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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, containing the first six books, with a selection of ... - Σελίδα 199
των Euclides - 1874
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## The British Annals of Education for ...: Being The Scholastic ..., Τόμοι 1-2

1844 - 688 σελίδες
...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 - 380 σελίδες
...Therefore the triangles ABC, DEF are equiangular : wherefore, if the sides, &c. PROP. VI. THEOR. — If two triangles have one angle of the one equal to...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 - 218 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...

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

Euclides - 1845 - 544 σελίδες
...AB, BC, a mean proportional -DB is found. QEF ^ PROPOSITION XIV. THEOREM. 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 conversely, parallelograms...

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

Scottish school-book assoc - 1845 - 434 σελίδες
...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...

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

Euclides - 1846 - 292 σελίδες
...parallelogram BC. Wherefore, Equal parallelograms *rc. 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 triangles, which have one angle...

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

Euclides - 1846 - 272 σελίδες
...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....

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

Euclid, John Playfair - 1846 - 332 σελίδες
...the parallelogram AB is equal (9. 5.) to the parallelogram BC. 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 triangles which have one angle...

## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ...

Dennis M'Curdy - 1846 - 168 σελίδες
...of two triangles, &c. QED Kecite (a) p. 23, 1; Wp.9,5; (4) 32, 1 ; (Op.8,1: p. 4, 6; ax. 1,1. 6 Th. If two triangles have one angle of the one equal to one of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,...

## A collection of problems and examples adapted to the 'Elementary course of ...

Harvey Goodwin (bp. of Carlisle.) - 1847 - 130 σελίδες
...than the sum of the two sides by the diameter of the inscribed circle. 23. If two triangles have an angle of the one equal to one angle of the other, and also another angle of the one equal to the supplement of another angle of the other, the sides about...