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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 7
# Folio 4v, page id 00067966:0008
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 3r); this page is its left half.
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Datis  quator punctis in idem planum
non cadentibus resultat profundum, sieu  sot
Amplum, seu spatium profunditate profundum
Seu id in quo sumi potest punctum non commune
pars non communis quod ei cum altero nisi parta
partem aliquid quod Terminus non est, seu quod ei
non potest ei esse commune cum altero nisi pro
parte in ipsum immerso. Sunte qualator
Sento simto quatuor puncta A, B, C, d. dantur
et quatuo plana tres sufficit Hina dantur tres
sex redae AB, AC, AD, BC, Bd, Cd. Sed dufficient
tres AB, BC, Bd, Bd AB, AC, Ad, nam trios reliquae
ex his nascuntur quod si jum et per duo quaevis
puncta duarum quarumcunque ex tribus his rectis
qrant Datis his determinatis his rectis determinantur
R prosultantibus
et omnia earum
puncta, et rectae conjungentes duo quaevis diversarum
seu resultunt etiam re
his tibus rectis, prosultant
rectarum puncta, locusque adeo harum rectarum
omnium. porr  habemus et quatuor plana
ABC per AB A. B. C; per A. B. D; per A. B. d;
per A per B. C. d, quorum duo quaevis serunt
sectionem habent rectam communen; verb.gr.
AB per planu per A. B. C et per B. C. d habent
communem sectionem rectam BC per B. C. Haec
quatu plana claudent spatium. Itaut ex puncto
Eterecta quaevis ab uno plunu duo puncta duorum plancru + BEDca
conjungens habet omnia puncta, intra hoc spatium plta ut ex
puncto rectae extrimis interjecto nulla red recta
odast
quea enim queis Nulum Nam oania puncta profundi hudus untur ut ipse ABd
educi possit, quae non tdiam castr
determinantur ope duorum planoum profundi prosultant ex duobus planis per A, B, C et per B C,0
cta
dico
planis ABC, et ( jungantur recta GACGA, hB, GC, Gd, item
 continuatum
Planum er E
Triangatr ExH
constinet planum ebd secabit plana A.BC, ABd, ACD ut tribus rectis
mmip
Continuetur GE, dum ips per E
quae tres rectae constituent triangulum intru, quod caedet cujutria la
icadent intra ta a cujus intra tria latera ca
cujus duo latera cadent intra ambitum trianus tuia composita
ex tribus triangulis tota intriangulam duo extriangulis tribus
et punctum Gintra hoc triangulum cadet. Per Racta
ergo quaecunque transiens per G altemtrum ex illis duobus
ergo omniret recta GH
nui e occurrit uni ex  triangulis, ABd, ACd, BCd. in K
lateribus, ergo et recta GH
sed eadem etiam occurrit, uni triangulo ABC, ex hyp. nempe in G
so ostendetur et alio extremo occurre uni ex
sed brevius rem ostendemus
Esto punctum H, quod majis quodcunque dico non posse ex G ad H duci
aliis tribus triangulis.
ponatur illa recta produci quantum opus est,  ad punctum H, quod magis
absit a puncto G, quam tanu omnia puncta qua tuor triangulorum ABC, ABd, ACd, BCd.
proda Ex puncto H quantur normales in quatur plana, et itidem ex puncto 
sint ad easdem partes; id planus
amborum
aliquod ex hros planis debet k secare in triansulo cujus planum est continuatio
patie
unnu
la
claudunt autem
spatium quae ambitum
constituut continuum
plenum, nempe tal
inea
ec
bitup a
it ad part
e  e teta sit
i perven
oabi
quatuor Triangulis
planis ABC, ABd,
ACd, BCd, quae
spatii ambitum
facient
extr
merus
uere plues tri nagulom
i Y
du Y C L) sit pN - aZ
pl dx = ad2
eit sedreipr ey lis -m ss aut.
Aicd