 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
..."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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 426 σελίδες
..."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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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... 
