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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 ... - Page 47
by Euclid, Rev. John Allen - 1822 - 494 pages
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...two triangles of equal altitude, and on equal bases, are equal. Equal triangles upon the same base, and on the same side of it, are between the same parallels. If any two sides of any triangle are intersected by a line parallel to the third side, the intercepted...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...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—...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...lines shall be parallel to one another. 5. Equal triangles on equal hases, in the same straight line and on the same side of it, are between the same parallels. 6. If a straight line be divided into any two parts, the squares of the whole line and one of the parts...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...us from any . in a side of а Д to divide it into two eq. parts. 39. 120. Eq. Д8 on the same base and on the same side of it are between the same parallels. The loci of the vertices of eq. Дз on the same base, form a st.linc 40. 121. Eq. дз on eq. bases...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...same are equal to one another,' (ax 7.) PROP. XXXIX.— THEOREM. Equal triangles upon the same base and on the same side of it, are between the same parallels. (References — Prop. i. 31,37; ax. !._) Let the equal triangles ABC, DEC, be upon the same base BC,...
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Responsions

University of Oxford - Education, Higher - 1863
...greater than the base of the other. 8. Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. 9. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...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....
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865
...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....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be on the same base BC, and on the same side of it : they shall be between the same parallels. Join AD. A p AD shall be parallel to BC. For if it is not,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...join AE, BD intersecting at P ; shew that the angle APE 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...
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