 | John Keill - 1723 - 444 páginas
...that are about the equal Angles of the Triangles ABG, DEF, are reciprocal: But thofe Triangles that have one Angle of the one, equal to one Angle of the other; and the Sides about the * Def. .10 Rig* 11: Lines be proportional, the firft has * a dupliif ifofthis.... | |
 | Euclid, John Keill - 1733 - 444 páginas
...is equal to the Angle GFL; and BA is to AE, as GF is to F L. Therefore the two Triangles BAE, GFL, have one Angle of the one equal to one Angle of the other, viz. the Angle BAE equal to the Angle GFL, and the Sides about the equal Angles proportional. Wherefore... | |
 | Robert Simson - 1762 - 488 páginas
...pxrallelogram BC. Therefore equal parallelograms, &c. Q^ED PROP, Book VI. PRO P. XV. THEO R. U*VN£> AL triangles which have one angle of the one equal to one angle of the other, have their fides about the equal angles reciprocally proportional: and triangles which have one angle in... | |
 | John Keill - 1772 - 462 páginas
...one Angle of the other, have, thesr Sides about the equal Angles reciprocal; and thofe Triangles that have one Angle of the one equal to one Angle of the other, and have alfe the Sides about the equal Angles reciprocal, are equal; which was to be de-« monft rated.... | |
 | Robert Simson - 1775 - 534 páginas
...proportional DB is found. Which was to be done. PROP. - *'' BookVL PROP. XIV. THEO R. EQUAL parallelograms which have one angle of the one equal to one angle of the other, have their fIdes about the equal angles reciprocally proportional: And parallelograms that have one angle... | |
 | Robert Simson - 1781 - 534 páginas
...equal e to the parallelogram BC. Therefore equal parallelograms, &cQE. DBookvr PROP. XV. fHEO k. EQJJAL triangles which have one angle of the one equal to one angle of the other, have their fides about the equal angles reciprocally proportional, and triangles which have one angle in... | |
 | Euclid - 1781 - 552 páginas
...parallelogram BC. Therefore equal parallelograms, &c. Q^ED PROP. Book VI. PRO P. XV. THEO R. EQtJAL triangles which have one angle of the one equal to one angle of the other, have their fides .jabout the equal angles reciprocally proportional: And triangles which have one angle... | |
 | John Keill - 1782 - 476 páginas
...Angle of the clber, leave, tbrir Sides about the equal Angles reciprocal; and tbofe Triangles that have one Angle of the one equal to one Angle of the other, and have alfe the Sides about the equal Angles reciprocal, are equal. IET the equal Triangles ABC,... | |
 | Euclid - 1789 - 296 páginas
...equiangular with the triangle AGH (I. 7.) or ABC, as was to be (hewn. PROP. VI. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportional, the triangles will be equiangular. Let ABC, DEF... | |
 | Euclid, John Playfair - 1795 - 462 páginas
...equiangular to die triangle DEF. Wherefore, if the Cdes ; &c. OED PROP. VI. THEO R. IF two triangles have one angle of the one equal to one angle of the other, and the fides about the equal angles proportionals, the triangles fhall be equiangular, and ihall have... | |
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triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate consequence of this theorem. For let ABC and 
