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 Βιβλία Βιβλία 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 shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Σελίδα 161
των Euclid - 1810 - 518 σελίδες
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο ## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 σελίδες
...therefore, is equal to DFE. But BAG is equaj to EDF, and hence the remaining angle at в is equal to the remaining angle at E ; therefore the triangle ABC is equiangular to the triangle DEF. If, therefore, two triangles, &c. QED* PROPOSITION VII. THEOREM. If two triangles have one angle of... ## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 σελίδες
...therefore, is equal to DFE. But BAC is equal to EDF, and hence the remaining angle at в is equal to the remaining angle at E ; therefore the triangle ABC is equiangular to the triangle DEF. If, therefore, two triangles, &c. QED* PROPOSITION VII. THEOREM. If two triangles have one angle of... ## Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 266 σελίδες
...the other, have their sides about the equal angles reciprocally proportional ; and triangles which have one angle of the one equal to- one angle of the other, and their sides about the equal angles reciprocally proportional, are equivalent. Let the triangles be... ## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 σελίδες
...same reason, the angle ACB is equal to the angle DFE, and the angle at A equal to the angle at D : therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROP. VI. THEOR. If tix>o triangles have one angle of the one equal to one angle... ## Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 584 σελίδες
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . 66 (j) Two triangles are similar,... ## A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

...Ratios that are the same to the same ratio, are the same to one another. 13. 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. M. In a plane triangle, of which... ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 σελίδες
...the angle BAG is equal to the angle EDF (Hyp.); wherefore also the remaining angle at B is equal to the remaining angle at E. Therefore the triangle ABC...Wherefore, if two triangles, &c. QED PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 σελίδες
...triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED PROP. VII. THEOR. 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 the remaining angles... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 σελίδες
...the angle BAC is equal to the angle EDF (Hyp.) ; wherefore also the remaining angle at B is equal to the remaining angle at E. Therefore the triangle ABC is equiangular to the triangle DEF. 16 ' -k • PROP. VII. THEOR. If two triangles have one angle of the one equal to one angle of the... ## Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 σελίδες
...angles reciprocally proportional, are equal to one another; and, conversely, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional . .66 (g) Two triangles are similar,...