An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Seite 26
Anthony Dumond Stanley. D Produce the side AB , so as to make an angle CBD ... sides of the triangle that is polar to ABC , are supplements to the measures of ... opposite them are also equal . Let ABD be a spherical triangle of which the ...
Anthony Dumond Stanley. D Produce the side AB , so as to make an angle CBD ... sides of the triangle that is polar to ABC , are supplements to the measures of ... opposite them are also equal . Let ABD be a spherical triangle of which the ...
Seite 27
... sides and the in- cluded angle of one equal to two sides and the in- cluded ... side ; wherefore the angle EAF is equal to the angle EBF : but these angles ... opposite them are also equal . Let ABC be a spherical tri- angle , of which ...
... sides and the in- cluded angle of one equal to two sides and the in- cluded ... side ; wherefore the angle EAF is equal to the angle EBF : but these angles ... opposite them are also equal . Let ABC be a spherical tri- angle , of which ...
Seite 28
... side opposite it . Let ABC be a spherical tri- angle , in which the angle CAB is greater than CBA ; the side BC , opposite the greater angle , A is longer than the side AC . B Through A the vertex of the greater angle , draw AD an arc ...
... side opposite it . Let ABC be a spherical tri- angle , in which the angle CAB is greater than CBA ; the side BC , opposite the greater angle , A is longer than the side AC . B Through A the vertex of the greater angle , draw AD an arc ...
Seite 29
... side opposite it ( Prop . 26 ) : the angle opposite the longer of the unequal sides of a spherical triangle is therefore greater than the angle opposite the other . PROP . XXVIII . If on the same sphere or on equal spheres , the sides ...
... side opposite it ( Prop . 26 ) : the angle opposite the longer of the unequal sides of a spherical triangle is therefore greater than the angle opposite the other . PROP . XXVIII . If on the same sphere or on equal spheres , the sides ...
Seite 30
... sides of the former are sev- erally equal to those of the latter ; wherefore the angle DBE opposite the side DE , is equal to the angle D'B'E ' opposite the side D'E ' . But DBE is equal to the spher- ical angle ABC , and D'B'E ' to A'B ...
... sides of the former are sev- erally equal to those of the latter ; wherefore the angle DBE opposite the side DE , is equal to the angle D'B'E ' opposite the side D'E ' . But DBE is equal to the spher- ical angle ABC , and D'B'E ' to A'B ...
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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.