| Euclides, James Hamblin Smith - 1872 - 376 Seiten
...circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If two triangles, SIMILARLY SITUATED, which have **two sides of the one proportional to two sides of...angle, so as to have their homologous sides parallel,** each to each, the remaining sides must be in a straight line. Let the AS ABC, DCE be similarly situated,... | |
| Francis Cuthbertson - 1874 - 400 Seiten
...rectangle (FH, GS)+ rectangle (FH, SK) = rectangle (FH t GK). THEOREM (;'). 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** the former sides parallel to the latter respectively: the remaining sides shall be in a straight line.... | |
| L J V. Gerard - 1874 - 428 Seiten
...therefore the triangles ABC and DEF are similar to each other, WWTBD Inversely If two triangles have **two sides of the one proportional to two sides of the other,** and if the angles formed by these sides be not equal to each other, the third sides of the triangles... | |
| Richard Wormell - 1876 - 268 Seiten
...described figures upon the sides containing the right angles. . . 240 32. If two triangles, which have **two sides of the one proportional to two sides of the other,** can be joined at one angle, so as to have their homologous sides parallel to one another, the remaining... | |
| James Hamblin Smith - 1879 - 378 Seiten
...circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If two triangles, SIMILARLY SITUATED, which have **two sides of the one proportional to two sides of the other,** tie joined at one angle, so as to have their homologous sides parallel, each to each, the remaining... | |
| Isaac Todhunter - 1880 - 426 Seiten
..."Wherefore, in any right-angled triangle &c. QED PROPOSITION 32. THEOREM. If two triangles, which have **two sides of the one proportional to two sides of...remaining sides shall be in a straight line. Let ABC** and DCE be two triangles, which have the two sides BA, AC proportional to the two sides CD, DE, namely,... | |
| Arthur Sherburne Hardy - 1881 - 248 Seiten
...МНР = PD + BP, m = 1, »i=l, and OP = PD, BP = PA. .. , j / ./?„,' 3. If two triangles, having **two sides of the one proportional to two sides of...angle so as to have their homologous sides parallel,** the remaining sides shall be in a straight line. Let (Fig. 9) AB = a, AE = ß. Then, ^ F1*- 9Ъу condition,... | |
| Euclides - 1881 - 236 Seiten
...demonstration or confirmation of that proposition. PROP. XXXII. THEOREM. If two triangles, which have **two sides of the one proportional to two sides of the other, be joined at one angle,** to at to have their homologous sides parallel to one another and proceeding from their vertices in... | |
| 1884 - 538 Seiten
...point of contact shall be perpendicular to the line touching the circle. 14. 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 which are opposite to the... | |
| Euclid, Isaac Todhunter - 1883 - 428 Seiten
..."Wherefore, in any right-angled triangle &c. QED PROPOSITION 32. THEOREM. If two triangles, which have **two sides of the one proportional to two sides of...remaining sides shall be in a straight line. Let ABC** and DCE be two triangles, which have the two sides BA, AC proportional to the two sides CD, DE, namely,... | |
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