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# Piece: https://leibnizlegible.com/api/records/62566/text
# Catalogue record: 62566 — Sphaera gravis sustentata a duobus planis
# Incipit: Sit gravis sphaera ABC sustenta a duobus
# Date: 1690-05
# Akademie-Ausgabe: AA VIII,4 N. 075
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=62566&katnr=60113
# AA VIII,4: its series at Leibniz-Edition Potsdam II (CC BY-NC 4.0): https://leibnizp2.bbaw.de/de/leibniz-online
# In the Akademie-Ausgabe: AA VIII,4 (PDF, Leibniz-Edition Potsdam II, CC BY-NC 4.0): https://leibnizp2.bbaw.de/fileadmin/Webdateien/dateien/LSB_VIII_4.pdf#chapter.75
# Work: https://leibnizlegible.com/work/00068167
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 14
# Folios: Bl. 6 (from the shelfmark LH 35, 10, 14 Bl. 6): 2 pages, canvases 11–12, page ids 00068167:0011 to 00068167:0012
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068167&page=11
# Lines: 60 recognised on 1 of 2 pages, mean confidence 0.89
# 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.
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# 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 6r — 00068167:0011
# Source image: https://digitale-sammlungen.gwlb.de/content/00068167/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
nihil debet ad V. to ere
quae sit figura corpais ABC
modo normalis. 
incurrant in centra graviantis
Sit gravis sphaera ABC sustentata a duobus planis dB, EC, quaenitur quam cuique vim
imprimat, seu quae sint pondera F, C quibus plana sustinentur. Pono autem angulos BdF
esse rectos, et CEG esse rectos. in e et dE esse horifontalem. Ex A. F.G, in DE
agantur normales, HL AH, FK, GL quaeritur situs talis, ut centrum gravitatis sit
omnium possibilium minimum infime situm. sint pondera a, f, g. erit AH. a +FK. 5 +GL. C
divis. per a + F+ l distantia centri gravitatis a dE, quae debet esse ognium possibilium maxima
Alsiunamus DH et AH, inde caeteri situs determinabuntur DA = _H + AH Datur AB
radius datae sphaerae. Cujus quadratum detractum a quadrato du, reliaquet quadratum dB, ergo
fiet de =  D HF AH = AB) similiter CE EH + AH - AB est autem EH= DE- DH
DB: BM: Md: AB: MH: MB - AL seu BM: Md = DH - dM, :, MB - AH et
efi- Dm
fiet BM - AH. BM =: DH. DM - D M seu BM+ DM  seu AH. BM + DH. Dn = (B M + D,
 DH + AH  - AB = AH. BM + dH. DM quarum duarum aequatio tum 10 et 11.
ope dantur CM et BM et DM. similiter loco aeg9. 10 et 11. scribemus CN + EN = EH +AI- AD= AHeV , M 
im similiter dantur  CN :+ EN tantumque ad 549. 10. 11. 12. 13. adjungenda aegg. 5. postremo
ponimus autem DF = EC datas. Esoque FK = DF) BM- AH, : AB et similiter (L DF, CN- AH: AB
Ex aeq. 1. sib a sAH + f dEK + l dyL 76 et ex 1s fit ( deK. Om- AH d DC.  t BF dBM D d
et ex 15 sit AB. d. FK = DF d. BM = DF d. AH Ex 1 est Dm = DH + AH = AB  - A H. BM, : VH
et quanondo  BZ (BH + AH+ RB H. BM A (E, DHF: A H + 2. AB. AH. BM. = (E) AB. DN = 2AB. AH - 2AH. BM. dH. 2A N. Bm
vel si placet brevin
= (0O L AH. DH AB. VH - BA. DH
procedere DM = DB- AH. BM, : 1. (   + cy  3.) Cvgo per g sit DB L AH. B8 - = DB. AH. BM BH. B M
Dm = DB - BN = DB LAH. _- DB. AH XM,: B
= DH. DB  _A eG it DB. DH -
Ergo DB BH BM DH =DB+ + AH. BM, DB AHBM DB AB DH tAH. Ergo
PDB=+ DH -- aH + AB. Ergo fit DC A AH = AH + DH BM - 2. DB. AH RM. seu
Pm AB = DM. AH  BBB. AB BN. AH = AH. BM + BK Bm - 2. AH. BM - 2AH D M. dn
AH + AD N 2AH. AB
PMdDH
B BA dBTA + DM. dBm = DH dD.t +AH d AH LPAH dOM + BM + A H + DH + (e. (x)
et 2 DH dDH + ZAHd AH . AH d BBL + BM d AH F DH dDm F DM d3H,
sed possumus tamen et sic procedere, ut consideremus situm ipsius EC qualiscunu
sit tanquam datum, inde ponamus decurrere A, donec DB depumatur
ut amplius sescendi non possit et fiet a dAH + fd. FK =0.
similiter fiet a d. AH + l D d. GL = 0
Ergo fd. FK = l d. GL
sed haec non sunt conciliabilia cum
d. FK = = a: f d. AH, d. GL = - a: Y d AH
aeq. 17. quae tamen et ipsa videbatur esse debere vera nam fieret
jam viceo in quo pecca
ad AH = a. + AH + a d HA = 0 quad absundum
Tm in g. 17. nempe quod In eo et an percatum Hinc perficitur
un
Aestoius de Mayinis et Minimi. Nempe casibus casus sunt
infinities infiniti e et ex iis maximuue vel minimum quaeritur
possunt altergatim omnes assumi constantes prater unum. Nec licet
omnes assumere indeterminatas.
Applicandum hoc ad maximam
talicuius selperfiliei concave latitudinem, ubi etiam non licet omnes
simul assumere ut indeterminatas
=ABa: FP d. AH = DF dBM - DF. d. AH . Ergo d. BM  d. AH = F. DF _ - a E,: 35
possumus facere DB = DF, ita ut EG non sit g.  DF sed EC, et fiet in tado.
B  1. MB ut  om ergo sel prosibum unequoatias
Virendum an non eodem calculo res dequastretur ets et si A
mmoli ipso B in quo concurrunt noimales ad plana non sit centru
glantatis sloti

## Folio 6v — 00068167:0012
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