An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Seite 8
... quadrant . 13. A spherical polygon is a portion of the surface of a sphere , bounded by several arcs of great circles ; which arcs are called sides of the polygon . { 14. Each side of a triangle or a polygon must SPHERICAL GEOMETRY .
... quadrant . 13. A spherical polygon is a portion of the surface of a sphere , bounded by several arcs of great circles ; which arcs are called sides of the polygon . { 14. Each side of a triangle or a polygon must SPHERICAL GEOMETRY .
Seite 17
... quadrant ; and is at right angles to that circumference . Let DEB be a great circle , A its pole , and AE an arc of a great circle drawn from A to the circumference of the circle DEB ; the arc AE is a quadrant . D E B From C the center ...
... quadrant ; and is at right angles to that circumference . Let DEB be a great circle , A its pole , and AE an arc of a great circle drawn from A to the circumference of the circle DEB ; the arc AE is a quadrant . D E B From C the center ...
Seite 18
... quadrant . Again , the arc AE is at right angles to the arc DEB : for the spherical angles AED , AEB are the angles made by the plane ACE with the plane of the circle DEB : and these planes are at right angles to each other ; because ...
... quadrant . Again , the arc AE is at right angles to the arc DEB : for the spherical angles AED , AEB are the angles made by the plane ACE with the plane of the circle DEB : and these planes are at right angles to each other ; because ...
Seite 19
Anthony Dumond Stanley. Since AD and DB are quadrants , ACD and BCD are right angles ; and since DC is at right angles to the lines CA and CB , it is at right angles to the plane ACB ; which is the plane of the great circle to which the ...
Anthony Dumond Stanley. Since AD and DB are quadrants , ACD and BCD are right angles ; and since DC is at right angles to the lines CA and CB , it is at right angles to the plane ACB ; which is the plane of the great circle to which the ...
Seite 22
... quadrant ( Prop . 12 ) ; and since C is the pole of DE , the arc drawn from C to D is also a quadrant . Now when the arcs of two great circles drawn from a point in the sur- face of a sphere to the circumference of another great circle ...
... quadrant ( Prop . 12 ) ; and since C is the pole of DE , the arc drawn from C to D is also a quadrant . Now when the arcs of two great circles drawn from a point in the sur- face of a sphere to the circumference of another great circle ...
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.