De proiectione geographica de Lisliana in mappa generali imperii Russici usitata

which linelets Pp and Qq, even though they are circular arcs, can here be looked upon as straight lines normal to the meridian A B.

§. 8. Let a straight line p q O now be drawn through points p and q, meeting the produced principal meridian A B at O; and this straight line O q p will represent the meridian next to the principal one, removed by one degree according to longitude: in the same way, all the remaining meridians can easily be drawn from point O. However, for finding the point of concurrence O, let Pp — Qq : PQ = Pp : PO be done; that is: δ (cos. p — cos. q) : q — p = δ cos. p : PO, whence it becomes $PO = \frac{(q - p) \text{cos. } p}{\text{cos. } p - \text{cos. } q}$. Thus, if p = 50° and q = 60° be taken, the interval PO = 45°. 1' will be found. Since, therefore, point P is 50° distant from the Equator, the distance of point O from the Equator will be 95°. 1', and thus it will fall beyond the pole of the Earth at a distance of 5°. 1'.

§. 9. Since, therefore, that point O, from which all meridians are drawn, has turned out different from the true terrestrial pole, from which all meridians emerge on the sphere, a most absurd representation would naturally arise in regions close to the pole. But because it is assumed that no places beyond the 70th degree of latitude are shown in the general map of the Russian Empire, provided that the error for this latitude does not turn out enormous, that aberration will be easily tolerated. Having found this point O, first let a circle be described from it with interval O P, the periphery of which is divided into parts = δ cos. p, equal indeed to the degree of this parallel, and the straight lines drawn from that point O through the individual points of division will give all the meridians to be drawn on the map. And in this way, all circles described from center O through individual degrees of the meridian will give all the parallel circles to be constructed on the map, which will be so arranged that for the two latitudes p and q, their degrees of longitude maintain the true ratio to the degrees of latitude. In this way, therefore, the grid for such a general map will be easily constructed, and once that is done, the inscription of all the Provinces will labor under no further difficulty.