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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 18
# Folio 8v, page id 00068089:0016
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dependet quaesita sit Transcenders secundi generis, ipsa
quasca eit Trscendens tertii generit,  sic deincepus Evem
plum unum sufficiat ubi generatrix estrete transcendent
primi glneris ( sed sapissime ostendi fieri, potest, ut Tran
cendens seundi genens non vel astioris non nisi in speciem sit
talis qupossitque reduce adeundinturam generis inferioris
uti supra ostendi summas summam sterumque freduci
passead summas simplices +)
probl. 20 quaelitur ACFola ut posito AB, X. et BC, y
et E, a. sit et dux =0 sit 2 ax ddys dius XX ddyddus =
du  quaeritur natura suvae propositan etadus
alxdx: Hrax  xX) filt adque = dex  saclx: s(rax XX) quo summa
pendet a rectificatione sccrvo circularis, idea fiat (fius Q) mcr-
calus dFG diametto DG= 2C et absciudatur dH_ X, eut areus dF
= adx: Spax -XX), is sit Set fiet adq = sclx. curva itaque
sie construitur (fig. 9) ductis perpendicularibus ik LN sumatur
IL, a. et per L ducatur parallela Lq appliceturque ad IN X ecta
NM, 5. progenerabitur cupea )M i problemate p acedenti
explicata quae Transcendens est. sumto ergo rectangulo LP, a
aequabi fta adspa aequante spatium imN, eret punctum
Secursus B in curva quaesita 10
probl 21 datur Curva AE Datur curva AE, quaertur
curva AC tatis ut perpendicularis de sit aequalis applieate
dE. fig. 10 sit AB, X. BC, y. Ad, m. DE n = dC. quia
Dd: D do = DC: DB, id est am: dn = n; Bd fiet Bd = ndn:
et AB = m - ndm idm = X Est autem quadratum DC = qu. Bd
=qu. BC id est nn- nnananidm dn) =gu et proinde
quia AE est curva data, quantitas an: am semper peraequam
tionemsedestinet, adeo ut AB et BC in quantitatibus Algebra
ieis proveniunt. Hincquotrescunque AE est cuva Algebraica
eNiam AC ergt talis sit v.g. AE parabola, parameter a
Ad m, d Ad, m. dE, n = sam, erit AB seu X = m- La
et ax = yy - =aa unde curva quaesita ACc est etia
grarabola, et quidem eadem cum isa AE sed cujus verlex es uttra
prunctum A. distantia quarta partis paramethi. Arg. 1
de Corculis osculentus separetur, et probsema solor possit supposita quadratara Hypertilae
S