| Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums have **an angle of the one equal to an angle of the other,** and if, also, the sides of the two figures, about each of their angles, be proportionals, the remaining... | |
| Adrien Marie Legendre - Geometry - 1819 - 574 pages
...proportional to the sides FG, GH, so that AB:FG::BC:GH. It follows from this, that the triangles ABC, FGH, **having an angle of the one equal to an angle of the other** and the sides about the equal angles proportional, are similar (208), consequently the angle ECA —... | |
| Daniel Cresswell - Geometry - 1819 - 446 pages
...:HE::AF:AE; that is, FG is to GE in the given ratio. PROP. XVII. 23. THEOREM. If two trapeziums have **an angle of the one equal to an angle of the other,** and if, also, the sides of the two figvres, about each of tJieir angles, be proportionals, the remaining... | |
| Rev. John Allen - Astronomy - 1822 - 508 pages
...BL oy HE. Cor. 1.—By a similar reasoning it may be proved, that triangles, which have an angle of **one, equal to an angle of the other, are to each other,** in a ratio, compounded of the ratios, of the sides including the equal angles, Cor. 2.—A right line... | |
| Peter Nicholson - Architecture - 1823 - 210 pages
...CAG equal to D, take AG equal to DE or AB, and join CG ; and because the two triangles CAG, DEF, have **an angle of the one equal to an angle of the other,** and the sides which contain these angles are equal, CG shah1 be equal to EF (theorem 5). Now there... | |
| Adrien Marie Legendre - Geometry - 1825 - 276 pages
...putting CM in the place of CA we shall have CP : CM : : CM : CQ ; consequently the triangles CPM, CQM, **having an angle of the one equal to an angle of the other** and the sides about the equal angles proportional, are similar (20") ; therefore MP:MQ::CP : CM or... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...putting CM in the place of CA we shall have CP : CM : : CM : CQ ; consequently the triangles CPM, CQM, **having an angle of the one equal to an angle of the other** and the sides about the equal angles proportional, are similar (203) ; therefore MP : MQ : : CP : CM... | |
| George Darley - Geometry - 1828 - 190 pages
...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have **an angle of the one equal to an angle of the other.** For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road... | |
| James Hayward - Geometry - 1829 - 218 pages
...BD . ... ABC ABXAC the common factor =-, we snail have —AE~V~AF' That is — If two triangles have **an angle of the one equal to an angle of the other,** their areas will be as the products of the sides containing the equal angles. Fig. 94. 17o if we take... | |
| Timothy Walker - Geometry - 1829 - 138 pages
...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have **an angle of the one equal to an angle of the other,** and the sides including these angles proportional — . Thus if the F45 angle A=A (fig. 45), and if... | |
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