 Carol. 4. Parallelograms, or triangles, having an angle in each equal, are in proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXII. IF a line be drawn in a triangle parallel to one of its sides, it...  Elementary Course of Geometry ... - Pàgina 60per Charles William Hackley - 1847 - 103 pàginesVisualització completa - Sobre aquest llibre
 | William Grier - 1832 - 366 pàgines
...rectangle of A and D be equal to the rectangle of B and C; or the rectangle AD = BC— (Fig. 62.) 67. Let DE be parallel to the side BC of the triangle ABC; then will AD : DB : : AE : EC. AB : AC :: AD : AE, AB : AC :: BD : CE.— (Fig. 63.) 68. Let the angle ACB, of the triangle ABC, be... | |
 | William Grier - 1836 - 384 pàgines
...the rectangle of A and D be equal to the rectangle of B and C; or the rectangle A . D = B . C. 66. Let DE be parallel to the side BC of the triangle ABC ; then will AD : DB :: AE : EC. AB AB AC AC AD BD : AE, CF, 67. Let the angle ACB, of the triangle ABC, be bisected by the line CD,... | |
 | Joseph Gwilt - 1842 - 1114 pàgines
...the triangle DFG. Wherefore the triangle ABC is triple of the triangle DFG. 938. PROP. LX. If a linn be drawn in a triangle parallel to one of its sides, it will cut the other two sides proportionally. In the triangle ВАС (fig. 293.), if the line DF be parallel to the side BC, it will cut the other... | |
 | William Grier - 1842 - 320 pàgines
...each other in the compound ratio, or as the rectangle or product of their bases and altitudes. 66. Let DE be parallel to the side BC of the triangle ABC ; then will AD : DB :: AE : EC. AB : AC :: AD : AE, AB : AC :: BD : CE. 67. Let the angle ACB, of the triangle ABC, be bisected by... | |
 | George Roberts Perkins - 1847 - 326 pàgines
...triangle, cutting the other two sides, these sides will be divided into proportional parts. Let DF be parallel to the side BC of the triangle ABC ; then will AD : DB : : AF : FC. For, draw BF and CD ; then the triangles DBF, FCD are equal to each other, because they... | |
 | George Roberts Perkins - 1850 - 332 pàgines
...triangle, cutting the other two sides, these sides will be divided into proportional parts. Let DF be parallel to the side BC of the triangle ABC ; then will AD : DB : : AF : FC. For, draw BF and CD; then, the triangles DBF, FCD are equal to each other, because they... | |
 | Anthony Nesbit - 1859 - 494 pàgines
...angle ABC in that semicircle is a right-angle. (Euc. HL 31. Simp. III. 13. Em. VI. 14.) THEOREM X. If a line be drawn in a triangle parallel to one of its sides, it will cut the two other sides proportionally. Let DE be drawn parallel to BC, one of the sides of the triangle ABC... | |
 | Charles Hutton - 1860 - 1020 pàgines
...proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXH. If a line be drawn in a triangle parallel to one of its sides, it will cut the other tico sides proportionally. Let DE be parallel to the side BC of the triangle ABC ; then »ill AD :... | |
 | William Grier - 1861 - 316 pàgines
...the rectangle of A and D be equal to the rectangle of B and C ; or the rectangle \. . D = B . C. 66. Let DE be parallel to the side BC of the triangle ABC ; then will AD : DB : : AE : EC. AB : AC : : AD : AE, AB : AC : : BD : CE. 67. Let the angle ACB, of the triangle 1BC, be bisected by... | |
 | Gerardus Beekman Docharty - 1867 - 474 pàgines
...proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM IV. If a line be drawn in a triangle parallel to one of...proportionally. Let DE be parallel to the side BC of the A triangle ABC ; then will AD : DB ; : AE : /\ EC. For, draw BE and CD ; then the triangles DBE, DCE,... | |
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