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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 70r, page id 00068193:0141
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icto
x
ali
us
et
es
ita
M
qui
fio.
es-
d
P.1
m
1A
tus
per
M
m
1m
ectam
Sett. 11. Cap. 5. De Matu simpl.
sit (Fig. 32.) mobilis punctum quodcunque A describens
pap. simplilides
lincam 1A2 A3A; si motus mobilis ett simplea, ajo lincam
deseriptam ette rectam. Sit enim non recta, si possibile ett,
et sumto aliquo puncti A loca intermedio ut 2 A pon cadente
m directum cum primo et ultimo punctis 1A et 3A, ubique
functae rectae 1A2 A et 3A2 A, facient angulum 1A2 A3 A.
simpliciter
tus simplicis) angulus 2A2 A3A semper erit aequalis, uoi-
cunque durante motu sumatur punctum 2 A vel (2) A, (itnque
s
lnea 1A 2 A (2) A dit erit arcus circuli, ea elementis,) sed hoc
etse non potett.
semplicite
dungatur enim recta 2s 3A, necesse est
ob motum simplium) angulum 2 A, A3A aequalem etse an-
gulo (2) A1 3A; cumqe et angulus ad 2 A sit aequalis angu–
lo ad (2) A, etiam tentius m triangulis 1A2 A3A et 1AC)A3A
angulus erit aequalis, numpe 2A3 A1A et (2) A3A 1A; sunt
ergo triangula aequiangula, et cum habeant et latus eomu
ne 1A3 A, erunt et congrua, ad eoque latus 2A3 A erit aequale
A2 A
lateri (2) A3 A, ac proinde durante motu omnia puncti mobi
lis A loca intermedio ut 2A et (2) A semper aequaliter ditta
it
bunt ab extremo motus puncto hA, quod est absurdum, nun
q
quam enim perveniret mobile ad sA; necetse ett ergo ut
rectae 1A2t, 3A 2t nullum faciant angulum neque inter se
neque ad rectam 1A3A, hoc ett, necesse est motum 1A2A3 A
fieri im linea recta, seu puncta 2 A cadere m rectam 1 3 A.
rop. 3