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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 16v, page id 00067976:0032
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 si non cadant in
ectam
 Hino manifestum est omnem rectam omni plano con
gruere applicari posse; itemque rectam in plano pale ) _ via determinata a puncto A ad punctum B at recta AB.
utrique
moveri.
(25) Tria quaevis puncta de in plano sumta idem
planum determinant, seu punctum quodvis in plano ad
a sui ad tria plani puncta (non in eandem rectam
cadentia) situs unicum est. Hoc potest demonstrari ad
modum articuli, 6 in recta. item sic: Cuhe at punctum
ex tribus planum ex tribus punctis determinatum est unicum
per artic. 22. eper A sint illa tria puncta L. M. N. dico
ea determinare planum in quo sunt nam determinare utique
fZ.c. esse
et sunte in plano quod determinant. Ergo planum in quo sunt
26)  si recla uno Recta est locus omnium
determinant.
 Circumferentia circuli est   locus im plano omnium
punctorum quorum situs ad unum aliquod punctum sit idem
seu describitur ab extremo rectae in plano motae (quod fieri
potest per artic. 24.) uno puncto immoto. Et notis ita
si
A YA. = BA in plano, y est
pose demon strare quod omne planum sit plano Simi
designabitur:
circumferentia circuli
27) omne planum a definite planum plano simile est
si in definite sumantur, (seu si termini duorum planorum ambi
tus sint congrui ipsa plana congrua sunt) nam sumatur
si planum determinatur per A. B. C sumantur in alio plano
eris
puncta L. M. N Sic ut sit L. M. N V A. B. C
L. M. N. simile determinato per A. B. C.
eo scilicet sensa quo determinationem explicuimus
) si planum a plano secetur, sectio communis
et determinatum per
est recta. Sint sit Y. A. B C determ et .Z.
2
11.
planum si duo plana se secant, saltem plus quam unum
hac punctum sumamus ergo duo puncta
communia A et B. Et in uno plano Y sumamus fertium C in
punctum commune habent
determe
tertium L.   pro plano Y. erit Y. A. B. C det.
altero plano Z
 erit Z. A. B. L determ. ergo commune utra
pit ambubus erit recta determinata per
a
pro plano
B.
sita ut sit V. A. B determ. dico omne V fore
sit jam recta
q et imne V fore Y.
Nam et si V. A. B determ. Ergo et V. A. BC. determ. et V. A:B. L
determ. Ergo V est Y et V est Z
a
uod erat demonstrandum
virum nullum prreerca aliud punctum
mdnatu e his duobus plans
comhunne dari potest, quod non in usu re
cadit. Alioquo en Nam sitria nuncta utn in eandem rectam non cadenlia.
ad it et in Y et in Z
communia forent, coinciderent hnue plana ralia enim tat puncta
panum determinant