 | Education - 1852 - 512 pages
...triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras... | |
 | Euclides - Geometry - 1853 - 334 pages
...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. If two triangles have (!•) one angle of the one equal to one angle of the other ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third... | |
 | Euclides - Geometry - 1853 - 176 pages
...equiangular to the triangle def Wherefore, if two triangles, &c. QED PROPOSITION VII. — THEOREM. If two triangles have one angle of the one equal to one angle of tJie other, and the sides about two other angles proportionals, then if each of tlie remaining angles... | |
 | Sir James Kay-Shuttleworth - Church and education - 1853 - 522 pages
...triangles on each side of it arc similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...proportional DB is found. Which was to be done. PROPOSITION XIV. THEOR. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : and parallelograms that have one... | |
 | John Playfair - Geometry - 1855 - 334 pages
...the remaining angle at E. Therefore th« triangle ABC is equiangular to the triangle DEF PROP. VII. THEOR. If two triangles have one angle of the one...two other angles proportionals, then, if each of the remainmg angles be either less, or not less, than a right angle, the triangles shaU be equiangular,... | |
 | 1855 - 264 pages
...the segments of the hase shall have the same ratio which the other sides of thi; triangle have. 2. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles bhall be equiangular, and shall have those angles equal... | |
 | Euclides - 1855 - 270 pages
...extremity of one of the parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of the same affection... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...; the segments of the base shall have the same ratio which the other sides of the triangle have. 2. If two triangles have one angle of the one equal to one angh of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,... | |
 | Education - 1857 - 1266 pages
...lesson on the bent lever. BIGHEB MATHEMATICS AND MATHEMATICAL PHYSICS. SECOND YEAR. SECTION I. — 1. If two triangles have one angle of the one equal to...of the other and the sides about two other angles proportional ; then if each of the remaining angles be less or not less than a right angle, or if one... | |
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