 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...for bases, are together equal to the spherical wedge whose angle is BOD. PROPOSITION XVIII. THEOREM. The area of a spherical triangle is equal to its spherical excess multiplied by a tri-rectangular triangle. Let AB 0 be a spherical triangle : then will its surface... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...that the volume of an ungula will be expressed by twice its angle. PROPOSITION XXXII.— THEOREM. 99. The area of a spherical triangle is equal to its spherical excess (the right angle being the unit of angles and the tri-rectangular triangle the unit of areas). For,... | |
 | Edward Olney - 1872 - 270 pages
...have area ABC = 2*R' x - = 2;rRS x oou ooU 614. SCn. 2. — This proposition is usually stated thus: The area of a spherical triangle is equal to its spherical excess multiplied by the trirectongular triangle. When so stated the spherical excess is to be estimated in... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...for bases, are together equal to the spherical .wedge whose angle is BOD. PROPOSITION XVm. THEOREM. The area of a spherical triangle is equal to its spherical excess multiplied by a tri-rectangular triangle. Let ABC be a spherical triangle : then will its surface be... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...volume of an ungula will be expressed by twice its angle. . • , PROPOSITION XXXII.— THEOREM. 99. The area of a spherical triangle is equal to its spherical excess (the rigfit angle being the unit of angles and the tri-rectangular triangle the unit of areas). For,... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...for bases, are together equal to the spherical wedge whose angle is B OD. PROPOSITION XVIII. THEOREM. The area, of a spherical triangle is equal to its spherical excess multiplied by a tri.rectangular triangle. Let ABC be a spherical triangle : then will its surface be... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...of the numbers expressing the spherical excess of each triangle. BOOK IX. PROPOSITION XVI . THEOREM. The area of a spherical triangle is equal to its spherical excess, multiplied by the area of a tri-rectangular triangle. Let ACD be a spherical triangle lying on the... | |
 | 1876 - 646 pages
...of tbe same base and altitude. 7. Define the terms spherical excess, and tri-rectangular triangle. The area of a spherical triangle is equal to its spherical excess (the right angle being the unit of angles and the tri-rectangular triangle the unit of areas). ENGLISH.... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...a lune, is equivalent to an ungula whose base is the lune. (?) 479. Proposition XXVIII.— Theorem. The area of a spherical triangle is equal to its spherical excess multiplied by the area of the tri-rectangular triangle. Let ABC be a spherical triangle. Complete the... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...= 2*R" x *- +B ^- 1M ' = M* x J° = * ,R<. 614. SeH. 2.—This proposition is usually stated thus: The area of a spherical triangle is equal to its spherical excess multiplied by the trireetangular triangle. When so stated the spherical excess is to be estimated in... | |
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THEOREM. The area, of a spherical triangle is equal to its spherical excess multiplied by a tri.rectangular triangle. 
