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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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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1855 - 976 σελίδες
...; the segments of the base shall have the same ratio which the other sides of the triangle have. 2. If two triangles have one angle of the one equal to one angh of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular,...

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

British and foreign school society - 1857 - 548 σελίδες
...administrative improvements 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 - 412 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 :...

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

War office - 1858 - 578 σελίδες
...the angles at the base double of the third angle. 8 DIRECT COMMISSIONS. 2. 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. Show also how this follows from...

Parliamentary Papers, Τόμος 7

Great Britain. Parliament. House of Commons - 1859 - 140 σελίδες
...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...

The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 σελίδες
...and the angle BAC is equal to the angle EDF (g) ; wherefore also the remaining angle at B is equal to the remaining angle at E. Therefore the triangle ABC is equiangular to the triangle DEF. Hypoth. SCHOLIUM. This proposition corresponds with the fourth proposition of the first book. PROPOSITION...

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 σελίδες
...the angle BAC is equal to the angle EDE (Hyp.) ; wherefore also the remaining angle at B is equal to the remaining angle at E; therefore the triangle ABC is equiangular to the triangle DEF. PROPOSITION VTI. THEOBEM. IF two triangles have one angle of the one equal to one angle of the other,...

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

Robert Potts - 1860 - 380 σελίδες
...same reason, the angle ACB 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...

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

Woolwich roy. military acad - 1861 - 572 σελίδες
...described on P 0 as diameter will pass through all the points of contact. 8. 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 that have one...

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

Euclides - 1861 - 464 σελίδες
...into one Theorem, Prop. 1, VI, and might also be united here. PROP. 15. — THEOn. Equal angles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proD. 1 H. &C. 2 7. V. 3 1,V. 4 11, V. 5 Cone....




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