 If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different affection, the hypotenuse will be greater than a quadrant. Let ABC be a right...  Elements of Trigonometry, Plane and Spherical - Page 74by Edward Olney - 1872 - 201 pagesFull view - About this book
 | John Playfair - Circle-squaring - 1819 - 350 pages
...right angle. In the same way may tho converse be demonstrated. Therefore, &c. QED B \ PROP. XV. If the two sides of a right angled spherical triangle about the right anglt be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...than a right angle. In the same way may the converse be demonstrated. Therefore, &c. QED PROP. XV. If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant; and if they be of different... | |
 | Euclid - 1835 - 540 pages
...before, and BCA is greater than ECA, that is, greater than a right angle. QED PROP. XIV. FIG. 9, 10. If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...and BCA is greater than ECA, that i«, greater than a right angle. QED PROP. XIV. FIG. 9, 10. , If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different... | |
 | Mathematics - 1836 - 488 pages
...than quadrants, the opposite angles will be greater or less than right angles, and conversely. XV. If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypothenuse will be less than a quadrant; and if they be of different... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...than ACE, or than a right angle. In the same way may the converse be demonstrated. PROP. XV. Iftkf two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...greater than ACE, or than a right angle. In the same way may the converse be demonstrated. B PROP. XV. If the two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they be of different... | |
 | John Playfair - Geometry - 1855 - 334 pages
...greater than ACE, or than a right angle. In the same way may the converse be demonstrated. , PROP. XV. two sides of a right angled spherical triangle about the right angle be of the same affection, the hypotenuse will be less than a quadrant ; and if they bt of different... | |
 | Edward Olney - Trigonometry - 1885 - 222 pages
...are of the same species; two which are 120°, and 48°, are of diiferent species1 15- Ifapier*s Five Circular Parts are the two sides of a right angled...conventional, and are applied exclusively to right angled trianglesILL — In a spherical triangle ABC, right angled at A, the sides b and e, the complement... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...are of the same species; two which are 120°, and 48°, are of different species. 1 15. Napier's Five Circular Parts are the two sides of a right angled...spherical triangle ABC, right angled at A, the sides b and «, the complement of hypotenuse a, and the complements of the angles B and C, are the circular parts.... | |
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