| Dalhousie University - 1884 - 184 Seiten
...of which the well-known 47th Proposition of Book I. is a special case. 2. If two triangles that have **two sides of the one proportional to two sides of the other,** are capable of being joined at one angle so that the homologous sides are parallel, the remaining sides... | |
| Euclides - 1884 - 434 Seiten
...Prove As ABE, ADE similar, and that EC bisects L BED. PROPOSITION 7. THEOREM. If two triangles have **two sides of the one proportional to two sides of the other,** and the angles opposite to one pair of homologous sides equal, the angles opposite to the other pair... | |
| George Bruce Halsted - 1885 - 389 Seiten
...491, BD = BC, .-. £ C = 4 BDC. But 4 BDC + £ BDA = st. £, 513. COROLLARY. If two triangles have **two sides of the one proportional to two sides of the other,** and an angle in each opposite one corresponding pair of these sides equal, then if one of the angles... | |
| George Bruce Halsted - 1886 - 394 Seiten
...491, BD = BC, .-. 4 C = 4 BDC. But £ BDC + 4 BDA — st. £, 513. COROLLARY. If two triangles have **two sides of the one proportional to two sides of the other,** and an angle in each opposite one corresponding pair of these sides equal, then if one of the angles... | |
| Arthur Sherburne Hardy - 1887 - 264 Seiten
...PD, BP = PA. 3. If two triangles, having an angle in each equal and the including sides proportional, **be joined at one angle so as to have their homologous sides parallel,** the remaining sides will be in a straight line. Let (Fig. 9) AB = a, AE = /3. Then, Flg• 9by condition,... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 Seiten
...740 quadl. ANBO= AABL ; ?«a<#. AOBL. = ABDL. PROPOSITION 32. THEOREM. If two triangles which have **two sides of the one proportional to two sides of...the remaining sides shall be in a straight line. Let** FGA, ABC be two AS such that FG : GA :: AB : BC, and let FG, GA be || to AB, BC respectively; then... | |
| Euclid - 1890 - 442 Seiten
...on AB : sq. on AC, = Z: Y. . . X + Y = Z. EUCLID Proposition 32. THEOREM — If two triangles have **two sides of the one proportional to two sides of the other,** and are so placed at an angle that tJie homologous sides are parallel, the remaining sides of the triangles... | |
| George Bruce Halsted - 1904 - 324 Seiten
...from a given tangent a sect any multiple of the segment between 0 and tangent. Ex. 280. If 2 As have **two sides of the one proportional to two sides of the other,** and ^. s, one in each, opposite one corresponding pair of these sides = , the ^ s opposite the other... | |
| George Bruce Halsted - 1904 - 322 Seiten
...from a given tangent a sect any multiple of the segment between O and tangent. Ex. 280. If 2 AS have **two sides of the one proportional to two sides of the other,** and ^ s, one in each, opposite one corresponding pair of these sides = , the ^ s opposite the other... | |
| Trinity College (Dublin, Ireland) - 1907 - 534 Seiten
...a circle are equal to the angles in the alternate segments of the circle. 8. If two triangles have **two sides of the one proportional to two sides of the other,** and the angles opposite one pair of corresponding sides equal, prove that the angles opposite the other... | |
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