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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 29r, page id 00067970:0057
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17) Superficies est via Lineae
 ge  LBCtbegC 32b2933C36C39C
33C36c39 63c66c69 93c96e99c
(18) Planum est superficies tribus punctis
determinata, seu est via rectae ad punctum
 ex hoc ipso determinata.
aliquamdiu
(17) Recta minor supet inajori moveri
potest, ilet eisa.
id est ita ut du
ejus partibus congrua maneat. Nam recta
minor. partibu parti majoris aequalis est, quae etiam
recta est per prop. 8. huic ergo congruere potest
per prop. 16. ect utem et nn eadem parte continue
plares continue partes inter se aequales sumi possunt
ergo has  percurrere minor potest.
S. GC AgC B12C13C. N EF
sint, 6cgC A AB B  oc 12Cp B13C p EF
succestine
poterit esse Dc esse EF ∞6C9C  ∞ AB ∞ 9C1C ∞ B13C
id est novibitur super. idemque est, etsi plura
puncta intermedia assumantur. it id est
EF movebitur super bc AB13C
(15) superficies est via lineae 3cbegc
nempe 330 36CBgC  33C 36C 39C63C66C (C 93C 96C99C
(19) Planum est superficies tribus solis
punctis determinata seu est via rectae ad
punctum, ex hocist his solis determinatat
3A3cB64626694oc8
A.B L A B. 3 A3 sB6AScbB AB. SeE.
 3
unde patet tribus tantum punctis A. B. E determinari
(20)n Duo plana quae quantum satis est producta
non coincidunt, non possunt habere tria puncta
communia, sed duo ad summum.
Si sint 3A3c3B6AbCE6B9Agc9B  idem quod C
et sit 2FgH 3FsgBHSFSg6HE   idem quod)
Situs 6A ∞ 39 et gB ∞ 6H
coincident O coincident O et D. Quantum satis producta
sive nullum erit punctum in C cui non aliquod
respondeat in  coincidat in D et contra.
gaevius ABE superfic. ABE eoA
Greoigi superfic. ABEm LAm BnEp ∞ superf. 9ArBs Et
M
Nerando
(21) Pars Plani est planum.
nam pars plani C intelligi potest esse
3A3C3BCAOCE6B. quaentique est pranum.
(22) Duo plana quae producta non coincidunt
non possunt habere partem communem.
cum enim pars plani sit planum per Mop. 21.
tria minimum in eo designari poterunt puncta
quae ducobus planis erunt communia contra 2o.
Hoc etiam facile characteristice
desuinri in denstram possot
Notandum hic fieri posse, ut linea
durante motu de crescat
decrescat aut alias mutetur
et nihibo minus via ejus erit superficies
Fextra ipsam utcunque productam positum
Melius designibitur e lanum
via brevissimquele
anctum
nota rectae circa extremum
immotum, qua ad aliud
punctum bre aliquod pun–
ctum tendentis.
seu via et determinata