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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: Also the Book of Euclid's Data ...cor. viz. The ... - Σελίδα 163
των Robert Simson - 1804
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...of the 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. Let AB,...

Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED 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...

General Report on Public Instruction in the Bengal Presidency

1843
...equal to one angle of 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 equal. 5. A common tangent is...

The British Annals of Education for ...: Being The Scholastic ..., Τόμοι 1-2

1844
...with the touching line, shall be equal to the angles in the alternate segments. 12. 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. MECHANICS AND...

A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...the first and second terms AABD, we have AABC : ADBE=AB'BC : DB-BE, (Alg. 116) Cor. Parallelograms which have one angle of the one equal to one angle of the other, are to one another in the ratio which is compounded of the ratios of the sides about the equal angles....

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...equiangular to the triangle DEF. Wherefore, if the 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 proportionals, the triangles shall be equiangular, and shall have...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 σελίδες
...triangles ABC, DEF are equiangular : wherefore, if the sides, &c. 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 remaining angles are equal, each to each, viz....

Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 σελίδες
...equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. THEOB. — If two triangles have one angle of the one equal to one angle of the oiher, and the sides about the equal angles proportionals, the triangles shall be equiangular, and...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equiangular, and shall have those angles equal about which the sides are proportionals. Let ABC, DEF be two triangles, which have one angle of the one equal to one angle of the other, viz. the angle BAC to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,...

Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...as K to L ; and therefore ex oequali, BD will be to CG, as I to L (by Prop. 33, B. 5). COR. 2. — Triangles which have one angle of the one equal to one angle of the other, are to each other in a ratio compounded of the ratios of the sides about the equal angles. COR. 3....




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