232 GEOGRAPHY AND ASTRONOMY. The latitude of a place is its distance from the equator toward the north or south pole measured by the degrees on the meridian. So the latitude of London is 51 degrees 32 minutes, that is, about 51f. A place is said to have north latitude or south latitude ac- cording as it lies toward the north pole or south pole in its dis- tance from the equator. So London bas 51f degrees of north latitude. The elevation of the pole in any particular place is the dis- t nce of the pole above the horizon rf that place measuredby the degrees` on the meridian, and is exactly equal to the latitude of that place : for thepole of the world or of the equator is just so far distant from the horizon as the zenith of the place (which is the pole of the horizon) is distant from the equator. For which reason the latitude of the place or the elevation of thepole are used promiscuously for the saine thing. The truth of this observation, (viz.) that the latitude of the place and the poles elevation are equal, maybe proved several ways ; I will mention but these two. See figure iv. Let n c o bathe horizon, z the zenith, or the point over Lon- don, E z the latitudeof London 51f, P o the elevation ofthe north poleabove the horizon. Now that E z is equal to P o is proved, thus. Demonstration L The arch z r added to E z makes a quad- rant, (for the pole is always at 90 degrees distance from the equa- tor.) And the arch z r added to r o makes a quadrant, (for the zenith is always at 90 degrees distance from the horizon.) Now if the arch z r added either toE z or to r o completes a quadrant, then E z must be equal to r o. Demonstration H. The latitude E z must be the same with the poles elevation r o : For * thecomplement of the latitude, or the heighth of the equator above the horizon E n is equal to the . complement of the poles elevation r z. I prove it thus : The equator and the pole standing at right angles as E c p, they com- plete a quadrant, or include 90 degrees : Then if you take the quadrant E c r out ofthe semicircle, there remains r o the elevat- ed pole, and E n the complement of the latitude, which complete another quadrant. Now if the complement of the latitude added to theelevationof the pole, will make u quadrant, then the coin, plement of the latitude is equal to the complement of the poles elevation, and therefore the latitude is equal to the poleseleva- * Note, The complement of any arch or angle under 90 degrees denotes such a number of degrees as is sufficient to make up 90 ; as the complement of 50de- grees is 40 degrees, and the complement of 511 is 351 degrees. And so the com- plement of the sine or tangent of any arch is called the co -sine or co-tangent : So also in Astronomy and Geography we use the words co-latitude, co-altitude, co-de- clination, &c. for the complement of the latitude, altitude, or declination, of which words there will be more frequent tue among theproblems.
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