An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
Im Buch
Ergebnisse 1-5 von 45
Seite 11
... given for the circle in the third book of Euclid ; as for example , the propositions 7 , 8 , 14 , 15 , 35 , 36 , and 37 · of that book . 1 center to every point of the plane is therefore greater 2 * PLANE AND SFHERE . 11 Plane and Sphere.
... given for the circle in the third book of Euclid ; as for example , the propositions 7 , 8 , 14 , 15 , 35 , 36 , and 37 · of that book . 1 center to every point of the plane is therefore greater 2 * PLANE AND SFHERE . 11 Plane and Sphere.
Seite 50
... given above with respect to two lunes . PROP . XLVIII . If the circumferences of two great circles intersect on the convex surface of a hemisphere , the opposite trian gles thus formed , will be equal to the lune 50 SPHERICAL GEOMETRY .
... given above with respect to two lunes . PROP . XLVIII . If the circumferences of two great circles intersect on the convex surface of a hemisphere , the opposite trian gles thus formed , will be equal to the lune 50 SPHERICAL GEOMETRY .
Seite 55
... given its oblique angle or the opposite side which is a measure of this angle . These parts can neither of them be computed from the other parts of the triangle . Triangles of this kind may be called bi - quadrantal , and in what ...
... given its oblique angle or the opposite side which is a measure of this angle . These parts can neither of them be computed from the other parts of the triangle . Triangles of this kind may be called bi - quadrantal , and in what ...
Seite 61
... given , the remaining three may in general be determined by means of the equations numbered ( 1 ) , ( 2 ) , ( 3 ) , in the two pre- ceding corollaries . And as in each computation there are three parts concerned , two given and one ...
... given , the remaining three may in general be determined by means of the equations numbered ( 1 ) , ( 2 ) , ( 3 ) , in the two pre- ceding corollaries . And as in each computation there are three parts concerned , two given and one ...
Seite 63
... given , where A is the right angle ; and each of the five circular b parts , namely , b , c , comp . B , comp . a , comp . C , be in turn made the middle part , there will result the follow- ing equations , and sin b = tan c tan comp ...
... given , where A is the right angle ; and each of the five circular b parts , namely , b , c , comp . B , comp . a , comp . C , be in turn made the middle part , there will result the follow- ing equations , and sin b = tan c tan comp ...
Andere Ausgaben - Alle anzeigen
An Elementary Treatise of Spherical Geometry and Trigonometry Anthony Dumond Stanley Keine Leseprobe verfügbar - 2015 |
An Elementary Treatise of Spherical Geometry and Trigonometry Anthony D. Stanley Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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...
Seite 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...
Seite 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Seite 8 - Axis of a great circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.
Seite 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.
Seite 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...
Seite 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.
Seite 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
Seite 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.