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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 262v, page id 00068194:0524
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Trilineam
sed integram aream aliquam inter curvam evolutione.
descriptam, curvam evolutam, et filum describens
comprehensam metiri non ita facile est exempli
gratia totam 1E3A. AIE vel 1D+ AIA. Doxtensa e
Ponatur ipsae 1DLR, 3C+ C, 4 B1 B, 3A A applirari eorum
ipsi 1E5A, unde extiguia C fiet fig. D, et quia ipsae ,
AD2D, 2C3C, 3B+B, +A5 A, sunt progressionis Arithmeticae
ipsis 1E2D, 1E3C, EaB, 1ESA. existentibus.
E
Arithmeticis, patet ipsa puncta ejudem sili seu rectae describentis infig.d
tadent iterum in rectam, in fig. 3. Et figura
Consideremus potius arculum seq
Et area figurae, D aequabitur areae
figurae D.. Sed harum
duarum figmarum comparatio
non readit, dimensionem
A
faciliorem.
liquem indefinite parvumr 
1A 2 esse ad arculum A3A, et 2t
aliquem ut BA4A, esse ad arculum sequentem, 4 AsA, in composita ratione.
ex his duabus radii ratione radii, DA ad radium 1E4A; et ratione anguli icre
3A1D+A, ad angulum , D162D seu anguli complentis est autem angulus
IEF 1C 1d2C complementium ad duos rectos, anguli 1C1D.E, qui est angulus
a duobus curvae polygonis comprehensus. Itaque si circu serentia
semicircum ferentia circuli extendatur in rectam, aetaciis aividatur
hac recta in partes  qualescunque repraesentantes angulos, lefaciunt
107
inter se recta latera polygoni infinitanguli curvae aequenalentis; et
quod curve ABCDE aequi vatet, secundum eum modum, quo curvae puncta
infinita assignare placuerit; et his angulis, seu partibus rectae
infinite parvis applicentur radis, cu seu fila; seu radii A
AE cuilibet aug
lo respondentes; area hutus curc figurae
natae respond ebit proportione, arcubus, 1A2B, 1A3A, A4A; e
quoniam  Triangulum 3A1D+A, est ad triangulum 4AIE5A, in composita
ratione  ex rationib anguli 3A.D A. 1C 1D 2C, ad anguuum 1D1E2D, et
ratione duplicata radii iD3A ad rad. 1E4A, hinc qud summa
quadratorum a filis ad angulos applicatis, seu momenta
figurae inde untae, ad axem, respondebunt proportione areis
trilineis 1E3AIAIE, .DAAIADD, iC3A.A. C, ec.
1
Hinc si data Figura, invenir. (qua fingantur fita angulis
applicata) inveniri posset figura e ei respondens, seu 
Inveniri curva, cujus si anguliq sumantur aequales. vel responde tes
oudifferentiis abscissarum datae figurae; arcs elementa curvae quaesit
respondeant differentis ordinatarum datae figurae, tunc
sfita ordinatae figurae datae respondebunt filis figne
seu sarcu it ut AB, AC, AD, HE, t seu arcubus curvae ABE
et areae figurae datae respondebunt arcubus cuvae evobatione de scrplae,
1A2A, 1A34, 1A4A, A5A, et denique areae hilinea momenta seu so da
exaxe, figuae datae respondebunt tilineis figurae quaesitae O.