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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
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

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

Harvey Goodwin (bp. of Carlisle.) - 1847 - 136 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...

The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 σελίδες
...mean proportional between two given straight lines. PROP. 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...

Papers for the Schoolmaster, Τόμος 1

1851 - 268 σελίδες
...similar to the whole triangle and to one another. PAPERS FOE THE SCHOOLHASTEB. 2. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. .3. Equiangular paralellograms...

A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 196 σελίδες
...shall have to the second a greater ratio than the fifth has to the sixth. 8. Equal triangles which have one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional ; and conversely. 9. If two planes...

The English Journal of Education, Τόμος 6

1852 - 512 σελίδες
...triangles on each side of it are similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular paralellograras...

The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Βιβλίο 1

Euclides - 1853 - 334 σελίδες
...hence AB is to BC as DE to EF, and BC to CA as EF to FD. . Which was to be proved. PEOP. VII. THEOE. If two triangles have (!•) one angle of the one equal to one angle of the other ; (2) the sides about one of the other two pairs of angles proportionals ; and if each of the third...

Public Education: As Affected by the Minutes of the Committee of Privy ...

Sir James Kay-Shuttleworth - 1853 - 522 σελίδες
...triangles on each side of it arc similar to the whole triangle and to one another. 2. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about their equal angles reciprocally proportional. 3. Equiangular parallelograms...

The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 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, etc. QED PROPOSITION VI. THEOR. If two triangles have one angle of the one equal to one...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 σελίδες
...wherefore also the remaining angle at b is equal to the remaining angle at e. Therefore the triangle ab С is equiangular 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 tJie...

The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 σελίδες
...and the angle BAC is equal to the angle EDF (a); 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. SCHOLIUM. This proposition corresponds with the fourth proposition of the first bookPROPOSITION VII....




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