Of Latitude.
After having well explained the armillary sphere with all its parts, and their use according to the system of Ptolemy, the author goes on to teach the method of taking the altitude of the pole, on which the latitude is calculated; fixing the pole at 0° and the equator at 90°.
“The Polar star,” he says, “is not precisely on the point corresponding to the axis of the earth; but it turns round it, as do all the other stars. In order to know its true position with regard to the pole, it must be observed where the Guard stars[421] stand. If these are on the western arm,[422] the polar star stands one degree above the pole: if they are on the line[423] the pole star stands 3 deg. 30 min.[424] below the pole: if they are on the eastern arm the pole star is one degree below the pole. When one wishes to take the altitude of the pole star, in whichever of the above-mentioned four places the Guard stars may be, the degrees which the pole star has above the pole will be subtracted from its altitude, or those which it has below the pole will be added to it. I have spoken in the account of the voyage of the stars of the Antarctic Pole.”
“The latitude of the place may also be ascertained by the sun’s altitude. 1. If you find yourself between the equinoctial and the arctic pole and the shadow falls towards that pole, look how many degrees and minutes meridianal declination the sun has that day; and this you will subtract from the altitude of the sun which you have taken: afterwards, deducting the remaining degrees from 90 deg., you will have in the residue the number of degrees of North latitude, that is your distance from the equator. 2. If the sun has a boreal declination, in such a manner that the shadow falls towards the south, take the sun’s declination on that day, and add it to the sun’s altitude which you have taken, from that sum subtract 90 degs., and the remaining degrees will indicate your boreal latitude. 3. If the sun is between the equinoctial and the antarctic, and the shadow falls towards the antarctic, observe the sun’s declination for that day, subtract it from the altitude taken, according to the first rule, and you will have the degrees of south latitude. 4. If, when you and the sun are between the equinoctial and the antarctic pole, the shadow falls towards the north, you will add the altitude you have taken to the sun’s declination that day, and act according to the second rule. 5. When you have an altitude of 90 deg., you will be so many degrees distant from the equator as there are degrees of the sun’s declination, and if the sun has no declination you will be under the equator. 6. If you are to the north of the equator, and the sun is in the southern signs you will look what is its declination, you will add these degrees of declination to those of the altitude observed, and as many degrees as are wanting from 90 deg., so many will you be distant from the equinoctial. 7. You will do the same when you find yourself to the south of the equinoctial, whilst the sun is in the northern signs.”