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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 59v, page id 00067976:0118
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quoniam diximus Rectam esse locum omnium punctorum ex
suo situ ad duo data puncta determinatorum, patet rectam
si
ut utcunque producte intelligatur, per duo puncta tranfenntem non
esse nisi unicam, ac proinde rectam duas non posse se secare in duob
punctis, cum ergo duo puncta communia non habeant, multo minu p
segmentum commune habebunt. sed nec spatium comprehendent
alioqui a se digussae ad se se iterum revertentur adeoque sibi bis
occurrent.
patet
Demonstratur et rectam rede non redire in se ipsi
quia ut cum recta sit via brevissima a puncto ad punctum daretu
distantia puncti a quo ad quod redit a se ipso. Recta quoque rectam
non tanget sea secabit, nam omnis linea lineam tangens secan
tam intelliuitur in duabus punctis sed quae in casu contactus
coincidunt. Recta autem rectam in duabus punctis secare non
potest. Habemus ergo demonstrata Euclidis Axiomata
10. 11. C_ et 14. Se ec clarius exponentur
Rectam ita exprimere licebit: A. B. Z
punctum C esse in hac recta sit
Ut exprimatu
Rectam ita exprimere licebit A. B.
si Z. A. B. ∞ Y. A. B erit
unica
primetur. C est Z
Lecolligendo
 unira
ecece ec
Z(VeY L
a
seu
Y
A∞ Distantia duorum punctoram: AB. si C eadam intiqe A et B
sn a de ret Ct A_ AC + CB AB.
Recta intercepta inter duo puncta distantium eorum
exprimens: A.B)
si C cadat inter A et B, et sint in eadem roctaerit
AC+ FB = AH
omnis Recta rectae similis, seu AB V CD
Si Ax recta rectae sit aequalis erit congrua seict seu 
si sit AB = CD erit AB ∞ CD.
Si duo extrema duarum rectarum puncta coincidant ipsae
rectae coincident. ut si A ∞ b et B X D erit AB g CD.
Hinc et habetur generatio Rectae et circuli, quae nec rectam
sec Circulum, nec planum supponit. Corporis cajuscunque duobus
vilmeda si duobus corporis rigidi punctis manentibus immotibus abiu
aliquod vinctum moreatier tunc omnia puncta cereruis quae
maneu im motat cadent in rectamsquia cnsitum ad pundet in motta
prediante rigido
semper connexum
manet, adeoque
eundem situm
servat
ex hypothesi
rigidi corpori
connectentis
variare non
nec locu
epsis immotis
possunt s
untare
A quodlibet
aliud punctum
extra have
detam descrbet
circumferentum
Ciunti senlinear
eandem silumad duo
puncta A et B habentem
quia punctum describens M il B
cum ipis Imto
poss