erit 01 400p seu 0b it n pro 15+2hs+ 4 hks ponetur o1 +0011 4 00001I seu 6021004 loco scchist ahx. 5 r8 hLElS poretur 0r0101 01 a 01O1OI ( 00B 1 paritatis esse volurt sit ∞ = st fit sstK + sts= s(9) + (Y) debet (Y) - r divitibilis esse per 5 = 55 Sr abie, p 11 l= ~ g +r = 5(9) + (Y) et eut stK + +8 - (9) = f An sum 18+2+ cob CStahstahk seghik Isibhtelms = ((osiB)h (ass a (. so Mh (ot )A) K) L(((0) h (osis) kIK ((0(is h (15os) H)K) L)m (CLC, 101) ACot h)K (3 5) M C1sos 2 D) L (( ) )a C. e, Ia LBa B) 000v01L1I10000000020 scunta s secuma e 000000111cct lao14111114C3 ubi justi cage st pro. a mhontus (C in tus iadem alteratio inter 0 et 1 quae supre nili quod illic cccedum coefficientes facile supplentur nam ex 01101001 obfocto tien pb (0s. s) h (so1) h)K (150s) t( 0s 1 5) t) K) L quia in columnae expressione C, sequias pay Lorpri 1 121 2311 (1212311131321H, vel sic, 01 12y, 12, 23, 12,23, 23, 34, commasia orres pon ectu siclvetr er uu agi et qi seu apiat auguitum de sig aut lonin at sinisstis partilium Ut dato loco inveniatur numerus sediem sit locy 39, ause auter 4. esta 3. auser crrbium idee sil +1 (ob ablat 4) et sob abbt 21+ es 1bonie est 1 ipsius o et 1 quaecunque ut per h, repetitio ipsius 2Bsi) seu ipsius 25, per krepelitio ipsius 4E, per repenatio osuls iit hinc + 1.) rest. 22 ausad u g1) ntitr i brpe t utibr 110210 lisi put.