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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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## Parliamentary Papers, Τόμος 7

...ratio. 17. Inscribe, in a given circle, first, a regular hexagon ; secondly, a regular pentagon. 18. 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. 19. Investigate a trigonometrical expression...

## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 σελίδες
...is the income tax.? 10. Extract the square root of 6575-5881. Voluntary Portion. 2. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, each of the remaining angles being greater than...

## Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860
...Triangles of the same altitude are one to the other as their bases. fi. PROP. VI. — 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...

## A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service
...Triangles of the same altitude are one to the other, as their bases. PROP. VI. — 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...

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

Robert Potts - 1860 - 361 σελίδες
...to the triangle DEF. Wherefore, if two triangles. &c. QED PROPOSITION VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be eitlter...

## Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportionals, and if each of the remaining angles be not less...

## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 σελίδες
...isosceles triangle having each of the angles at the base one-third of the third angle. 2. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then if each of the remaining angles be either...

## Report on the examination for admission to the Royal military academy at ...

...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. 9. Prove...

## Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...2. & H. 6 22, V. 7 6, VI. 8 Sim. 9 Cone. 10 H. 11 22, V. 16, V. PROP. 7. — THEOR. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals ; then, if each of the remaining angles be either...

## The Messenger of Mathematics, Τόμος 4

1868
...Let the lines 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 triangles...