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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 113v, page id 00068196:0224
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in sectore curvitineo
in segmento curvilineo
in polygonis (inscribendis per triangula
maxima in segmentis, et polygonis
Circumscribendis per tangentes ad triangulorum
apices ductos. put pri designabimus
puncta in curva, seu apicesra
adscriptionis per praesicnumeros 1, secundae per praefivaseZ
nntias per 3; ita polygonum inscriptum et circumscriptum
seu condscripta ha ejuidem numeri laterum seu polygona duo
coadscripta haboet eandem notam praefixam, deslingui
autem possunt per affixam, quae pro numeris punctis in curva
sit par, pro punctis concursus tangentium extra curvam sit impar
ita polysgontm primum inscriptum K. AB
kR 29
secundum
Ztium
circum scriptum K. A 11. B
K0. 3624. 3832
Ita polygonum primum inscriptum KAB
ita polygorum primum inscripsum R.
KB22IH.
secundum
tertium
quartum
K. 134. 22364
K. 10. 25. 27. 12
habent latera in scripta
Fg K. Hao324OI. 41. 36. 4 4)
K 10.39 X17133 15. 12
primum circomscripsum K. A11 B
ila polygona inscripta primum secundum tertium quartum
habe et sogm
1
polygona circum scripta primum secundum 3tium quartum
H. 13. 125. D
a
K, H. 31. 39. 311.313,B
P M. H. 4G. 9 19. 4ul. 423 4r5. 127. 429
med Geom. inter A et L
.
velC.
et ita porir
B et M
m med Harm. inter B et L
1
et ita porto
C et M
unoplum glam circum scripta latera unitate plura respondentibus in scriptis
2
habent latera circumsripta
Habemus relationem inter areis pelygonorum conicorum ad sectores
ectoribus adscriptorum; desiderantum perimetritt ergo in hos
Nitit possumus autem ex positis commude invenire per theoremq asvod
ergo inqui rere operae pritium est
ex datis duobus ateribus Trianguli, et area exhabet tertium abus. sint
trianguli latera l, m, neit arflmn, 1+m.n, lmta, L+mn
in area a
ponamus dari latera L et m, fiet
a - (U + mm F 2 (( p + Umm))
sit arca pp fiet 16 = 2Umm - 17
= Ha.
=n2
Eu nn
punctum qo) secantur bisecantur subtensa, denominatur nota quibus puncteres
2mmnn
quoquibus biecentur as circumprisita polygom proxime altioris, eb solum
bisecta intelligatur in 12 ut paralleta ei 23, 24bfrcatur 23. 25 bisecatur in 22. Et A 2
Ex in Triangulo
t
eiscrimine, ut praefiva sumatur uniate
H 12, H H. 12. 12 ex lataribus H12, 11. 2, et are a trianguli D Hna2 habetur tertium latus n,
et H. 22, 1. 22 b isecabuntur, in 24 et 26
quod duos habet valores pro dubus radicitus, H. V. et E. it data enim et relatio sunt eadem pro utoq
vel
tutque majus  i. 1 = sUtmm +  Cumm-4p)) et minus H. 1 = eCU+mm- SUmm- 4 p +)
vel 1. 12