An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 σελίδες |
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise of Spherical Geometry and Trigonometry Anthony Dumond Stanley Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
An Elementary Treatise of Spherical Geometry and Trigonometry Anthony D. Stanley Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a=cos AB+BC adjacent angle ABC angle ACB angle opposite B+sin B cot b=cos BC and B'C C+sin C=cos c=sin circle circumference comp complemental computed corresponding cos C+sin cos C=cos cosec cosine distance drawn equal spheres equal to A'B formulæ given gles Hence hypotenuse included angle intersection Let ABC lune measures middle Napier's rule Napier's theorem oblique angles opposite angles opposite side pole of AC polygon quadrant radii radius remaining sides right angles right-angled spherical triangle right-angled triangle severally equal side AC side opposite sides AB sides and angles sin A+B sin b sin sin BC sine of AC smaller sphere sphere whose center spherical angle spherical polygon spherical triangle supplements tangent tangent of half three quantities three sides tri-quadrantal triangle trian triangle ABC trigonometry unequal vertex whence wherefore x=cos x=tan
Δημοφιλή αποσπάσματα
Σελίδα 50 - ... fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 106 - ... that the sine of half the sum of any two sides of a spherical triangle, is to the sine of half their difference as the cotangent of half the angle contained between them, to the tangent of half the difference of the angles opposite to them : and also that the cosine of half the sum of these sides, is to the cosine of half their difference, as the cotangent of half the angle contained...
Σελίδα 94 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Σελίδα 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Σελίδα 8 - Axis of a great circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.
Σελίδα 27 - Therefore, if two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Σελίδα 101 - Law: cos a = cos b cos c + sin b sin c cos A cos b = cos c cos a + sin c sin a cos B cos c = cos a cos b + sin a sin b cos C cos A = -cos B...
Σελίδα 96 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Σελίδα 27 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C
Σελίδα 74 - Given two sides, and an angle opposite one of them, to find the remaining parts. 19. For this case, we employ proportions (3); sin a : sin b : : sin A .Ex. 1. Given the side a = 44° 13• 45", b = 84° 14• 29", and the angle A = 32° 26• 07" : required the remaining paris.