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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18B
# Folio 157, page id 00068192:0157
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iphius AE, ad tractum ipsius BM, ut
cubus AL. ad cubum BM2. Nam punctis
M L, rectre CL. fradii circusi) applicen
tur normaLes MN, I. P itauF. sit MN ad
L. P in ratione composita circumferen-
Ha M 2M 3M ad circumferentium
IL. 2L. 3L. item que spatii, quod dederi-
bit M, ad spatium quod L, idestiterum
circumferentiae ad circonferentium
id est in ratione dupdicata circumferenti
arum seu diametrorum, crit figura L. PNC
proportionasis tractui, per construeti
onem problematis, in prop. 6. Sed
trikineum parabolicum M W C(cujus
est
rextex C. 8 tangens verticis M C) ad.
trisineum Parabolicum L. DC intri
plicata ratione CM ad CT. ergo
tractus circusi BM est adtractum cir
cusi AI. (idemque est in cxLindris aeque
altis) ut (ubus diametri BMI ad cubum
diametri AL.
Pro
Fractus sphaerarum rigidarum, eos
dem rerolutionis angulos (res integram
rerosutionem absolventium sunt
in qua drupsicara ratione diame-
trorum.
ehonstratun
Demonstratur eodem modo cum
Sphaera resolratur in superficies con
centricas motus aequaliter distribuli,
quae sunt in duplicata ratione dia=
metrorum H tractus earum in tripti-
cata diametrorum, S adeo summae
tractuum, seu tractus integer sphaerae
in quadruplicata
Definitio 2.
LOGISVDO DERCVRSA, VeI.
SpA SIV ABSOLVdI sev.
CAda P
SRAC3VSdA est Longi
tudo Lineae, quae ducta in rolumen mo-
bilis dat tractum. Itag spatia per
cursa sunt in ratione composita vosu
minum mobilis et Longitudinum percur
sarum.
Itaque si mobidie sit Linea V et
superficies representabitur bractus
per rectangulum cujus altitudo sit
ipsa Longitudo tractus, basis rbits
mobilis
sit Linea rel superficiesn rectam.
vel planam extensa. Cuod si mobile
sit solidum, poterit ei eRiberi pLa-
num proportionate quod in Longitudinem
percursam duetum represent et tractum
prop.