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# Piece: https://leibnizlegible.com/api/records/5655/text
# Catalogue record: 5655 — Rudolf Christian von Bodenhausen für Leibniz: Solutiones problematis de Templo Hemisphaerico von G.F.A. de Hospital
# Incipit: Probl. Extruere in testudine (Gallice Dome) perfecte hemisphaerica 4 f
# Date: 1692-07-12
# Sender: Bodenhausen, R.C. — Addressee: Leibniz
# Akademie-Ausgabe: AA III,5 N. 092
# Other printings: Bernoulli,Jac.: Werke 2 (1989) S.529-531.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=5655&katnr=35614
# AA III,5: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-5
# In the Akademie-Ausgabe: AA III,5, p. 417 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III5A.pdf#page=417
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 36–37 (from the shelfmark LH 35, 15, 5 Bl. 36-37): 4 pages, canvases 69–72, page ids 00068207:0069 to 00068207:0072
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=69
# Lines: 81 recognised on 4 of 4 pages, mean confidence 0.86
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 36r — 00068207:0069
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 37v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000069.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
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.

## Folio 36v — 00068207:0070
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29. 5.
f2y. 5
V. 2.

## Folio 37r — 00068207:0071
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 13 lines, status machine
V. 3.
l. 6.
(Fig. 5. b. se
Tertia solutio:
tatis, ut trajecto libere quadrante AAM, pars MH uit = arcuo TV, cujus
sinus rectus aV sit quarta xportionalis ad mediam partem radi CF, sinum
rectum Mh, et parallelam Si, sumpta Ot = FP. Samatur nunc in
quadrante AT. ubivis arcus aequalis arcri BT et describut  utray
parte curva eodem artificio quo BHF descripta ett. Dico spatium con-
tentum his 2 carvis ete unam e fenettiis quaetitis.
Demonitmom omitto, qd longiuscula sit, et illpenti reliquas sponte
nascatur. Porcem infinitus abias adjungere, sed sufficiant ha tres qua
mino simpliciores tunt vitae-

## Folio 37v — 00068207:0072
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 36r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000072.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 30 lines, status machine
N. dia demonckian der 2 tolution habe ich outgelaßen, der 3 aber den Au-
ton selbst. dir 3 conttruction ist Tuone die chne rese, ab ere weege der positur
H. genichformuus keit in deae Secrudine od gnroilbe die schouste, dia 2 abere die-
nnt hur prani nist, wnil doo ganter grnbolbe nnr auf 4 pancte stehan wiede
daansin dir 2. ind B8. F. Dergleich imomiditat fallet ouch vor in
in
Msse constraction; duum nonir in Dnineae figur Podere A deae zendth ist, so ru-
het dori guitre gebene aucf 4. punten. Wo orber 2 der Zcuithist, so ist das
grwolor oben gante offen, V. also min ein fenster aub 4 trilineis LPLA com-
poniret. Ware also pglisere, nenum mon gedachtes trilincum et LA quadrivet,
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seign, H. ich desten anahy sin gerere sehen mucsta, id alche wrelleich. die 1 Constur
etiorum des Anonymi Galli auhargen weired.
S. Der Parillus G. weie ich ver nomen, hat Reina order weder wonr . erten
noch vom frintie gnhabt, das protl. Mehln. Zu uterefande, d. hat sich diur
liantiam Poeticam genomen b dam Ab. Mortacuti, fo fem fa rund ist, daß
er also sone der rembdus tolationes fahen, _. solche von fi applieiran,
Wenil er sson vorconen bin dem printee, mis feinene ob wol mechanichen
solution, kom an doch olheit sorgen, ne hate ehr durchh. nicht Zu inomodir
domroito nicht weitlauffig sern wollen, eb Kon serich e onandar
Iventis so viel zu den fimen flicke alt en wil; dieses ist die gan
o sulise politique.
en ubrigen bedonba nich fuahlicht von dir honorable mention mniuru
fo an in Mminam schrniben om den G. Printhe gathom, deßenich unch ncht we-
19Y0
far wurdigs chat, al nonit is mics von Mnimen obliguete diteipat eaeknne,
V. dahoro von einen recutation indirecte participixe7.
N. Ech bitta mit gelagnnhnit ssu. D. Devitium Zu grrß, V. umb dat benenisu
Ms. Carraniamum su tollicitir p.