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. 1862 Excerpt: ...side and equal angles opposite to this side, to determine that whose area is a maximum. 3. If R (Lesson VI, Exercise 36), and the three angles of a triangle be given, the area has for its expression 2R-sinAsinBsinC. 4. If the three angles of a triangle be given, the ratio of R to r (Lesson VI, Exercise 34), has for its ...
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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. 1862 Excerpt: ...side and equal angles opposite to this side, to determine that whose area is a maximum. 3. If R (Lesson VI, Exercise 36), and the three angles of a triangle be given, the area has for its expression 2R-sinAsinBsinC. 4. If the three angles of a triangle be given, the ratio of R to r (Lesson VI, Exercise 34), has for its expression sin A+sinB+sinC 2 sin A sin B sin C. 5. Given an angle of a triangle, the straight line joining its vertex with the middle point of the opposite side, and the perpendicular from the angle upon this side, to compute the area, sides, and angles of the triangle. 6. Given in a triangle the area, perimeter, and one of the angles, to compute the sides and angles. 7. Given in a right-angled triangle the hypotenuse and r, to find the area, sides, and angles. 8. Given in a right-angled triangle one of the sides and r, to compute the area, hypotenuse, and angles. 9. Express the area of a triangle in function of the three sides and R 10. In a triangle, if T be the area, (1) sinAAsiniBsinlC=----sabc -T (2) cos JA cos iB cos AC= abc (3) tanAtanp tanJC= (4) T-=rrW. 11. Given in a triangle a side, the angle opposite to it, and the area, to determine the remaining parts. 12. Given the area of a triangle and two angles, to calculate the sides. 13. Given the side, the perimeter, and the area of a triangle, to calculate the angles and sides. 14. If the points in which the perpendiculars from the angles of a triangle upon the opposite sides meet these sides, be joined, the triangle thus formed has to the given triangle the same ratio as twice the product of the cosines of the three angles has to 1. LESSON X. Regular Polygons inscribed and circumscribed, their Areas and Perimeters--Series of polygons formed by continual bisections ...
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