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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 3
# Folio 13r, page id 00068205:0043
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conctituunt e e consconene cum MX ~KH item ML e LG seuo sint aegnaelaae conctar
i guantitati Cunua L3 erit lig grimum ascuptum) portio gurobolae cujus cantium
et
seu forus in M:
Porro dum filum hoc jam ullarius concirite evolvi semper NdNF aequantsaacti
d
e
lincia _M M2 ex hypothosi unqus ad punctium Oubi OtdBB rectam linuam esi
ed
ciant et go consequene eum  dN, itam 0, DE el: scurs conctanti quanti
e
tati agnalae, errva ONL erit patio Larabolae (ea as cumplin aijus docqii 
e
en
Eadem ratione demonctrats cunnam A0 esta gambolam cujus Jorus in B, quia ascripat
verncto ad libilum B hiirc recte BZd SD reuiper sunt aegualac tabus rectia B, cem,
Mir. hoc E conctanti quantitati.
sic in prascnti figura omnes MB, NN, oH RW c: denotant incidentes rodior solis. Porro in hisce portionibus Parabalarum A0, OL, L hc E in toto Curivo ADL3 quoe
ax ecolutione hrium lineanino BCM , M3 descibits; dangene seug agnalaae
aeroulor num incidente daflexa facit ( 2d: ascungti) jam vero hoc idem seuper
it solum cumtrac recte ascumphe; eed guotuu int et cujuscuus tongitudinia
Op
e
ut facile patat eis modo ontensae: ad niminum totidem portionec Parabolarum
C
C
hinc describent e gd proinde in integra seure evoluta tancentae aequalae angulas
C
cum recta incidente ed viflexa faciunt: Patet e consegume gdhoc idem fiit in eo
e
e
ns
lygono indefinitonim latem hoe e5axio: vd: n fg:) eunva AHE xquo
e
~F.
erolutione describate quoque dargenae L angulorx tampet aegnalee afficiet LHR
c.d
dHS cum incidente SH D reglexa HA: A. E. D.
Propositio Eda Throremi
i curva quodumque data (vid: a Fi: in precedunti proposit:) AHE et haugante L; formet
et
t hinc alia lno BRE tric conditonibus; ut Anguli LHR ad HS vint continue aequalea
Omnie incidnbas SH epeudiculanae ad CE D rflaxa HR Tanpentae teugen huna BR in
alioua puncto ex: gr: R: Diro Curvam honie BRE evolitam esce:
3d
Demonctratio
2 figi eit data Cnno ONz (vid: afir:) quam evolutam ut
E
cumus; formets hinc jixta a defin:) Cumva ex eroentiope
desaigta EFGHI Stunc ex hypothisi limae MF, LG, KH
equae ut parum a se invicem dictantae concigienda
liat ne hac in figura aliter exgrescum quo hac
etiam alignomudo ipsie omlis srubjiciants) erunt egindicular AI; jam F8, GC, AD ieflaxae io
dispositae cunt ut anguli inaidentra d reflexioniae sint aeguales; qua a poinde linrae SB, GC, H (ut
an
dex
facila ot) se intersecobunt dlinea intersectionia art NZ qua (juxta 5 axio2) ut labus Pobus gone
coiiigiendam cujus omnia latera Curvami BNR2 scu euolatum constituunt; Hisca sic positia (vidal
e
alcumalsjam recipron cima ex avolutione descugta (eodem nimir: quae aubea e erotutum et
diformata efotri tanguam dati et ascumals anc, al, at aequalas AM, AL, At e fiant hinc qp
demularae infiles, tete, qua necascano aeguatae erun lincie  in 2fig.) MF, LG, KM Ccum etehi eudem qua
linca quam ee GHi nositionam) ducants jam linca f.b, gr. ad ita ut anguli incidentia dreflario
di
nie cint agnalac (edcerti fieri polecti cum cuvno esga  cum dangtitibus postionie datas ta lincai
e
He,eoho; ancascano aegnalaae ne linue fB, GC,  n Lf. Ccum utrogius eadem daguoam ascimipte ad
aidem hic d adnalia itecescario inveniante de consignemae intersectionit linem is, egnatia erit Ne