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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Σελίδα 182
των Euclid, Isaac Todhunter - 1883 - 400 σελίδες
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 σελίδες
...ABC is equiangular to the triangle DEF. Wherefore, if the sides, 2cc. QED Book VI. PROP. VI. THEOR. 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...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 σελίδες
...triangle D£F. 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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813 - 714 σελίδες
...a mean proportional between two given straight lines. Prop. XIV. Theor. Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proport ional : and parallelograms that have one...

An Easy Introduction to the Mathematics: In which the Theory and ..., Τόμος 2

Charles Butler - 1814 - 528 σελίδες
...a •••• b : ai=the square of the product, wherefore ^/afc=the product. 234. Prop. 23. Hence, if two triangles have one angle of the one equal to one angle of the other, they will have to each other the ratio compounded of the ratios of the sides about their equal angles;...

A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 352 σελίδες
...(Art. 97.) BA is equal to FE, and the angle ABC to EFG. PROP. XIX. (114.) Theorem. If two spherical triangles have one angle of the one equal to one angle of the other, and have also the two sides about another angle in each severally equal, and if the third angle, in each,...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 σελίδες
...parallelogram BO. Therefore equal parallelograms, gtc. QED, PROP. XV. TIIEOR. EQU AL 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....

An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 454 σελίδες
...two given circles, and also touch the chord on the same side as the less circle touches it. (XI 1 1.) If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,...

A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - 446 σελίδες
...figure FDHG, having its base DH in BC, and terminated by the given point D, is a rhombus. PROP. XI. 17. THEOREM. If two triangles have one angle of the one, equal to one angle of the other, and also another angle of the one, together with another angle of the other, equal to two right angles,...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1819 - 800 σελίδες
...shall be equiangular, and have their Cjuil angles opposite to the homologous sides. Prop. VI. Theor. If two triangles have one angle of the one equal to one angle of the other, arid 'be tides about the equal angles proportionals, the »angles shall be equiangular, and shall have...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 σελίδες
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. Q, ED PROP. VI. THEOR. If two triangles have one angle of the one equal to one angle of the oiker, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...




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