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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 131v, page id 00068197:0262
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Votabile Theorema Transfo
matorium curvarum.
fingularis dimetiendi motus
EBBB arcus circuli, EC ejus tangens AB radius
trianus A. C1d ad triangu. A1
rad
2B
eL quadr. HiCad
cad qo
ut quadrat A1 C, ad quadrat A1B. et similite
quadrat triangu. A2C id ad trianque
A2BZB. ut quadrat. A2C ad qudt
ad quadratum radii A2B.
Ergo aggregatum triangulorum AiC1d. + A2C2d etc.
otrigngulum
ad e hoc est spatuem A+C3C. (quiae quae supersunt
sunt infinite parva e negligenda) est ad sectorem
AIB3B ut qu summa secantium quadrulorum
ab A, C  ab A2 CidZC. seu summa quadintirum a
ecantibus est ad summam quadratorum girdintorum
padarcus
la radiis ad arcus, ut triangulum 1CA3C
ad sectorern 1B A3B.
Generalis est haec methodus quae cunque lprea loco C8 assum atqu
ut positis F loco C et G loco d. erit summa quadratorum
omnium AF ad arcum agealis applicatorum ad syctorem
D.BA summam omniam quadratorum radiorum ad arcum
applicatorum, ut fector trilineum 1FA3F ad sectorem
circuli BA3B. Z si AF AB. AC. AF sint continue
propvrtionales ope curo tunc ex data quad ratura figurae ad
curvam FF, habebi (Saltem ex posita circuli) habebitur apeam (303
secantium adarcum ermnt etiaque A3k singu A3I tangens et E3h. a
continnt proportionales, sit AH, X. et A3K  B. AE, a. ASi CA3C: A3K:: AE. 
seu A3B f2av-bV: a = va A3Frgo a. p a ∞
A
t
eu A3H aequra v- W , () a B Aaqu. Z et 3C7 +i seu Co0gu a  + V.V
 et
poterit nbeniri relatio inter
2a0. vb ela B, rav. 
AMa unde