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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 51r, page id 00067970:0101
# Scan: The same scan is also registered as fol. 52v; its text is given once, here.
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Duae rectae quae duo puncta habent communia
productae coincidunt:
A. Y S B. Y Y C. Y
(2)
DXY EXHFX.
XF (A. XY BXYGC.XZ D. XYGEXYG F. XY.)
AGG, BG8CG. DGBEGGFG
AHG BHGCH DHGEHG FH
probari debet inde qu
Hinc probari debet, esse
AXGBXGCX. et esse DYGEYGFY
Ex 3 et 5 fit: AGHg BGHg CGH
Ex4et 6 fit DGH EGH8 FGH
EH
EG8DG
THGS DH EHGS DHG
AGH∞ BGH
AHG BH. AG yBG E Ad∞ BE
Hd G HE. Bd 8GE deteminitu
Ergo
AG HD GBGHE
Nam si modus determinandi situm et quae per
D ad A, congruit modo deter
a
ageter
minandi situm E ad B, congnien ema sunt con
tunc DA erit _ BE Haec regula, ionsiiieae congruunt
pulchernimm est summius usus. et earum entrama
Hinc quin re duo quolibet quolibet punctu
ad data duo puncta in eodem plano eodem
modo se habentia cadunt in eandem rectam
Hinc sequitur puncta quaelibet eodem modo
se habentia ad d. E. etiam eodem modo
se habere ad A. B. adeoque omno cadere in
Sed demon
Cunum rectam.
strandum qrius duas rectas datas
scadere in idem planum; si habeant
punctum commune.
Ex hoc quod duae rectae non habent
nisi unum punctum commune demon
spatur. Quod an tersectio rectarum
sit punctum, seu quod isit AFY BV∞CF DY
est lucure Y est unicum. Eodem modo erit
etiam punctum unicum si sit intersectio quaera
tur tium planotum item si quaeratur intersectio
trium sphaerarum, item sphaerarum duarum
et unius plani, item planorum ductum et unius
phaerae. id est intersectio circuli et rectae
Aut punctum licet duplex. Et hoc quo
intersectio ducrum circulirum determinet uni
punctum hoc videtur natura prius eo, quire
de
que la
punctum d. ex puncto A determinadi e G. D,
et Hd. quae in plano se intersecantur dant unu
punctum. demonstrandum ergo Arius esse
aliquod centrum in circuto, ex quo in plano
et necesse est id facere
antequam sermo sit de recta. qoia
is describatur
hoc ipsum delenn proobandum quoque
nobus
determinatum sit punctum d ex
sitibus Gd. Ad ab uno renae latere
i edem perr
ricr
Gd. HD
E HE