Overlay plot and histogram in R with ggplot - r

Question

I am trying to overlay a Plot and a Histogram in R, usign the ggplot2 package.
The Plot contains a set of curves (visualized as straight lines due to logarithmich axis) and a horizontal line.
I would like to plot on the same image an histogram showing the density distribution of the crossing ponts between the curves and the horizontal line. I can plot the histogram alone but not on the graph because the aes-length is not the same (the last intersection is at x = 800, while the x asis is much longer).
the code I wrote is:
baseplot +
geom_histogram(data = timesdf, aes(v)) + xlim(0,2000)
where v contains the intersections between the curves and the dashed line.
Any ideas?
edited: as suggested I wrote a little reproducible example:
library(ggplot2)
xvalues <- c(0:100)
yvalues1 <- xvalues^2-1000
yvalues2 <- xvalues^3-100
yvalues3 <- xvalues^4-10
yvalues4 <- xvalues^5-50
plotdf <- as.data.frame(xvalues)
plotdf$horiz <- 5
plotdf$vert1 <- yvalues1
plotdf$vert2 <- yvalues2
plotdf$vert3 <- yvalues3
plotdf$vert4 <- yvalues4
baseplot <- ggplot(data = plotdf, mapping = aes(x= xvalues, y= horiz))+
geom_line(linetype = "dashed", size = 1)+
geom_line(data = plotdf, mapping = aes(x= xvalues, y = vert1))+
geom_line(data = plotdf, mapping = aes(x= xvalues, y = vert2))+
geom_line(data = plotdf, mapping = aes(x= xvalues, y = vert3))+
geom_line(data = plotdf, mapping = aes(x= xvalues, y = vert4))+
coord_cartesian(xlim=c(0, 100), ylim=c(0, 1000))
baseplot
v<-c(ncol(plotdf)-1)
for(i in 1:ncol(plotdf)){
v[i] <- plotdf[max(which(plotdf[,i]<5)),1]
}
v <- as.integer(v[-1])
timesdf <- as.data.frame(v)
# my wish: visualize baseplot and histplot on the same image
histplot <- ggplot() + geom_histogram(data = timesdf, aes(v)) +
coord_cartesian(xlim=c(0, 100), ylim=c(0, 10))