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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Σελίδα 47
των Euclid, Rev. John Allen - 1822 - 494 σελίδες
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 σελίδες
...join AE, BD intersecting at P; shew that the angle APJB is constant. 520. If any number of triangles on the same base BC, and on the same side of it have their vertical angles equal, and perpendiculars, intersecting at D, be drawn from B and C on the...

Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey

Euclid, F. B. Harvey - 1880 - 119 σελίδες
...Wherefore, Triangles on equal bases, 'Ssc. QED PROP. XXXIX. THEOREM. Equal triangles on the same base, and on the same side of it are between the same parallels. Let ABC and DBC be equal triangles, on the same base BC and on the same (viz. the upper) side of it....

Papers for teachers

1880
...(1) Euclid, i, page 214. Let ABC be an isosceles triangle, and let DBC be any other equal triangle on the same base BC, and on the same side of it. Join AD (draw figure so that D is to the right of A). From B draw BE perpendicular to AD produced ;...

The preliminary army examination made easy, a guide to self-preparation

John Gibson - 1881
...Triangles on the same base and between the same parallels are equal. 4. Equal triangles on the same base and on the same side of it are between the same parallels. 5. Prove that the diagonals of a parallelogram bisect each other. 6. Bisect a given triangle by a straight...

The Cambridge Examiner

...rectilineal figure said to be inscribed in another rectilineal figure ? 9. Equal triangles on the same base, and on the same side of it are between the same parallels. 10. Describe a square that shall be equal to a given rectilineal figure. 12. One circle cannot touch...

Class lessons on Euclid

Marianne Nops - 1882
...same base and on the same side of it a re between the same parallels. Let the equal As ABC, DBC be on the same base BC and on the same side of it. They shall be between the same parallels. AD shall be || to CD. If not, through A draw AE || to BC,...

The papers set at the professional preliminary examination

College of preceptors - 1882
...proposition in the course of the proof of which reference is made to it. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. Prove that diameters (produced, if necessary) of any pair of parallelograms about the diameter of a...

Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1882
...two sides of the quadrilateral are parallel to each other. (10.) 10. Equal triangles on the same base and on the same side of it are between the same parallels. If a quadrilateral is divided into four equal triangles by its diagonals show that it is a parallelogram....

Annual Report

1886
...two sides of a triangle are together greater than the third side. 4. Equal triangles on the same base and on the same side of it, are between the same parallels. 5. If a straight line be divided into two equal, and also into two unequal parts, the squares on the...

The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 σελίδες
...join AE, BD intersecting at P; shew that the angle APB is constant. 520. If any number of triangles on the same base BC, and on the same side of it have their vertical angles equal, and perpendiculars, intersecting at D, be drawn from B and C7on the...




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