 | George Albert Wentworth, David Eugene Smith - 1913 - 496 σελίδες
...CA xBC = ~CP* + APxPB. Ax. 9 .-. >CP1'=CAxBC — APxPB, by Ax. 2. QED PROPOSITION XXIV. THEOREM 305. In any triangle the product of two sides is equal...circumscribed circle by the altitude upon the third side. Given the triangle ABC with CP the altitude, ADBC the circle circumscribed about the triangle ABC,... | |
 | George Albert Wentworth, David Eugene Smith - 1913 - 491 σελίδες
...CAx BC — AP xPB, by Ax. 2. QED PROPOSITION XXIV. THEOREM 305. In any triangle the product oftivo sides is equal to the product of the diameter of the...circumscribed circle by the altitude upon the third side. Given the triangle ABC with CP the altitude, ADBC the circle circumscribed about the triangle ABC,... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 490 σελίδες
...parallelogram is equal to the sum of the squares of the diagonals. PROPOSITION XXXIX. THEOREM 338. In any triangle, the product of two sides is equal to the square of the bisector of the included angle plus the product of the segment* of the third side. Given... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 328 σελίδες
...(336), reduce the result of the preceding exercise to the following form PROPOSITION XL. THEOREM 339. In any triangle the product of two sides is equal to the altitude upon the third side, multiplied by the diameter of the circumscribed circle. Given d, a diameter... | |
 | Edward Rutledge Robbins - 1915 - 280 σελίδες
...drawn, the triangle ABC is similar to the triangle CED. [Use 306.] 169 PROPOSITION XXXIV. THEOREM 328. In any triangle the product of two sides is equal to the diameter of the circumscribed circle multiplied by the altitude upon the third side. Given : A ABC... | |
 | William Betz - 1916 - 536 σελίδες
...formula for the length of the median mc upon any side of a triangle, as c, may be derived, namely, 425. In any triangle the product of two sides is equal to the square of the bisector of the'included angle, increased by the product of the segments of the third... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1918 - 486 σελίδες
...preceding exercise to the following form 2 t = . ' a +6 Vo6s(s — c). PROPOSITION XL. THEOREM 339. In any triangle the product of two sides is equal to the altitude upon the third side, multiplied by the diameter of the circumscribed circle. Given d, a diameter... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1913 - 484 σελίδες
...the preceding exercise to the following form 2 t = a+b \'abs(s — c). PROPOSITION XL. THEOREM 339. In any triangle the product of two sides is equal to the altitude upon the third side, multiplied by the diameter of the circumscribed circle. Given d, a diameter... | |
 | David Eugene Smith - 1923 - 314 σελίδες
...238 197 Proposition 22. Product of Two Sides 238. Theorem. The product of two sides of any triangle is equal to the product of the diameter of the circumscribed circle and the altitude upon the third side. Given the A ABC with the altitude CP (or K), and CD (or d) the... | |
 | Walter Burton Ford, Charles Ammermann - 1923 - 406 σελίδες
...Hence show that AD • AE is a constant for all positions of the point D on the arc BDC. 44. Prove that in any triangle the product of two sides is equal to the diameter of the circumscribed circle multiplied by the altitude upon the third side ; that is, in the... | |
| |
In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side. 
