| William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...a triangle .divides the other two sides proportionally. PROPOSITION II. If a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** PROPOSITION III. Two triangles are similar when they are mutually equiangular. PROPOSITION IV. Two... | |
| James Wallace MacDonald - Geometry - 1894 - 76 pages
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the **sides of a triangle proportionally, it is parallel to the third side.** Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
| James Wallace MacDonald - Geometry - 1889 - 80 pages
...segments. See Book II., Proposition VI. Proposition XVII. A Theorem. 142. If a straight line divide the **sides of a triangle proportionally, it is parallel to the third side.** Proposition XVIII. A Problem. 143. To divide a given line into parts proportional to given lines, or... | |
| Edward Albert Bowser - Geometry - 1890 - 414 pages
...angles with AB and AC : prove that Proposition 1 3. Theorem. 301. Conversely, if a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** Hyp. Let DE cut AB, AC in the A ABC so that 7^ = -r=. To prove DE || to BC. Proof. If DE is not ||... | |
| William Chauvenet - 1893 - 340 pages
...of a triangle divides the other two sides proportionally. PROPOSITION II. If a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** PROPOSITION III. Two triangles are similar when they are mutually equiangular. PROPOSITION IV. Two... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...determining ratio is their ratio of similitude. AB is parallel to A'B', BC to B'C, etc. § 273 [If **a straight line divide two sides of a triangle proportionally, it is parallel to the third side.]** Hence angle ABC=A'B'C, angle BCD = B'C'D', etc. § 5 1 [Having their sides respectively parallel and... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...determining ratio is their ratio of similitude. AB is parallel to A'B', BC to B'C', etc. § 273 [If **a straight line divide two sides of a triangle proportionally, it is parallel to the third side.]** Hence angle ABC=A'B'C', angle BCD = B'C'D', etc. § 51 [Having their sides respectively parallel and... | |
| George Albert Wentworth - Mathematics - 1896 - 68 pages
...number of parallels, the corresponding intercepts are proportional. 312. If a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** 313. The bisector of an angle of a triangle divides the opposite side into segments proportional to... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...we have AB _AC Ab~^A~c Therefore the line be is parallel to BC. § 273 [If a straight line divides **two sides of a triangle proportionally, it is parallel to the third side.** ] And the angle Abc = the angle B, and Acb=C. § 49 Hence the triangles ABC and Abe, being mutually... | |
| Henry W. Keigwin - Geometry - 1897 - 254 pages
...11. In Fig. 101 draw KJ parallel to AB ; then prove PROPOSITION II. THEOREM. 235. If a line divides **two sides of a triangle proportionally, it is parallel to the third side. In the triangle ABC let** PR divide the sides AB, AC proportionally. It is to be proved that PR is parallel to BC. Through R... | |
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