 | John Keill - Logarithms - 1723 - 444 pages
...to AE asGFis to FL. Now fince ABE, FGL, are two Triangles, having one Angle of the one equal to one Angle of the other, and the Sides about the equal Angles proportional; the Triangle ABE will be * equiangular * 6 of tin's. to the Triangle FGL; and fo alfo fimilar to it. Therefore... | |
 | Euclid - 1728 - 236 pages
...DEFINITIONS. [milar right-lined Figures, as ABC, DCE, are fuch chat have each Angle oí the one equal to each Angle of the other, and the Sides about the equal Angles proportional. в с" The Ang. В= DCE ; and AB : BC : : DC : CE. alfo the Ang. A = D ; and BA : AC : : CD : DE. and... | |
 | Euclid, John Keill - Geometry - 1733 - 444 pages
...AE as GF is to* FL. Now fmce ABE, FGL, are two Triangles, having one Angle of the one equal to One Angle of the other, and the Sides about the equal Angles proportional ; .the Triangle ABE will be * equiangular * doftbit. to the .Triangle FGL; and alfo fimilar to it, Therefore... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...Wherefore, if the sides, &c. QE *D. PROP. VI. THEOR. IF two triangles have one angle of one equal to one angle of the other, and the sides about the equal angles proportional, the triangles will be equiangular, and will have those angles equal which are opposite to the homologous sides. Book VI.... | |
 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...have CP : CM: : CM: Cq ; consequently the triangles CPM, riy.U, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208) ; therefore MP : Mq ::CP : GMor CA. But the proportion CP:CA::CA:Cq gives, by dirision,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...: : 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 BCA = GHF. These equal angles being subtracted from the equal... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...seen that the angle ACD = FHI ; consequently the triangles ACD, FHI, have an angle of the one equal to an angle of the other and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed in the same manner to demonstrate, that the remaining... | |
 | Euclides - 1826 - 226 pages
...their sides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides, For to the right... | |
 | Euclid - 1826 - 234 pages
...their «ides, &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides. Let ABC, DEF,... | |
 | John Playfair - Geometry - 1829 - 210 pages
...sides &c. QED PROPOSITION VI. THEOREM. If two triangles have one angle of one triangle equal to one angle of the other, and the sides about the equal angles proportional, the triangles will he equiangular, and will have those angles equal which are opposite to the homologous sides. Let the... | |
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If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles shall be equiangular, and have those angles equal which subtend the homologous sides. 
