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

Euclides - 1874
...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 3. DE is parallel to BC. WTierefore, if a straight line, &c. QED PROPOSITION 3.—...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...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 1iE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...DEF. Therefore, triangles, &c. QED Proposition 39. — Theorem. Equal triangles upon the same base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and on the same side of it ; They shall...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 pages
...circle has double the perimeter of that inscribed in the same circle. 43. If any number of triangles on the same base BC and on the same side of it have their vertical angles equal, and perpendiculars meeting in D be drawn from BC on the opposite...
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Civil Service of India: Open Competition for the Regulations, Examinations ...

Civil service - 1878
...Rev. HW WATSON, MA Wednesday, 25th June 1879. 2 PM to. 5 PM 1. There are two triangles ABC and DEC on the same base BC and on the same side of it; AB and AC are each equal to one-half the sum of DB and DC, and DB cuts AC in E. Prove that BE is greater...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...the same base and on the same side of it are between the same parallels. Let the equal As ABC, DBC be on the same base BC, and on the same side of it. Then the As ABC, DBC shall be between the same ||s. Constr. Join AD ; AD shall be || BC. For, if it...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 266 pages
...triangles will be halves, and apply Prop. 34.) Proposition 37. Theorem.—Equal triangles on the same base and on the same side of it are between the same parallels. Let ABC, DBC be equal triangles on the same base BC; they will be between the same parallels. For if...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...equal to each other. Prove that it is a parallelogram. Section IV. 1. Equal triangles on the same base and on the same side of it are between the same parallels. The straight line which joins the middle points of the sides of a triangle is parallel to the base....
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880
...base and on the same side of it are between the same parallels. Particular Enunciation. Given. — The triangles ABC, DBC on the same base BC and on the same side (a) of it, equal to one another. . — v Required.— -To prove that they are between the same parallels....
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Report on Foreign Systems of Naval Education

James Russell Soley - Naval education - 1880 - 335 pages
...invariable. Under what conditions will this difference be zero ''. 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The sides AB and AC of a triangle are bisected in D and K respectively, and SE, CD are produced until...
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