 | Euclides - 1834 - 518 pages
...triangles, &c. o. ED PROPOSITION XXXII. THEOR. — If two triangles, which have two sides of the one, See N. proportional to two sides of the other, be joined...have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let ABC, DCE he two triangles, which have the two... | |
 | Euclid - 1835 - 540 pages
...together. Wherefore, " in right angled triangles," &c. QED PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides...other, be joined at one angle, so as to have their liomologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC,... | |
 | Mathematics - 1836 - 488 pages
...similarly described figures upon the sides containing the right angle. XXXII. if two triangles, which have two sides of the one proportional to two sides...their remaining sides shall be in a straight line. XXXIII. In equal circles, angles, whether at the centers or circumferences, have the same ratio which... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...and similarly described figures on BA, AC (V. B). PROPOSITION XXXH. 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, DCE, be two triangles which have the two... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...together equal to that on BC ; and they are similar figures. PROP. XXXII. THEOR. If two triangles, which have two sides of the one proportional to two sides...at one angle , so as to have their homologous sides pa-* rallel to one another ; their remaining sides shall be in a straight line. Let ABC, DCE be two... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...(I. '29.) the angles B and D are equal, and likewise C and E. * PROP. VII. THEOR. IF two triangles have two sides of the one proportional to two sides of the other ; and if the angles opposite to one pair of the homologous sides be equal, and those opposite to the... | |
 | Euclides - 1838 - 264 pages
...is equal to the sum of the similar figures on AB and AC. PROP. XXXII. THEOR. 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, DCE be two triangles which have the two... | |
 | Euclides - 1840 - 82 pages
...described figures upon the sides containing the right angle. PROP. XXXII. THEOR. If two triangles, having two sides of the one proportional to two sides of the other, be joined at one angle, so that their homologous sides be parallel to each other, the remaining sides shall be in a straight line.... | |
 | Euclides - 1840 - 192 pages
...together, that is, in a ratio of equality. PROP. XXXII. THEOR. If two triangles (ABC, DCE), having two sides of the one proportional to two sides of the other (AB : AC :: DC : DE), be joined at one angle, so that their homologous sides be parallel to each other,... | |
 | Euclides - Geometry - 1841 - 378 pages
...Wherefore, in right-angled triangles, &c. QED * 8. 6. •4. 8. PROP. XXXII. THEOR. 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, DCE be two triangles which have the two sides... | |
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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... 
