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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 232v, page id 00067993:0466
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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