Figure 1: A View of Amsterdam from the North West, Rembrandt Harmensz. van Rijn
In order to compare the the skylines of Amsterdam and New Amsterdam and their general representations in the seventeenth century, we must first choose which depictions of the skylines of Amsterdam and New Amsterdam are most representative of the whole range of depictions of the time.
Rembrandt is a quintessential Dutch etcher and painter, and thus his work is a good standard to represent the whole body of illustrations of Amsterdam in the 17th century. This etching is from around 1640, which is about 15 years after Fort Amsterdam was built and the island of Manhattan became truly inhabited by European settlers. Figure 2, below, is a contemporary drawing of New Amsterdam, from around 1643.
Figure 2: Novum Amsterodamum, Laurens Block
Both of these depictions of the cityscapes of Amsterdam and New Amsterdam are line drawings, and in Rembrandt’s case, were probably not meant to be the final illustration, but rather a rough sketch or guide for a later painting.
When examining the skylines in both of these drawings, there is one feature which the eye may be drawn to which is almost exactly the same in form: the windmill. In fig. 1 a windmill can be seen to the right of the middle, jutting up abruptly out of the otherwise uniform height of the surrounding buildings. The only other form in the skyline which is about the same height is a church steeple, which serves to balance the composition by being slightly left of center. At other points in the skyline, smaller, less detailed windmills can be identified, all sharing a very similar form with the central windmill.
In fig. 2, a windmill can also be seen, but is featured less prominently, as it is in the far left of the drawing, and seems to be placed farther towards the horizon line that most of the other buildings in the skyline. In fact, this windmill seems to be set apart from the skyline itself, and is instead a part of the natural horizon, because it is separated from the rest of the buildings by open land and trees. There are also two other, smaller windmill figures, which are placed even closer to the horizon line, and are scaled so as to appear very far away.
In Rembrandt’s drawing, the windmill is very obvious, as well as being conveniently placed for aesthetic value, because it serves as a dual focal point along with the church steeple. These structures serve to bring the eye inwards but not to centralize it on one object. Because of this convenience, it is possible that the placement and size of the windmill may not be supported by the actual skyline of 1640s Amsterdam. In the case of fig. 2, the inclusion of the windmills may have less to do with aesthetic value and more because of symbolism, and an attempt to connect the isolated settlement to the home country for which it was named.
A more general dimension of the drawings which is similar is the composition, or the amount of space each section of the drawing takes up in the visual field. Both share three similar compositional components: the sky, the earth, and the water. However, fig. 1 also has an additional piece of land closest to the viewer, which gives the appearance that the view is being seen from a physical location. Fig. 2, on the other hand, has only water up to the viewer, which conveys the feeling of the viewer hovering above the water, without any concrete location.
While the view may have been sketched from the vantage point of Brooklyn, the lack of physical markers change the perception of the viewer. It is important to note that other sketches and painting from the era include land directly in front of the viewer, similar to that in fig. 1.
Harmensz. van Rijn, A View of Amsterdam from the North West, etching,
circa 1640, http://www.christies.com/lotfinder/prints-multiples/rembrandt-harmensz-van-rijn-a-view-of-5150527-details.aspx.
 I. N. Phelps Stokes, Victor Hugo Paltsits, and F. C. Wieder, The Iconography of Manhattan Island, 1498-1909 Compiled from Original Sources and Illustrated by Photo-Intaglio Reproductions of Important Maps, Plans, Views, and Documents in Public and Private Collections, vol. 1, 6 vols. (New York: Robert H. Dodd, 1915), https://archive.org/details/iconographyofman01stok.
 I. N. Phelps Stokes, The Iconography of Manhattan Island, 1498-1909 Compiled from Original Sources and Illustrated by Photo-Intaglio Reproductions of Important Maps, Plans, Views, and Documents in Public and Private Collections.