An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Seite 22
... triangle whose verticles are poles of the great circles passing through the sides of the first triangle . Let ABC be ... triangles as those above mentioned are called 22 SPHERICAL GEOMETRY . Spherical Triangles.
... triangle whose verticles are poles of the great circles passing through the sides of the first triangle . Let ABC be ... triangles as those above mentioned are called 22 SPHERICAL GEOMETRY . Spherical Triangles.
Seite 23
... triangle are supplements to the measures of the angles of its polar triangle . B D Let ABC , DEF , be polar triangles , A , B , C , being poles of EF , FD , DE , respectively , and D , E , F , poles of BC , CA , AB ; the sides of the ...
... triangle are supplements to the measures of the angles of its polar triangle . B D Let ABC , DEF , be polar triangles , A , B , C , being poles of EF , FD , DE , respectively , and D , E , F , poles of BC , CA , AB ; the sides of the ...
Seite 24
... triangle ABC , are respectively supplements to the measures of the angles F and E of the triangle DEF . Schol . From this property of polar triangles , they are often called supplemental triangles . PROP . XXI . Any two sides of a spherical ...
... triangle ABC , are respectively supplements to the measures of the angles F and E of the triangle DEF . Schol . From this property of polar triangles , they are often called supplemental triangles . PROP . XXI . Any two sides of a spherical ...
Seite 25
... triangle ; the sum . of the sides AB , BD , and DA , is less than the circumference of a great circle . For if C be ... ABC be a spherical triangle ; each of its angles A , B , and C , is less than two right angles , and the sum of the ...
... triangle ; the sum . of the sides AB , BD , and DA , is less than the circumference of a great circle . For if C be ... ABC be a spherical triangle ; each of its angles A , B , and C , is less than two right angles , and the sum of the ...
Seite 26
... ABC ; these angles are together equal to two right angles ( Cor . Prop . 17 ) ; therefore ABC , one of them , is less than two right angles : in like manner it may be shown that A and C , the other two angles of the triangle , are each ...
... ABC ; these angles are together equal to two right angles ( Cor . Prop . 17 ) ; therefore ABC , one of them , is less than two right angles : in like manner it may be shown that A and C , the other two angles of the triangle , are each ...
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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.