 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...the circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If two triangles, SIMILARLY SITUATED, which have two sides of the one proportional to two sides...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,... | |
 | Euclides - 1874 - 342 σελίδες
...Wherefore, in right-angled triangles, &c. QED PROPOSITION 32. — Theorem. If two triangles which haw two sides of the one proportional to two sides of...have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles, which have the two... | |
 | 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
...[Const.] ; 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 third sides be not proportional to the first, ihe angles formed by the proportional sides... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 σελίδες
...circle. PROPOSITION XXXI. THEOREM. (Eucl. vi. 32.) If tivo triangles, SIMILARLY SITUATED, which ham 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,... | |
 | Robert Potts - 1876 - 446 σελίδες
...QRD PROPOSITION XXXH. THEOREM. // two triangles which have tieo sides of the one proportional to turn sides of the other, be joined at one angle, so as...have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles 'which have the two... | |
 | Richard Wormell - 1876 - 268 σελίδες
...similarly 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
...the 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
...[VA "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...have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let ABC and DCE be two triangles, which have the two... | |
 | 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,... | |
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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 ABC, DCE be two triangles... 
