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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 242v, page id 00067993:0486
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Yla similia Es T. et ADC.
prop. 18.
prop. 19.
AD
DC AC.
AET E5,
prop. 26.
5+
yid est spatium Hyperbolicum
(aode prop. 21)
ADESCDCET. secantes complementi in basm, aequantur Tangentibus complementi in arcum.
ADST = AC ET. summa secantium complementi aeguatur radio in arcum. adde rop 25- adde prop. 26.
DCST = AC ES. summa tangentium complementi aequatur Radio in sinum. adde prop. 25
Vlasimilia: Es. T et _  WW R. ergo uA UA ud. tam losest AED KCB.
prop. 31.
prop. 32.
Wo Hi. autem
sic nvenicms W0k - AE. Engo WoA) AE uA. At (A est Ad - XE. est AH est AL∞. ergo -
UR AH.
AH
W0R = AE URC EN seu UREN. UX seuna = Ad - KE
AEN.
patium hyperbolici
Ctan gentes complementiim encum perp. 18.) (quadrabilibus prop. 12)
decantium
asin demsimit in basin aequantur, rectangulis sannum
Tammerabilit
complementi demtis rectanin sinus complementis demtis, rectanguli sinuum on sinus complementi
de propis
XBE
ds in arcum; divis is per Radium. Cector duplicatus) (seu portione cinulari) est
URST = UW ET. summa secantium complementi, demta summasinuum (residuum quadrabile esse necesse est)
aequatur Ul in arcum; vel  sectori duplicato, demtis XE H in arcum.
Coroll. Ergo XE H in arcum aequantur seu quadrata sinun  per radium divisa, in carcum, aequantur porte
summae sinuum, seu portioni circulari. adde prop. 17. et 36. 23.
Co Hy) _ WWRST= UWES. seu summa rectangulorum momentum secantium complementi ex radio
quadrabi
sa basi parallelo, demto momento sinuum complementi, ex eodem radio aequatur uto in bastri
 demlis sinubus in basin, per radium divisis. At sinus in basim
prop. 12.) ideo
ant quod rabile
(oroll. 1. ergo Momentum secantium complementi ex radio basi parallelo quadrarip
Coroll. 2. Ergo habetur cylinder aequalis conoeidi secantium complementi Coroll. 3. Ergo sinus
Pla similia EsT et ENR.
EK NR ex
Cgominabile ET AE SY
Oratiuty conchocidale
ERES = NRET. Tauyeat si basi dem tangentes opplementi in basin aequatur summa secantium com–
plementi (rad sectori, e mmtudine at Sinuum (partione tari) secantibus complementi
in arcum, demtis sinubus in arcum (quadrabilit.)
cons. prop. 4. ubi dicitur: secantes inarcum
aequari spatio conchocidati momento arcu ex radio basi parallelo
seudisser in estantem isecatem
Coroll. Ergo differentia inter secanteain arcum, et secantes complementi in arcum quadari potest, prop. 36.
complement
ERSTLEN EY summa tangentium in arc aequatur momento arcus ex radio basi parallelo. quadrabilis
ergo catde prop. 23. 20. et alias passim.
NR ST= EN ES. Summa secantium complementi, demta summa sinuum, aequatur sinubus complementi
in basin, seu duplex sector accy, (prop. 19) demta summa sinuum; aequatur  quadrilineo inter
auum dbasi, radio et sinu complementi compretenso. Quod facile indiatu, comprobatu, calculi
nostri confirmatio est.
Fla similia EsTADEF.
De
DE
EF
EY Es STCspatium conchocidate
DFS = DEET Serantes Tangentes complementi in basmi, demtis Tangentibus semicomplenenti in basiri (id est per
propi 13. tangentis in basin, quadrabiles, demtis duplex sector dentis tangentibus in basin, quadrabilibus) aequanttud
secantibus in arcum, demto radio  (conspatio conchocidali addito momento arcus ex ba radio bi
paralllo) demto radio in arcum, (seu duplici sectore.) Manffesta horum omnium aequatio est, docu–
mentum calculi veri.
DFS7 = EFET. summa tangentium complementi (quad rabilis) demta summa tangentium semicomplementi
aequatur tangentibus semicomplementi in arcum, ade prop. 19. et Ergo 34. 42
indito
inplex sector) radio in ultitudinem
DEST = EF ES. Summa tangem secantium complementi, demto summa sinuum, aequatur tangentibus semicom-
plementi in basin adde prop. 15. adde prop. 31.
V2
Es
Vla similia: Es T. et DEG. R a
B
DE ES = DGET. secantes complementi in basim (spatium hyperbolicum e intellige sciliced inversum id,
enim semper intelligendum est ita Tangentes complementi in basin sunt conchoeidate inversum,
simus complementi in basin sunt spatium circulare inverum.) demto radio in sinum,
aequatur. Tangentibus complementi i arcusm demtis sinuibus complementi in arcum seu momen
to arcus ex bo radio basi parallelo. Sed cum per prop. 10. aequentur secantes complementi in basin
et Tangentes complementi in arcum rursusque radius in sinum, et momentum ars ex tadio radio
basi parallelo prop. 4. Hinc rursus calculi veritas comprobatur dita
10 in atiridh pation
DEST= EGET. summa secantium complementi duplem sector) denita smma
t aegratur.
radio inarcum demtis simub,s ad arcum, ruisus conprobatio eorum, quae prop. 29
equatu
DGST~EG Es radius in sinum, demtis sinubus ad basi (pundabilibus altitudinem, demtis summa tangentium compleman
matidenta summa sinuum complementi, aequatur radio in sinuum, tentae sinubus ad basin, hinc confirmatur
quadratura sinuum ad busin, de qua propt. 23 12. et 23
na
prop
Cspetio operbolicus
pros. 22
prop. 23.
prop. 29
profit.
prop. 26.
pro
po f. 28.
fif. 29.
prop. 30