An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Ergebnisse 1-5 von 17
Seite 12
... point in the cir- cumference of the circle described about P as a center in the plane AB , as in the surface of the sphere : this circumference therefore is the intersection of the plane with the 12 SPHERICAL GEOMETRY .
... point in the cir- cumference of the circle described about P as a center in the plane AB , as in the surface of the sphere : this circumference therefore is the intersection of the plane with the 12 SPHERICAL GEOMETRY .
Seite 13
Anthony Dumond Stanley. circumference therefore is the intersection of the plane with the surface of the sphere , and the circle itself is the intersection of the plane and sphere . Cor . The nearer the cutting plane is to the center of ...
Anthony Dumond Stanley. circumference therefore is the intersection of the plane with the surface of the sphere , and the circle itself is the intersection of the plane and sphere . Cor . The nearer the cutting plane is to the center of ...
Seite 16
... , the surfaces of the spheres will intersect in the circumference of a circle perpendicular to the line which joins the centers , and having its center in that line . + Let C , O be the centers of two 16 SPHERICAL GEOMETRY .
... , the surfaces of the spheres will intersect in the circumference of a circle perpendicular to the line which joins the centers , and having its center in that line . + Let C , O be the centers of two 16 SPHERICAL GEOMETRY .
Seite 17
... circumference of a circle at right angles to CO , and having its center in this line . With the radii CB , OP , draw in any plane passing through CO , arcs of circles meeting in A : draw AD perpendicular to CO , and let a plane pass ...
... circumference of a circle at right angles to CO , and having its center in this line . With the radii CB , OP , draw in any plane passing through CO , arcs of circles meeting in A : draw AD perpendicular to CO , and let a plane pass ...
Seite 18
... circumference of an- other great circle be quadrants , the point is a pole of this great circle . Let AD and BD , arcs of great cir- cles drawn from D to the circumfer- ence AB of another great circle , be quadrants , then will D be the ...
... circumference of an- other great circle be quadrants , the point is a pole of this great circle . Let AD and BD , arcs of great cir- cles drawn from D to the circumfer- ence AB of another great circle , be quadrants , then will D be the ...
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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.