Mathematics; Compiled from the Best Authors and Intended to Be the Text-Book of the Course of Private Lectures on These Sciences in the University at

Mathematics; Compiled from the Best Authors and Intended to Be the Text-Book of the Course of Private Lectures on These Sciences in the University at

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1801 edition. Excerpt: ...secant. Therefore, &c. Which was to be proved. equator, which set off on the meridian. These distances are found in a table of meridional parts to each latitude, where it is to be noted, that if the equator be graduated into minutes, the meridional parts are to be taken as in the table 5 but if it be divided only into degrees, the meridional parts must previously be reduced to equatorial degrees by dividing by 60. THEOREM III. The proper difference of latitude: The meridional difference of latitude on Mercator's chart.:: The departure: The difference of longitude. Cot. Demonstration. Let there be taken an indefinitely small put of an oblique rhumb on the globe; then, radius: cosine lat.:: difference of longitude: departure. And secant lat.: radius:: difF. long.: departure. Or, departure: radius:: difF. long.: sec. lat. Now, any definite part of the rhumb may be conceived to be composed of a number of such indefinitely small parts, crossing a like number of parallels of latitude. Therefore, the sum of all the departures, or the whole departure answering to the definite part of the rhumb: the like mul- tiple of radius:: the sum of all the differences of longitude corresponding with the departures, or the whole difference of Ion. gitude made: the aggregate of the secants of all the latitudes. That is to say, the departure: difference of longitude:: the multiple of radius answering to the number of parallels of lat. crossed: the aggregate of all the secants of those latitudes. Again, let the, same indefinitely small part 'of the same oblique rhumb be taken, and, by Theorem II. secant lat.: radius;; indefinitely small part of Mercator's meridian in that latitude, or the; meridional difference of latitude: like part of the painik-l, or prshow more

Product details

  • Paperback | 84 pages
  • 189 x 246 x 4mm | 168g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236583574
  • 9781236583574