 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 σελίδες
...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... | |
 | Euclides - 1874 - 342 σελίδες
...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 - 1876 - 446 σελίδες
...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 - 130 σελίδες
...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 - 452 σελίδες
...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... | |
 | 1878 - 228 σελίδες
...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 - 146 σελίδες
...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 - 1879 - 282 σελίδες
...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 - 94 σελίδες
...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 - 152 σελίδες
...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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Equal triangles on the same base, and on the same side of it, are between the same parallels. 
