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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 49
by Rev. John Allen - 1822 - 494 pages
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...on the other side of the base. QED Cor. — Hence it follows that if two isosceles triangles stand on the same base BC, and on the same side of it, the one triangle must be entirely within the other. For if not, let them stand as in the figure. Then...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 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 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 - 1876 - 446 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 - 130 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 - 452 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 - 228 pages
...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 - 146 pages
...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 - 282 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 - 94 pages
...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 - 152 pages
...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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