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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 124r, page id 00068195:0247
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Unde intelligi potest res mirabilis, appliculam altitudinus
quilibet assignabili minoris esse mediam proportionalem inter altitu
dinem qualibet dabili minerem, et eam, in qua a applicata basi
quae applicatae suae aequalis est. seu quadratum applicatae esse aequale
rectangulo altitudinis applicalae suae aequalis cum altitudine minima.
Hinc data e altitudine applicatae suae aequali, c. erit
d = C. et b =
Rg4.
Ergo intervalla tangentium ita stabunt:
36
R42 a + 1. = Bg12 +a
hg1ofa
latus currae, minus qualibet nca asigatit
Quod si jam sint Triangula infinita, quorum basis sit β.
altitudines intervalla tangentium, Triangula ipsa erunt.
3c ( 4c(
SC B
etc. Quorum infinita simul
2+ a _43 +  144+ a N4 +  sumta, aequantur;
x
Segmento parabolico, seu residuo semiparabolae Triangulo inscripto
adem to quod si ergo praboli Rectangulum Parabolae incircumscriptum
sit 3. et parabola 2. et Triangulum inscriptum 3 erit
seg mertum Parabolicum 2 - 3 seu 4 - =  = Ac
proinde si semiparabolae altitudo et et applicata sit c. cum
Rectangulum futurum sit c. et rarabola et Triangulum 
et Parabola 2C erit segmentum 2C c - 4c 3C
Ergo C- erit omnibus illis Triangulis simul sumtis, dividatur
utraque aequationis pars per c. Erit E=
si tamen B. maximum horum se
ultinum (nam ininfinitum progredi
alioqum licet) definiatur.
EA 
a
+dC
Rtea
et.
c are
ha 4c
14 +1 146+L
t
8+ a 3 2+4 Egsta
ota
et