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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 18
# Folio 23v, page id 00067980:0046
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alicujus
LB
distantia puncti indeterminati  in plano sumendi, a puncto fixo A
er seu recta AB, erit
Xx F yy +7Z aequ. v. rebi pro aliqua
harum trium, X vel y vet Z substitui potest valor ex aequatione
paulo ante inventa.
Videamus an calculo possimus invenire
Minimam plani distantiam a puncto A.  XX+yy + ZZ vocemus C)
LB
et Z vocemus e, fiet
O aequ v. unde fiet aequatio differentialis.
aequ. , se seu quia hic ob minimam fit du aeq.
habebimus dO aequ. O. seu X dx + y dy + Z dz aequ. O.
jam semper
alxs in dx -  dy + = dZ aequ. O. ex natura
plani in universum.
sufficienter de terminari,
determinationem pro
Sed hinc patet nondum quaesitum
etque poterimus assumere aliquam
Bonamus punctum quaesitum esse B
seu rectam AB esse minimam ex puncto A ad planum LB.
unde tollendo valorem ipsius dz. fit dz aequ = dy - = dx et rursus
quae inclusa
prom
potius omit.
tentur,
quia
imperfecta
aZ aequ - x dx ∞y dy,: Z. fiet Z aequ.   xdux xdX + ydy: x dx Xdu
rursus Zaequ. 7y = Y +  X Ergo  dx x dus aequat x
aequ ryx de rx dx + rXX dx + ryy dy - rydy +rXY dy.
Ergo X dx +y dy aequ. rr ydx - rrax + xdx - ydy +rrdy-rexdus
Unde
2 XX + 2yy aequ
19 - XYX
X X y
l9
n
19
ErrXX = Erryy + 2r y. si qui demlice
9
differentialem convertere, in summatricem
erit.
Ul
Sed ista ad huc ciuda
atque indigesta, omittere satius
Videamus, quomodo angulus, quem planum facit ad LB facit ad tria reliquo
aliquod reliquorum planorum, determinetur, (exempli casu causa angulus plani =B
in plano LB ducatur recta ad communem planorum tamti pla
LB qua in plano AR ducantur rectae alia e 6 et 27 (Ducantur duae rectae e
ad planum AB
illa in plano ALB, haec in plano AR, ambae perpendiculares in eodem puncto Z. ad
rectam ZB duorum planorum sectionem communem; manifestum est, angulum
via
fore angulum planorum inter se determinat enim quantitatem mobus
alicujus puncti plani LB, scirca axem QP, donec  plano LB incidente in planum AR, etiam
quoque
motis
ad angulo rectos occurrere rectae QD, et quidem ad angulos rectos, ipsa a
QB incidat in 
ergo Ot esto perpendicularis ad 28
Datur BE seu y ex datis  seu Z, et AN seuX
Est autem angulus QEVE rectus ergo quadra LW, seu quad seu q rqu+ xx, cum quadrato
VE seu Zq aequatur quadrato ZE, ergo quade ZE, aequ 44 29X +XX + ZZ at qua
dratum BE seu ys aequ
quoniam datur punctum g. Commgne tribus planis LB, AR, A
qvot in recta a p atuatm