Verwandte Artikel zu A treatise on spherical trigonometry Volume 1 ; with...
A treatise on spherical trigonometry Volume 1 ; with applications to spherical geometry and numerous examples - Softcover
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Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: ... a cos 0 cos 7 1 + cos a + cos b + cos e. = i = =------= si n o; a b e a, o e cos-cos--cos-4 cos-cos--cos--2 2 2 2 2 2 and hence, if one of the arcs be a quadrant, the triangle-whose sides are a, $, and 7 is quadrantal. (See Ex. 3.) 5. If the side c of a spherical triangle be a quadrant, and 5 the arc drawn at right angles to it from the opposite vertex, show that cot2 5 = cot2-4 + cot2 B. Science and Art Exam. Fapen.) Let x be the foot of the perpendicular 5 on the base AS; therefore tan 5 = tan A. sin AX = tan B. cos AX; therefore, &c. G. Given the vertical angle in position and magnitude, and the ratio of the cosines of the base angles, find the locus of the pole of the base. Let the perpendicular on the base divide the vertical angle into parts o and 0; then by Art. 26, Ex. 6, cos A sin a cos B sin P' therefore the perpendicular is fixed in direction, and it obviously contains the pole of the base; therefore, &c. 7. Prove that in fig. 18 2cot XY = cot A Y + cot BY For sin AY _ sin AX-sin (AY-XY) smBY sin XB sin (XY-BY)' therefore, &c. 8. If a, b, c, d be the sides of a spherical quadrilateral taken in order, and 5 and 8' the diagonals; the arc p joining the middle points of the diagonals is given by the equation cos a + cos b + cos c. + cos d cosf» = 5-&, 4 cos-cos--2 2 and give the corresponding theorem in piano. (See Art. 36, Ex. 14.) The sum of the squares of the sides of a quadrilateral = the sum of the squares of its diagonals + four times the square of the line joining the middle points of the diagonals. (See M'Dowell's Geom. Exercises.) 9. The arc p joining the middle points of the opposite sides c and d of a quadrilateral is given by the equation cos a + cos b + cos 5 + cos 5' An arc AB divided internally in X and externally...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1886 Excerpt: ... a cos 0 cos 7 1 + cos a + cos b + cos e. = i = =------= si n o; a b e a, o e cos-cos--cos-4 cos-cos--cos--2 2 2 2 2 2 and hence, if one of the arcs be a quadrant, the triangle-whose sides are a, $, and 7 is quadrantal. (See Ex. 3.) 5. If the side c of a spherical triangle be a quadrant, and 5 the arc drawn at right angles to it from the opposite vertex, show that cot2 5 = cot2-4 + cot2 B. Science and Art Exam. Fapen.) Let x be the foot of the perpendicular 5 on the base AS; therefore tan 5 = tan A. sin AX = tan B. cos AX; therefore, &c. G. Given the vertical angle in position and magnitude, and the ratio of the cosines of the base angles, find the locus of the pole of the base. Let the perpendicular on the base divide the vertical angle into parts o and 0; then by Art. 26, Ex. 6, cos A sin a cos B sin P' therefore the perpendicular is fixed in direction, and it obviously contains the pole of the base; therefore, &c. 7. Prove that in fig. 18 2cot XY = cot A Y + cot BY For sin AY _ sin AX-sin (AY-XY) smBY sin XB sin (XY-BY)' therefore, &c. 8. If a, b, c, d be the sides of a spherical quadrilateral taken in order, and 5 and 8' the diagonals; the arc p joining the middle points of the diagonals is given by the equation cos a + cos b + cos c. + cos d cosf» = 5-&, 4 cos-cos--2 2 and give the corresponding theorem in piano. (See Art. 36, Ex. 14.) The sum of the squares of the sides of a quadrilateral = the sum of the squares of its diagonals + four times the square of the line joining the middle points of the diagonals. (See M'Dowell's Geom. Exercises.) 9. The arc p joining the middle points of the opposite sides c and d of a quadrilateral is given by the equation cos a + cos b + cos 5 + cos 5' An arc AB divided internally in X and externally...
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- VerlagRareBooksClub.com
- Erscheinungsdatum2012
- ISBN 10 1130907953
- ISBN 13 9781130907957
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten26
- Kontakt zum HerstellerNicht verfügbar
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