Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 58v
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: 0.81.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 63r); this page is its left half.
The machine reads it as
- Quaerruntur numeri triangulares seu summe naturalium; procedetur deinde ad summas sumarum
- Tuanut
- a naturalibus seu triangularium, hoc est ad pyramidates, inde aad triangula atue ita poroo. Porro cuq
- naturales constent ex columnis, quaeque earum summabitus sepuntim, ac tum demuu summationes conjun–
- ergo ad summas prima volumnae quia constat ex meris o et 1; ideo dissimulatis o, per inde ac si non adessent
- pro gressio
- gentur. prima et liolumnam
- quaerentur summae unitatum, id est porentur pro summis harum unitatum exhibebuntur ipsae columrnae numerorum
- porro quia qua
- naturalium qui utique nihil aliud sunt quam summae unitatum. Subsribentur ergo hae summae unitatum sedibis,
- Sed postea in sedibus Nullitatum supplebuntur loci vacua, scribendo tantum otam in columna propime
- Quam maxime compendiosam
- dradice. Hoc jam in nostris naturatium coumnis summandis
- praecedentem, ita absoluto est. Habemus ergo methodum generalem
- actu ipso tentabimus, et indroabimas a priaca. In progressu, o interpolatam exprino per , et 1 interpolatam per,
- col. 1. summatrip (0u 1 11001. 001, 001, (0,1, 001, vo l 1001, 00 11 0011 001, 00t, 00t, 00l e01, out, rex Oot seu 0011 seu
- O,d.1, 1, seu 000b111
- 600011, 1,t
- Colmna (sumanoa X 1 91 0101 91O(0191919101010101V10I0101V10101910101019]010101010101501
- 0b0 00l, 1, 0000 1, 1, 00001, 1,0000 1, 1, 00001, 1, d0001, 10 0000111111
- Ascrpsimus hic interpolationes pro locis vacuis, in sequentibus omittamus, quid semper sabintelligitur nota praecedens inert
- 00 00000,1, 1, 1, 1,1000080B19191 e t, 000 vD0 D, , H1, 000 , , 1,1
- interpolandam; pervodos tamen integras colligemus sub finem cujusque columnae summatrias
- D212
- col. Summunda p01100I10011001100100110011OSII0011OI 00HIOBIIVO11OORIDIDOII jo2
- 10 10 10 10 10 10 10 10 10 10 10 10 10
- 4 9i 1d
- 10 8
- .o 0d 1,I 1,11000 o1 21 1000 01
- 10 B1
- ot 10 01
- anmuda OBODMTOODOMLOOBBTMTLOBBBELHBBBOILLLDBBOIELTOBBBLLLLBDBOIL
- 1010
- eii0
- 1010
- 1010
- 1010
- orio oitu
- 11110
- - 1040Co1
- 0001
- 111
- 1010
- ouo oiio
- 0001
- 0001
- OucO1
- 1110 5000
- 0611
- 081
- 0000
- 016. l16
- QQDDONDOTLILMTISOBODBDOMLMMLLLOOBOBPDBLILIL LOBBBBOSOMMMMII
- -- 01110
- 0010000000001, 1111, 1110
- 10101010
- 01 100110
- 00oui
- 210001,
- (0vo0von0101010
- 0000000000i100i
- 1010101b
- 01100I
- 00011
- 10101010
- 0110011O
- 00011110
- 0000000
- ete
- Ovouv00000001111110000000, IIIMI
- Dovorvovooo
- OlL vivvvr.0000000000001
- 900000DO00D0VONGHITE CCLHVOHBOWOVOOE
- 10vonv1101010 1010101(0)
- vor vovvvm o110o11voooio
- vnov0oov D0011100001110
- 101010 10101010r0
- 01o 010o11Bo
- 00o1OOMI
- ovovoII
- O vor vvor vorr ovver 00090006O0DD0OD(111 119)I F, IILILILII
- ol vovvov0vvv 000000011 1111116
- haec quidem suficiunt ad legen progressus in infinitum cognoscendam.
- da periodi e
- naturalium
- uimanda sit periodiD
- 091010101
- O(2) (2). Erit columnae summatricis primae periodus 0 (22 H). 1. 01
- urad
- im periodus, O(a (, 6.1) 1 (35.) O( . , (a (2
- erit columna usscunque, quae voretur R.
- Usquead R cutside vol, o (). (0 (2t) 1(2-1) 7(27
- Sed a (pt ma inclusive erit in infinitum
- Columnae summatius f, pericdus erit O (2) 1 (35)
- itaque notae cujusqerdi ante (n + 1 mam) columnam summatrilem
- acujusque periodi priorum n columnarum
- erunt semper edem ejusdem multitudinis nempe 2
- et
- Sed notae cujusque periodi post n(mam) columnam, variabunt, et
- si columna sit ab initio fma erunt notae el 35+1
- secundae
- tertiae
- ete usgad
- 0(2+2) 1(2) 1)1(2)
- (n man plitous O ( t )1 (2
- R + , naepesi, OE ut1), (uru codnesit
- post hoc
- (n + 2) mol O (ant 1), (4+2)
- Et ita porro in dafinitum
- puorenita notio communis ex natum lillocavis
- supest jam at suommas columnas summ atrices diversarum summandarum combinemus
- inter se. Hoc modo:
- combinabentur summandae primae summatrix an
- secundae
- da Etia ata sta Cta
- jura
- ada atia ita
- 2da etia ita
- een inn 2daa
- praberea secnda columna ex A addena 3. secmnda Ca B in C; Sunia ex C in D, etita ex C in E, Et ila porro, pront istsae
- Tertiae
- quatae
- A, B, C, d, E etc longe porrigi possunt sic D cum ex quiaque columnis confletur, potest alicubi habere
- requipere adbitionem quinque unitatum, seu 101 ergo 1 dextra scribtur ibi in D, et otrans fertur (sed trustra ) in E,
- 03101
- et ita porri
- col. 1. summatrix ((0:1l0 10
- col. 1. sumatrs
- Ergo Generaliter, si colum
- 0000doII seu OB 18
- sen 0414
- 00D 1 seu 03. 1.
- 0000111Iseu 0914
- opgioou
- O(+ 1)101
- 3(19) 11. Ou B
- 0 (20). NII. Dvor
- 024) 1(8)
- (1612) H. 0r1 (3
- sen O (1 1) , (4 ovovee (1)
- esu B (16+8) 1(8)
- u
- 032) 1(32
- O(2+1) 1()001 (222 1)
- )
Cite
Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 58v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0116?run=74