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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 first six books of the Elements of Euclid, with numerous exercises - Σελίδα 126
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## The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 σελίδες
...parallels passes through the extremities of all the parallels. PROP VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the sides about another angle in each, proportionals ; and if the remaining angle in each be of...

## The Educational record, with the proceedings at large of the ..., Τόμοι 3-4

British and foreign school society - 1857 - 548 σελίδες
...are due to the eighteenth century? HIGHER MATHEMATICS AND MATHEMATICAL PHfSÏCg. 1. If two triangles have one angle of the one equal to one angle of the other atid the sides "aboiift two other angles proportional ; then if each of the remaining angles be less...

## The Quarterly Journal of Pure and Applied Mathematics, Τόμος 11

1871 - 420 σελίδες
...the proposition and reduces it to a case of ambiguous equality. Let the triangles ABC, DEF (fig. 9) have one angle of the one equal to one angle of the other; namely, L ВАС =¿ DEF, and the sides about two other angles ABC, EDF proportionals, so that AB :...

## The Calendar of King's College, London

1857 - 486 σελίδες
...and the angle in a segment less than a semicircle is greater than a right angle. 9. 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...

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

War office - 1858 - 578 σελίδες
...triangle having each of the angles at the base double of the third angle. 8 DIRECT COMMISSIONS. 2. Equal parallelograms which have one angle of the one...about the equal angles reciprocally proportional. Show also how this follows from the arithmetical method of representing a parallelogram. 3. Solve the...

## Parliamentary Papers, Τόμος 25

Great Britain. Parliament. House of Commons - 1858 - 694 σελίδες
...Triangles of the same altitude are one to the other as their bases. 6. 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...

## Parliamentary Papers, Τόμος 7

Great Britain. Parliament. House of Commons - 1859 - 140 σελίδες
...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...about the equal angles reciprocally proportional. 19. Investigate a trigonometrical expression for the area of a triangle in terms of two sides, and...

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

Sandhurst roy. military coll - 1859 - 672 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...

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

Civil service - 366 σελίδες
...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 - 380 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...