Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 232v
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One image of two folio pages side by side, registered by the library under both labels (also fol. 231r); this page is its left half.
The machine reads it as
- prop. 62.
- prop. 6B.
- Ila similia: AHE et EZF. Angs XAE = Angula EFZ AE - AX. 1N XE
- ZF = EG E7=GF.
- AEEG= AKEF EN EF momenta tangentium semicomplementi = Cylindro Trilinei ocavicircularis seu ratii demto simu.
- Coroll. Momenta Tanus entasm arcus dimidii seu conchocidis falsae dimidiatae appliculae, in sinus; radio in sinus versosarus dati
- seu quadrabiles
- AEGF= VE EF. cylinder radii in snus complementi (quadrabits) demto cylendro radui in Tanus sinigpt (quadiab)
- Coroll.
- ductii sinuum in laugentis sem oplementi. Is ergo ductus quadiabilis. Hoc proisus coinerdit, prop. 46,
- huni monut radius in sinus, demto radio in tamus. fals dimid. (orim. dupl.)= Momento Tanus falsdemmd. ex basi.
- BEEN GF= KE EG. Seu quadrata sinnum complementi, (prrtiones ppumidis abasiabsissa) dentis momentis Tangentium semigalement
- quadabiibus quae pendent ex q. Ein) Ductui sinuum in sinps versos arcuum complementi, seu in dissenentias suas a radio
- (vroll. Sinus seipsum demto cnu in Tanus. arcus dimid. (quadrab.)
- seu cylindio finuum, demtis finuum quadratis
- Simubus versis (seudifferentis sinuum complementi et ratiorum) e in sinus complementi seu momento sinuum versorum.
- Plasimilia Ca D, et AEH. N
- AE
- HE
- CD HC = CAH EN AH. (cyl. tung. compl. F cyl. tanus) demtus su cantibus in sinus cit, cond.)
- quceitos
- CD HE = AH EN. seu sets dangentes in tangentes complementi, = Momento seurntium quadrabilit. adde 33. 43
- a D HE = EN AE. secaptes complement in sus, tangentes, demtis Tangentibus Sinubus in Tangentes= quadrabiles, seu aequales
- finubus coplamenti in radium. Porro per prop. 32. Sec ypl. in Tanus- rud. in sec. et per prop. 20 Sin. in Tanus. Ctisec. ad. in sec. radin
- Ca- EN
- XF
- LD -
- adde pos. 33
- ED EN. = ad AE. Momenta Tangentium complementi = cylindio secantium complementi (dupl. sect.) - cyl. Sin. = quadili
- KE
- AX. EN
- ista similia. Ca D er AKE.
- CD HE. d = AE CN. Sangentes complementi in Sinus (momenta ex basi sua, si basi quadr applicentur). adde 42. 61. quadrabe
- aDHE = ENH. ExSinus complementi est n media proportionalis s inters sinum, et differentiam secantus compleniu
- e
- ti a simo sive secant compl. in sin,
- demtis quadiatis simum, quadratis simum spl. g Ergo dd ke.
- Da= DC H. (45) quadabasscentum complement, demtis secantibus aplenenti in cinosquadrabilibus) = quadratis tang; coul.
- 82 = D
- quadrabiles. utde duct. 29.
- ota similit: ACd et Ca D.
- D. EN. = AC DC. Seu Momentum serantum complementi (quadrabile, mnssiga. aB Covtl.t. Dud 18) = glindio ansentum s
- ex pasi
- adde duct. 11. 74.
- DCEN = a DAC. (AC = AE) habumus prop. 68
- Da CameN
- dCDG DE. Da Sangens aul in flipsum dento vanus complichoment exlusi = differertiae secantis complementi ed in
- EG
- lasimili Ca D et EGd. Cd.
- differentiam secantis complementi et sinus, seu 9- a, g - b. = g 4 ab - ga- gb. seu quadrata Lo cGplenent
- in itamus - gb = (perpoap. s1. si l. = Cunus gpl.) ideo 1 + ab - ga
- 2DE. seu la = 1b = 95 - af. Et quin per propt. 7 2. la = gf. ideo 1b = af. Tangens ypl. in
- ancta cylindio sinmum minutaque bE. Z conc
- Ergo ga - ab =
- Da EG = DGEN. Secans copl. dento Simui, in radium dento chau = Tonus. compl. in sin compt. demto sin. opt
- 1f. et
- CDEG- Ca
- in sin. compl. . quae post g- b a - b. seu ga + b gb - ba = lf - f. Ergo gb - b =
- smum= radio in sin. compl.
- ga- ab
- id est differentia inter tangentem veram+ faltam, momentum aequatur differentiae inter secantem et radium
- E Fig. 3. HGDS (AC) = D H D. ob Iam HGD. ex vatile
- in Tangentem semiarius minulum disferentia inter sinum Tangenteno semiareus. seu: C - 21, a-f = d a, 1- ba1.
- seu ca + 21f - cf - 3ia. = 2di + ab - db - 2 1a
- a - c f
- purg. et2
- duct.
- Cf = ab. prop. 19.
- Jea -2a1
- ea ral
- popi 18
- dich.
- rgo s
- Ergo ab=2ai, quod absundum errot ergo in cateuto.
- ra - ef + 2if. 2ia = 2 di + ab- db - 2ia
- ab rab- nai
- In endem Fig. 3. Tla similias quanqua non orthgoma. HGD et
- i x
- 21 -b
- Manifestum est omnia exacte
- convenire
- Nam angus GDH = Anus BDZ. et GHd = angalo DBZ. etc. Ergo DB- Rad AB, 9Z. A1
- AB GN= AI HD. Radius in diffcentiam setangentis et tangentis falsae, cangenti fulsae dimidrae in differentiam
- secaulis et radii. ac -2ai = id - ai. Patet ex calculo
- bolae cnvcisa (chorda semisuppe () demtae secente ancus dimtii, in radium (hae quandrabilin)=
- de aixrit
- 2 sec fals = chord. suppl. seca rad = 2 sec fals sec + chord suppl. rad - 2 sec fals rad - chord. supple sei. Et quia
- chord. supplerad, et 2 sec. fals. rad. quadrabilia, ideo 2 sec fals sec - choro suppl. Sec. quadrabile
- Iu fig. 2. expuncto D termino sinus complementi A0. duatur in radium AB perpendi calaris Oco. manitestum est:
- co =
- 9co- AD SIB. Gp ( K Ergo eylinder omni X
- AOYE. Cylinder omnium oco = momento sinuum, ideoque quadrabilis est summa omnium, Ok Oco.
- xetus
- AE. rad.
- AO = AK,
- ytas AyeM. ses
- lugo Dco AH= HE AK. seu tuctu hasperbeolicus in oco. momento Tangenhum periet ergo ext
- prop. 64.
- pronbs
- prs 6d
- prop. 70.
- prop. 69
- prop. 71.
- pp 7E
- praep. 76
- op. 77
- Dco AE =
- ponro
Cite
Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 232v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0466?run=44