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" DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 22
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 σελίδες
...BDE is equal to the triangle. CDE ; (v. 9.) and they are on the same base DE ; but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 39.) therefore DE is parallel to BC. Wherefore, if a straight Kne, &c. QED PROP. m.— THEOREM....

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

Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...[V. 9. And these triangles are on the same base DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I. 39. therefore DE is parallel to BC. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM....

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

Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...[V. 9. And these triangles are on the same base DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I. 39. therefore DE is parallel to BC. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM....

Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 σελίδες
...triangle BDE is equal to the triangle CDE (V. 9); and they are on the same base DE. But equal triangles on the same base and on the same side of it are between the same parallels (L 39). Therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III.—...

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

Robert Potts - 1868 - 434 σελίδες
...triangle BDEis equal to the triangle CDE: (v. 9.) and they are on the same base DE: but equal triangles on the same base and on the same side of it, are between the same parallels ; (I. 39.) therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III THEOREM....

The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 320 σελίδες
...on the same side of that line are between the same parallels. Corollary 2. — Equal triangles upon the same base and on the same side of it are between the same parallels. Corollary 3. — Equal parallelograms upon the same base and upon the same side of it are between the...

Dublin examination papers

Dublin city, univ - 1871 - 366 σελίδες
...in every respect ? 2. Equal triangles, standing on equal bases, situated ?T? the same straight line, and on the same side of it, are between the same parallels ? 3. If a right line be divided, the sum of the squares of the \i hole line and of one segment is equal...

Euclid's Elements of Geometry

Euclid - 1872 - 284 σελίδες
...Prop. 34), and therefore are also equal (by Ax. 7). PROPOSITION XXXIX. THEOREM. Equal triangles (BAC and BDC) on the same base, and on the same side of it, are between the same parallels. For if AD be not parallel to BC, draw through the point A the right line AF parallel to BC, cutting the side...

Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 σελίδες
...the point of intersection of the diagonals, are equivalent. 3. Equivalent triangles or parallelograms on the same base and on the same side of it are between the same parallels. 4. If through any point in the diagonal of a parallelogram lines are drawn parallel to the sides, the...

Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873 - 182 σελίδες
...Prop. 36. Therefore the triangles are equal, by Ax. 1. Proposition 39. — Theorem. Equal triangles on the same base and on the same side of it are between the same parallels. If ABC = DBC, AD is parallel to BC. If not, let DE be parallel to BC, and let it cut AC, or AC produced,...




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