An Elementary Treatise of Spherical Geometry and TrigonometryDurrie & Peck, 1848 - 122 Seiten |
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Seite 7
... radius of a sphere is any straight line drawn from the center to the surface . All radii of a sphere are equal . 3. A sphere may be described by the revolution of a semicircle about its diameter , the middle of the diame- ter being the ...
... radius of a sphere is any straight line drawn from the center to the surface . All radii of a sphere are equal . 3. A sphere may be described by the revolution of a semicircle about its diameter , the middle of the diame- ter being the ...
Seite 9
... radius of the sphere , this line touches the sphere at the foot of the perpen- dicular . For since the perpendicular is equal to the radius , the foot of the perpendicular is in the surface of the sphere ; the line therefore meets the ...
... radius of the sphere , this line touches the sphere at the foot of the perpen- dicular . For since the perpendicular is equal to the radius , the foot of the perpendicular is in the surface of the sphere ; the line therefore meets the ...
Seite 10
... radius , the line is wholly without the sphere . For no point of the line can be at less than the per- pendicular distance from the center : but this is greater than the radius ; wherefore the line must at every point be without the ...
... radius , the line is wholly without the sphere . For no point of the line can be at less than the per- pendicular distance from the center : but this is greater than the radius ; wherefore the line must at every point be without the ...
Seite 11
... radius of the sphere , the plane is a tangent to the sphere at the foot of the per- pendicular . For as the perpendicular is equal to the radius , the foot of it is a point in the surface of the sphere , and the plane meets the surface ...
... radius of the sphere , the plane is a tangent to the sphere at the foot of the per- pendicular . For as the perpendicular is equal to the radius , the foot of it is a point in the surface of the sphere , and the plane meets the surface ...
Seite 12
... radius equal to PD , will be the intersection of that plane with the sphere . Draw in this circle any radius PE , and join CE , CD : the angle CPE is a right angle ( Euc . , Suppl . 2 , Def . 1 ) ; and in the right - angled triangles ...
... radius equal to PD , will be the intersection of that plane with the sphere . Draw in this circle any radius PE , and join CE , CD : the angle CPE is a right angle ( Euc . , Suppl . 2 , Def . 1 ) ; and in the right - angled triangles ...
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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.