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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 36r, page id 00068207:0069
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anter h floraa apros p. Rocharski) abifrabus caso ex Hons p. 3, D 1692
Stobl. Extancre in tertudine (Gattice Dome) pferte hemdsphaerica . fenremas
aequales, tali configaraive, ut his detractis, supstes curva tertudinis supfiries
geometrice possit quadrari, ie abique supposita circuli quadratura.
se
solutro:) On Fig. 1. Circulus BEDF rpraesentet hemdalaram,
centrum A iprius potum, namitri ppindus 9D, EF, duos semicir culos norma-
liteo se decnstantes in polo A, et su dividentes hemisphaeram n q portiones a
quales, in quarum ingulis deseritat curra AAF propritate talis, ut traje-
eto libere quadrante AHM, pars MH sit aequalis arcur MF. uo supfirco
em contentam quadrante At et curva AdF etse unam ea fenettis quaer
sitio, ita ut his detractis reliqua supticies sumisphaica tet dupla quadrati.
inscripti m iphus bate
Demonitr. Fig. e repraesentat basem hemisphiora, super cujus cntinm
C, potus A ppendicularitor incumbit.
Fig. 1. 2.). Sumpto utcunque in circumfeuentia bateos, arcu MN indefi-
nite parve, ducantur quadrantes AAM, ALN, sinus recti MP, NQ, arcu
Mo HG cujus potus A, rectulae Ma oi, perallebe CF, ppend K in chordam
BF, ac tandem gangantur es, C0. Gropter similia tuangula M XR, CMP
et OSt, CFK, arcs MN (quint recta consdorat,, ob indefinitam parvu
tatem) ert ad Ma ut CM ad MP; et Os ad Or, ut et ad Ck. Ergo rctanu-
MN in M8 est aequale rrtang. CM in MX, vel CF n Oi, quod aequatur
rectang. Ck in 50. Atqui notum est ex Archimede, portiunculam honae GHMN
aequalem etre sinui uito arcus HM vel MF, id est M8 ducto marcum M N,
et ex Euclide rectorg. Cx in so duplum etec trianguli CS0; immu hoc utique
contingat, segtr ex methodo indivisidilium, tumam omnium portinacularum onae
GHMN, quae complent spatium semisphaericum AB MF HA duplam ette suma
omnium triangulorum C30, qui complent tiranguluv estF. 2. E. f.
Alia solutio:
Fiy. 3. 4.) Describatur m Octante AB hemisphaerica tusficier, curva
AAB proprictato talis, ut libori trajecto quadraneo AAM pars Mst sit a qualis
arcui FV, cujus sinus rectus Vk sit tertia proportionalis ad mediam partem
radi CMM et sinum rectum MP; similiter describat in Oetante A) F curva
AHF. Dico spatium AHRTFHA ette unam e 4. finertus quaesitis.
Demonstrarem hu omitto pp spus angurtiam.