| 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.—... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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.... | |
| 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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