# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068194:0666 # Permalink to this reading: https://leibnizlegible.com/page/00068194:0666?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1 # Folio 332v, page id 00068194:0666 # Scan: The same scan is also registered as fol. 333r; its text is given once, here. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=666 # Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000666.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 199 lines, status machine # Lines: 199 recognised, mean confidence 0.86 # 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. 1. 1. 1 i Membrum 1. 1. 2. 2 Membuum 1 3 4 4 sentum 1 4 4 1 4 6 Progressio ipsorum G capuet C D EFG 2. 2. 2. 3 54 23 3 4 82 5 =2 2 4 4 5 3 15 2 2 55 6 4 24 3 4 4 3 4 5 6 6 36 3 5 6 7 8 56 3 6 7 8 10 80 4 5 3. 8 12 966 4 6 +B 9 13 135 6 4 = 9 10 18 180 55 8 9 16 144 5 6 9 10 20 200 5 = 10 11 24 264 5 8 11 12 24 3367 quune s entaum noitud es ex capul 3 3= 3 3 2519 ,33 35 285, 447 6458193 4 4 400 v ne eu 2424 24 3 5 8 60. 1400. 230 4 3518, 512D, 6 6 10 11 25 275 850 6 7 11 12 30 360 6 8 12 13 35 455 10 6 9 13 14 40 560 17 43 81 131 193 3 3 4 223 520 975. + b. 2499) c6. 64 (3 5 5 129 151 1∞ 206 20 63 144 26 38 50 62 secer pd l 36 i p 1 3 4 6 Bi get 121 + 1592B 66 272. 320. 368 (ia 6. 7 4848 1d 6 8 36 9 em Caps 6B B ii 45495 6 99 12 54 64515 2 7 18 11 48 528,9224 5 8 9 12 60 72 Z 910 13 72 9 3 5+ o 7 7 10 ii 14 84 1= 38 10 13 75 9752852 8 9 11 14 3 10 12 15 205 1260315 30 3 11 13 16 1201920 2+8 99 12 15 108 162059625 9 10 13 16 126 20c6 9 i 14 17 144 2448 9 12 c5 18 162 2916 3 77 10 20 14 v7 147 2499. deapite in apit) 3 7 8 20 2i 15 18 ib8 202 3 5 5 7 8 10 3C 2 4 4 6 6 8 10- 32 2 4 6 6 8 10 12 + 7 6 9 11 13 5 6 5 5 7 7 10 12 5 6 7 8 11 13 2 5 7 7 9 12 14 70 2 3 8 y 10 13 15 6 6 8 8 12 14 72 10 6 8 8 10 14 16 90 5 9 8 ii 15. 17 108 12 16 20 14 36 72 120 180 25. 36 48 60 72 48 144 320 600 1008 96 176 280 400 quartum CagutE 8 8 B 12 64 768 13 vo 1040 310 10 14 96 2 8 i i 9 10 ii 5 4 3 in B 6 6 10 io i2 5 7 10 ii 13 8 10 12 14 14 100 ib 144 17 168 ig isis 4 8 8 i i 14 i8 196 4 2 8 n i2 18 ig 224 4 = 9 n 13 46 20 252 4 2 10 i 14 1Y 21 280 140040040 224 19 06 20 230455 2856 g 4102 48 3528 2856 5.880340 8 9 i2 13, vy 21 288 6048 s 10 i2 35117 272 525. 900i M3 48 243 768 1875 28881) 45 195 525 1107 80 252 324 M aequ. 33 Ad, Ad progressionem perfectam opus quatuor triangulis in Equolibet memoro quatuoem quinque nembris in quolibet capite Et denique sex capitibus pro rtoto calculo seuuddum caput D E FG Martii. 1678. 2 2 3 4 5 5 7 2 2 4 + 6 6 8 2 2 5 4 7 7 9 6 7 9 11 40 13 15 94 104 128 9 9 10 14 18 22 320 20400564 libet capite 2 8 i 12 15 19 23 352 8096 cuiglibet caepitus, sive transitus de capite in capul (G) 4 4 a 4 (F 50 24 98 122 Laqu. aptus. Pdsito q. ese smrimumA. cauitis 6 5 8 ) 11 6 7 8 9 12 12 8 9 9 2 0 10 13 15 2a 48) 37 10 10 13 17 20 210. 420 5t 9224 rogressio puimorum G. F. E. in qu seu transitus seu inteminist 2 4 4. 72852 26503 22 4 8 8 12 12 16 20 256 5120 1 (3 7 9 c0 12 18 19 189 3591567 26, 08 5 6 p 1505 b st A numeri ordine combina item excessus duorum quorum libet frianguli laterum in B compre heusorum supratertium B. latera omnimo Triangulorum in numeris possibilia exceptis illis, qua pameris imparibus con sant, ut 1. 1. 1. 3. quel is enim duplicentur tans etiam sumantur eorum dupla, . 4. 4 vel 4.6. 8 euudra 15. vel 1 postea inventum quotiens ri quadratumarea triangul quaesi umma ipsorum numerorum sub A vel dimidia summ comprehensolum productum ex tribus numeris A productum ex C quadratum area i ensinti tianteie dratarum arearum se G. diffecentiae du 455bro26 3 v 1 1 17 160 13 B 14 20 294 Optima via est per logerithmos numerorum sub A et quam logarit huri invicem addantur somadin n os quaternani restat erit Logarithum areae Triars Iucehit 388 erentiae ie loganthu vero t