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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 95r, page id 00068193:0191
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ta
n
V
ad
u
na
trs
ibet
a
De Tractu seu spatio et.
altitudinis cum ipto AL) circa axem C. Ajo eso tractum ipsus
AL, ad tractum iptius BM, ut cubus AL ad cubum BM. Nam
punctis M.L. rectae CL (radi crculi) applicentur normales M. N.
LP, ita ut sit MN ad L P. in ratione comporitâ circumferentia  M-
2M M ad circumferentiam 1L2L3L, itemqi spaty, quod deseribit M, ad
iptium quod L, id ert iterum circumferentiae ad circumferentum,
idert in ratione duplicata circumferentiarum seu diametrorum; erit
figura LP.XC proportionalis tractui, per constructionem problenatis, in
prop. 6 Sed trilincum paratolicum M. NC (cujus vertea C, et tan-
si
gens verticis Me) est ad trilineum harabolicum LFC in tripli–
cata ratione CM ad CL. Ergo tractus circuli BM, ert ad tractum
circuli AL (idemque est in eylindris aeque altis) ut Cubus diametri
se
Gnc
BMad Cutum diametri AL
Prop. 10.
Tractus spehaerarum rgidarum, eordem revolutionis angu
los vel intearam revolutionem) absolventium sunt in quadi–
plicata ratione diametrorum.
1.
Demonstratur eodem modo, cum sphaera retolvatur m su
perficies concentricas motus aequaliter distributi, quae sunt in du-
plicata rationo diam etrorum et tractus earum in triphenta
diametrorum, et adeo summae tractuum, seu tractus integer
sphaerae in quadruplicata.
Defin 2. Loxgisroo deserasA, vel S AT71
ABSeLVSI seu Loxgis voOJ R A ers est longitudo lincae
qua ducta involumen mobilis dat tractum. Hnqi spatia per-
So(p.
cirsa sunt in ratione composta voluminum motius et lon-
gitudinum percursarum.
Itaque si Mobile sit linea vel superfieres, reprae centabitur
traitus per rectangulum cujus altitudo ut ipta longitudo tra
 C.
ctus, besis sit linea vel superficies mobilis in rectam vel planan
Itr
ab
sar
2V
d
po
M
t
utit