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" Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. "
Five Years in an English University - Σελίδα 348
των Charles Astor Bristed - 1852
Πλήρης προβολή - Σχετικά με αυτό το βιβλίο

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 σελίδες
...position, as GE, GF, then upon the same base and upon the same side of it there can be two A s which have their sides which are terminated in one extremity of the base equal, and their sides which are terminated in the other extremity of the base also equal : which is impossible....

The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...a different situation as EG, FG, then upon the same base EF, and on the same side of it, there can be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible ;...

Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...Hence it follows that an equiangular triangle is also equilateral. Proposition 13. — Theorem. On the same base, and on the same side of it, there cannot be two triangles having tlie sides terminated by one extremity of the base equal, and also the sides terminated by the...

The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...angles, &c. QED Cor. Hence an equiangular triangle is also equilateral. PROPOSITION 7. — Theorem. Upon the same base, and on the same side of it, there...terminated in one extremity of the base, equal to one another, and likewise those which are terminated iw the other extremity. C .0 A ~~ "' t. If it...

Pure mathematics, Τόμος 1

Edward Atkins - 1874
...* COROLLARY. — Hence every equiangular triangle is also equilateral. Proposition 7. — Theorem. Upon the same base, and on the same side of it, there...terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity. Let the triangles ACB,...

A Handbook of Applied Mechanics

Henry Evers - 1874 - 208 σελίδες
...geometric figure that cannot alter its form without altering the length of its sides. It is Euclid I., 7. " Upon the same base, and on the same side of it, there cannot be two triangles which have their two sides terminated in one extremity on the base equal, and likewise those terminated...

A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874
...aho bisects the angle A and OA, BO and CO are all equal to one another. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles which have their sides which are terminated in one extremity of the base, equal to one another, and...

Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...line. .. 28 3. From the greater of two given straight lines to cut off a part equal to the less. 28 7. Upon the same base and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to one another, and likewise those which are terminated...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 349 σελίδες
...AB-AC. QED NOTE 13. Euclid's Proof of I. 7. Upon (he same base and on Hie so/me tide of it, tJie.rc cannot be two triangles that have their sides which...are terminated in one extremity of the base equal to one another, and their sides which are terminated in the other extremity of the base equal also. If...

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

Robert Potts - 1876 - 403 σελίδες
...equilateral. PROPOSITION VIL THEOREM. Upon the same base, and on the saute side of it, there cannot bt two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the Other extremity. If it be possible, on...




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