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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. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 127
των John Playfair - 1837 - 318 σελίδες
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...mean proportional DB is found. Which was to be done. PROP. XIV. THEOR. Equal parallelograms, which have one angle of the one equal to one angle of the other, ham their sides about the equal angles reciprocally proportional : and parallelograms that have one...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...equiangular, and shall have those angles equal which are opposite to the homologous sides, PROP. VII. THEOR. If two triangles have one angle of the one...equal to one angle of the other, and the sides about two other angles proportional; then, if the remaining angles be each either less or not less than a...

The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 σελίδες
...the parallelogram BC. Therefore equal parallelograms, &c. QED PROP. XV. THEOR. 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 triangle* which have one angle...

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

Euclides - 1842
...parallelogram в c. Therefore equivalent parallelograms, &c. QED PROP. XV. THEOR. EQUIVALENT 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 the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...straight linos AB, BC, a mean proportional DB is found. PROP. XIV. PROB. • 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 : And parallelograms which have one...

General Report on Public Instruction in the Bengal Presidency

1843
...angle, and one of the other sides of a triangle are given ; construct it. 4. 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...

The British Annals of Education for ...: Being The Scholastic ..., Τόμος 1

1844
...this line makes 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...proportionals, the triangles shall be equiangular. MECHANICS AND HYDROSTATICS. MONDAY, JANUARY 15. 9.. .12. MR. HATHIBON, TRINITY COLLEGE. Pint Division...

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

Euclid, James Thomson - 1845 - 352 σελίδες
...to DFE, and A to D. Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two triangles have one angle...the sides about the equal angles proportionals; the remaining angles are equal, each to each, viz. those which are opposite to the homologous sides. Let...

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

Euclid - 1845 - 199 σελίδες
...ABC is 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...

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

Scottish school-book assoc - 1845
...halves of parallelograms, upon the same base, and having the same altitude, equal triangles, which have one angle of the one equal to one angle of the other, have the sides about these angles reciprocally proportional ; and if two triangles have one angle of...




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