 In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.  The Elements of Geometry - Page 167by Webster Wells - 1886 - 371 pagesFull view - About this book
 | Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...6 = 18, c = 12, and pc = 4. PROPOSITION XXII. THEOREM 311. In any triangle having an obtuse angle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, plus twice the product of one of these sides and the projection of... | |
 | William Betz - Geometry - 1916 - 536 pages
...the angle B. 4. Show that in the above proposition e2 = a2 + b2 — 2 ab cos C. 421. In any obtuse triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of those sides and the projection... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...+ n2 = a* and h? + m2 = b2. §196 6. .-. a2 = 62 + e2-2e7w. Ax. XII 198. Theorem. — In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides plus twice the product of one of those sides and the projection of the... | |
 | Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...6 = 18, c = 12, and pc = 4. PROPOSITION XXII. THEOREM 311. In any triangle having an obtuse angle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, plus twice the product of one of these sides and the projection of... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...square root of a number. Definition. Projections. Theorem X. In an obtuse angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other two sides, plus twice the product of one of these sides and the projection of... | |
 | Edith Long, William Charles Brenke - Geometry, Modern - 1916 - 292 pages
...square root of a number. Definition. Projections. Theorem X. In an obtuse angled triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other two sides, plus twice the product of one of these sides and the projection of... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Plane - 1917 - 330 pages
...8. "B'C' &Vr2 AB AC ' A'B' A'C' .:AABC~A B'C' A'B'C'. BC PROPOSITION IV. THEOREM 417. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of those sides by the projection... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...of these two sides and the projection of the other upon it. [240] 427. In a triangle the square on the side opposite the obtuse angle is equal to the sum of the squares on the other two sides, increased by two times the product of one of them and the projection... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...upon 21. [See practical problems, pp. 298 and 299.] PROPOSITION XXXVII. THEOREM 333. In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection... | |
 | Matilda Auerbach, Charles Burton Walsh - Geometry, Plane - 1920 - 408 pages
...briefly how you might find a fourth proportional to three given straight lines. 4. Prove that in any obtuse-angled triangle the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of these sides and the projection... | |
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