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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 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
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 σελίδες
...the quadrilateral, in which case it is equal to that sum. " 23." If two triangles or parallelograms have one angle of the one equal to one angle of the other, their areas have to one another the ratio compounded of the ratios of the including sides of the first...

First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879 - 414 σελίδες
...other part. 11. Inscribe an equilateral and equiangular hexagon in a given circle. 12. If two equal triangles have one angle of the one equal to one angle of the other, they have the sides about their equal angles reciprocally proportional ; and if the sides of two triangles...

The Madras University Calendar, Τόμος 1

University of Madras - 1879 - 674 σελίδες
...IV. In a given circle inscribe an equilateral and equiangular quindecagon. V. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional ; and triangles which have one angle...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879 - 376 σελίδες
...proportion being DR is to BE as GB is to BF. PROPOSITION XIV. THEOREM. Eq'ual parallelograms, which have one angle of the one equal to one angle of the ntlur, have thtir sides about the equal angles reciprocally proportional. \ \ \ Let AB, BC be equal...

Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 396 σελίδες
...other, have their sides about the equal angles reciprocally proportional ; and parallelograms which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. 11. On a given...

Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 σελίδες
...the segments BG, GD, GC of the base shall be in harmonical proportion. 12. 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. ALGEBRA. 1. Prove that se и х...

The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 σελίδες
...same reason, the angle ACB is equal to the angle DFE, and the angle at A is equal to the angle at D. Therefore the triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides &c. QED PBOPOSITION C. THEOREM. If two triangles have one angle of the one equal to one angle...

The Cambridge Examiner, Τόμος 3

1883 - 536 σελίδες
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle...

Elements of Geometry

Simon Newcomb - 1881 - 418 σελίδες
...the other two angles each equal to its supplement. I "i 1 . Corollary 2. If two parallelograms Itave one angle of the one equal to one angle of the other, all the remaining angles of the one will be equal to the corresponding angles of the other. 125. Corollary...

University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - 1882 - 152 σελίδες
...circle. 10. To describe a circle about a given square. 11. Define equal triangles, and prove that ifequal triangles have one angle of the one equal to one angle of the other, then the sides about the equal angles are reciprocally proportional. 12. Show that the linos which...




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