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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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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 σελίδες
...angle EDF (H,,p.') Therefore the remaining angle at B is equal to the remaining angle at E (I. 32); and the triangle ABC is equiangular to the triangle DEF. Wherefore, if two triangles, &c. QED (V. 11); and ED is equal to DG (V. 9). PEOP. VII. (THEonEM.)—If two triangles (ABC and DEF) have...

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 σελίδες
...same reason, the angle A CB 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 PROPOSITION VI. THEOREM. If two triangles have one angle of the one equal to one...

The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 σελίδες
...equiangular, and shall have those angles equal which are opposite to the homologous sides. Prop. 7. If two triangles have one angle of the one equal to one angle of tha other, and the sides about two other angles proportionals ; then, if each of the remaining angles...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 σελίδες
...same reason, the angle A CB 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 PROPOSITION VL THEOREM. If two triangles hare one angle of the one equal to one...

A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - 1866 - 428 σελίδες
...the other have their sides about the equal angles reciprocally proportional: and parallelograms that 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. CO-ORDINATE...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 424 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 PROPOSITION C. THEOREM. If two triangles have one angle of the one equal to one angle...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Isaac Todhunter - 1867 - 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 PROPOSITION a. THEOREM. If two triangles have one angle of the one equal to one angle...

The Edinburgh university calendar

Edinburgh univ - 1868 - 336 σελίδες
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of...

The Oxford, Cambridge, and Dublin Messenger of Mathematics, Τόμος 4

1868 - 272 σελίδες
...joining the point P to the points A and B cut a line in the points a, /3. The areas of 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 the sides. Applying this to the...

Modern Methods in Elementary Geometry

E. M. Reynolds - 1868 - 172 σελίδες
...; Therefore ABC is equiangular to A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC'...




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