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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 324v, page id 00067993:0650
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secaus tangusdimud
AHBCt
taag. tans. Dund.
uE+ EF.
Nota idemsi pro totis smpla sumant, syuper enim partestolis, e
Hinc ingens numerus aequationum:
demto.
YGKE = HA AH. KA AH L EF HAA it est cyluder ax quadrantis aquatuo mmentosutis hyprbluri pdi moneato figs mae lansentur
dimidiatu arcus conplementi. Eag ex basi AC ergo si hujus solidum devolutione semti
circa AC; haberi posset, haberet quod detragoni sim,.
Nam Monculum idem est, quod appliculae alicuius figurae, in portiones regult seu altitudins a basi
abscissus, ductae
vieA
KG. Padsen B rad = momento tangentis, HA HE + EF. seu cubus radi aequatuo momento tangentibius addito nomento tangendu
arcuum coplementi dimidiclorum. At momentum tungendtium haberi potest, si moio a momento secantrm seu
P. opus habenus ducn quorantus hyperbolico, auferatur cube radii, quia semper quadrato radii a seantis abt quadnto alllatus relinquite
hyperbolae quiaue permprum quadiatum tancentis Tabitus autem momento tangentias dimiadi, haberet Cytrude padrantis
licta quare aut halrabitur tetrago nnsin, aut ernor erit in calculo. Cibuad nom Misprba cub. gad. + mom. bus. din.
Resulae XA b erit et radio a. erit quod si ergo momentum langentum
quad sui se controcidis haberi posset ) berchompB monenture tangentiuno seu asemplota in (inita, haberet et momentur
tangentu arcum coptementi dimidiatoreum et ideo per aequationem praecedentem tretrasonisum
Polita cu
Errgo mome
Hincu si quis exhibere possit solido conchocidis circa Asymphitam aequalemcylindium, uuti
aoetunsent
et mo auto in Hyperbola mon
Bad Aecaurs atanu. ditid= sin tang. + tang. dinid. seu Cylinder Hyperbolius dento cytindrotansenlum accus supplementi dimiditi
habemus solido Ague
pag. pusce) aequatur. Quadranti ducto in conchocidem figura tunus. dimid anctam.
exemto quadu
ut hunc ductum quadrantis supnastensum aequari cylindio cujus basis conchocis elfitudo radius; Ergr
Coluder Hyperbulicus, demto spatium Hyperbolium demta figura tange atium sape ltibru
it
iui. rectium
H KG - AH-EF- HE + EF Ergo HG GF = EG AH - EF, seu cytindere in dmangitur euseniquada applicatus
areus semisupplementi aequatur condioerdi
siineo e
isteutus
hepiti
seu moricto
circulere
Trianguli demto cylindro tangentium ac semituplementi
equatur Tgilineo oncavo circulari ducto in spatium Hyper
bolium, ducto demto eodem hilineo concavo ducto
tamgentes arcus semo sumplementi
ryt. tang. arcus sem spl. Male
quatraliit esua cp
S tam Tongentes arcus sumsupplementi in conavn shilinem = ytindro inailic. timus.
quadr. airc cl. hyperb. = an J. targ. acus seguisess
Cyl. tam orcusemisurpl. = cyliud. Hyp. . cyl. tamu ac sam sappl. + fad. m appic liaas) cub rad simidan
us
SErgo 3. Cylindr. tanq. crcus semisuppl.  Cylind. Hyperb.  cub. rad.   amm i i sun portiomes crcplares. Ego data quadatura
Ergo Ergo data quadratura Huperbolae datur figura tangentum semi supplemcentatium. At hac data datur figura Tangentium
seu conchocis exenta Eti circuli generatoris portionet. Ergo data quadiatura Hyperbola datur quadcatura
ce Conchocidis. .. At gimentio exenta scilicet portione ciculius generantis. Aera methodo qua
draluram concrocidis ex quadratura Hyperbolae demonstravit gregonus videndum an idem pitoveniat
targin
Squadcari potest, ceri
bE 5C
inginem AB appliculi
XGEF= EG HE + EF. seu Cylindeo tangentum arcusemi spplenti=drilipeio concavo clucto tam intententes qua ni trysritus
sto e
ut sane videh.
18 eut  srissil ct e n at ladi
l E et supa ostensum quod
cylilanus sonitisplat cyl lypur Est tons bnipiat Cyl. Hyplilus  Epgo Hapus
la
Jum susta Cyl. Hyp. = 3. cylilamus fupl. = cubirad. Ergo 3Gt. tanus
Tilia gero in tonus lomiseplt. condre.
quadun cucmlari ductrtam in-
eoluid semi tan + cyl. tenus semuisa suppl
= AK EFa
n egna tergentum datom
Ilem 2 cyl. Hyp. = cyt. cam semi AH = EF DEF= HE+ EF GF. seu Hyperboludnta in figuro bangentum
1 Ergo 2. cyl. tam. suppl. - cubrad = degl. tang.
semi sappe. dentis horum lansent
Ergo et
HE + EF
AK = EF
s
AKHE + AK EF - HEEF = EFEI
EF H. fier.
yl. hypidemt. cnt. rad.
imilia sunt la HAKE et EHK. ergo AE =. KA = KE. habidins nisi fallor, sed repeti nil nocet.
mihohuus paginae
HE KE (KH
etiam momento spatii hyperbolici, demto monu. sus sin long. suppla aequetuo e cubus radii aequetu, mom. lanus.  monu lanus suppl.
fim
Ergo mom. tanus = mom. spat. hyp. = monu. suppl. tang. At Ergo mom. spat. hyperb. = mom. tanga +mom tanu, suypl.  cabo radii
 AE KH = KE HE. seu colindue spalii Eyperbolici, detus eylindio hianguli regulae, = quadranti ducto inconmhoerdem
po ade
ut jam aliunde demonstrclum, insigni documento veritatis calculi
At idem bylinder Hyperbolicuecl. lanus semi supl. = rq uadra duct. in andi cbmd. 4 quad rant duct. in tarius formi supsl
Ergo iyl. tang. semisuppl. + quadrant. duct in Tarus. semisuspt triangalo regulo portionis regulae, a basi abscissae inradium ducto
ddutur ductudi quadrantis Ductus Tulmei circuloris geavi, fiet cyl. tanus senti suppl.
KA KH= KE,I seui Pmiquadratum portinus regilae in conctolidem, in monentum dffitalia quodrae sercntum aa radio, aequitue quadralis si niniu
pro portionales.
in condioeidem ad quadratum
duotus quaddrensis in
nesvo
ductus aequatur in
simum per pro. preced