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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 10
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Generaliter Datu figura BDB quaeritur curva cC
talis ut sitit arcus iC 2C, 2C3C, ut spatia 1D1B2B. D.d,
2D2B3B3D2D posito puncta 1D. B. 1C, et 2D2B2C, ex
esse in eadem recta, et has rectas semper esse parallelas,
et si placet dxi BB normales.
Quaeritur ergo relatio inter AB absissas, et BC ordinatas hujus
curvae. i obscissae AB siat Z. A Ordinatae BC sint .
V ax 1C2C
a aut z(3C
Axem cpAB constituta sit figura
plata constitutum sit quadcilineum DBBd
ns
ut arcu DD, ordinatis IB duabus,
et parte axis B
comprehensum, Graeritur curva haic figurae
proportioralis, ita, ut si ordinata DBsiopus
producta alteri cur occurrat in E
et ex E edacta noraralis se ipsi DE, seu parallela
ipsi axi AB, curvae quaesitae CC occurrat in C
sint arcus 1erE, 2C3E proportionalis spatiis
quadrilineis, DIB2B2d1d 2D1B36302d
per punctum fixum A educta recta axi AB
normalis secet ipsas CE (si opus productas in F.
et ex punctis C educanturl ordinatae
m AB.
sam AB vel FE sit X. 1B. B (sire 263B)el
1Et (sive 2E2t) sit e
FX. sit AB vel FE
dx 1B2B vel. EiL
ut 2B3B vel 2E2l
BD
BE vel AF vel GC
dzul BAx. 11.E vel 1F2 F vel . C.M
auF2HSvel ZFBF vel 2C2M
posito a esse
constantem
D AG vel FC C 1C2C
d9  4 1G2G vel H2C
a
a
aequo
2) K ax
Posito jam puncta 1D2D. 3D. etc. distaentiam habere infintre indefinite parvam
es: a
eodemque modo et caetera, tunc quad rilinea D.B2B2D1B aequipollebiit rectangulis
ut 1D. B2B. et recta arcur, C2C equi polle b rectis, et quia haec prquadrilinea
deb vel haec rectangula, nempe 1D. B2B, 2D2B3B, proportionalia sunt arcubus
sive rectis. C2Cp2F3C, et eadem rectangula proportionalia sunt ordinatis
1D1B, 2D2B, ob communem altitudinem, seu ob 1B2B, 2B3B aequales, igitur
rectae 1CrC, 2C3C, proportio nalia esse debent ordinatis 1B1D, 2B2D. sive
recta indefinite parva (vel etementum curvae CC) nempe 1C2C erit ad constam
tem indefinite parvam 1B2B(vel BB, quae sune aequales) nempe dx, , ut
hatulimus aegu. I  arie hadebimus aequationem 33 dx aequ.
aa
t paa
nempece aequ. deue + a
aa
aequatione divisa per dx fiet 3y aequ. v0 +coco. Haec aequatio
aa
Sed eadem 1C+C  habetur per 1C,M et 1M2 C. equia quadratum il C aequale aequatinibus 12. 3.
est m quadr, C.M + quadr. 1M2 C quorum cum salores paulo ante posuerimus
vo
ordinata, Bid est ad constantem rectam a. eritque. 1C, C ext 2C3 C aequ 3 dx aequ. c.
x aequid
4)