BİRİNCİ FEN · ÜÇÜNCÜ BÂB · YEDİNCİ FASIL · Birinci Madde
The First Article
States that the surface of the earth is divided like a chessboard with lines of latitude and longitude, and that determining these lines allows for comparison of the locations, directions, and distances between cities and regions on Earth.
O esteemed one! Know that astronomers and geometers have drawn eighteen meridian circles (daire-i nısf-ı nehâr) upon the globe, along with the equator line, and eight latitude circles (daire-i arz) north and south of it, assuming this to be so. They have then divided each of these circles into three hundred sixty degrees in this manner. Thus, the longitudinal degrees are determined by the meridian circle, and the latitudinal degrees are established parallel to the equator. The distance between these two circles has been defined as ten degrees – by way of calculation or any multiplication – according to chess reckoning. The beginning of the climatic latitude is considered to be the latitude of the waist, two sides of the equator. In this case, one line becomes the northern latitude and the other the southern latitude. The starting longitude of the climate and the starting longitude of the waist are known as the arc commencing from the intersection point of the meridian circle and the equator of the Islands of Khalidat in the accepted Western Ocean, between the intersection points of the assumed waist’s meridian circle and the equator. The latitude of the waist is defined as the arc formed between the zenith (head) point and the equator on the waist's meridian circle. This latitude of the waist has been found to be equal to the altitude of the pole in both the south and north, and to the depression of the opposite pole depending on which side is taken as a reference. By determining latitudes and longitudes in this way, the locations of cities and regions on Earth are ascertained, their directions known, and their approximate distances from one another are understood. It becomes clear whether two cities lie to the east or west, north or south of each other.
For example, our beautiful city of Erzurum is said to have a longitude of seventy-seven degrees (from Khalidat Islands) and an approximate latitude of forty degrees (from the equator). Egypt has a longitude of sixty-three degrees and a latitude of thirty degrees. Egypt lies southwest of Erzurum. It is known that Erzurum lies southeast of Cairo, because Egypt’s longitude is less than Erzurum's, placing it to the west, and its latitude is less, placing it to the south. Similarly, since Erzurum’s longitude is greater than Egypt’s, it lies to the east and north of it.
The method for finding the distance between any two cities is as follows: If the latitudes are suitable but the longitudes differ, then the difference in longitudes gives the distance between them, as with Erzurum and Tokat. And if the longitudes are the same but the latitudes differ, then the difference in latitudes gives the distance between them, as with Erzurum and Mosul.
If two cities have different latitudes and longitudes, then their distance is the hypotenuse of a right-angled triangle, where one side is an arc drawn from the city's meridian circle and the other side is an arc drawn from the city’s latitude circle. This arc’s hypotenuse is the arc between the two cities on the circle passing through both zenith (head) points. For here, we know the measure of two of the angles in this triangle – namely, the differences in longitude and latitude – so that with these two known sides, it is easy to find the unknown side which is also the hypotenuse. This is the distance between the two cities. For example, the difference in longitude between Erzurum and Cairo is fourteen degrees, and the difference in latitude is ten degrees. The sum of the squares of ten and fourteen is two hundred ninety-six. The square root of this sum is approximately seventeen. Therefore, it is known that the distance between Erzurum and Cairo is seventeen degrees. We can find the distances for other cities using the same method. This method can also be used to determine the direction of qibla, as will be explained in detail in a subsequent article.
The diagrams of these circles will be provided at the end of this section.