 | Dalhousie University - 1884 - 184 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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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If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let... 
