 | 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... | |
 | 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... | |
 | Euclides - 1879 - 146 pages
...triangles, &c. QED PROPOSITION XL. THEOREM. Equal triangles, on equal bases in the same straight line, and on the same side of it, are between the same parallels. Let the = As ABC, DEF be on == bases EC, EF, in the same straight line BF, and on the same side of... | |
 | 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.... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...triangles &c. QED PROPOSITION 40. THEOREM. Equal triangles, on equalbases,in the same straight line, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DEF be on equal bases BC, EF, in the same straight line BF, and on the... | |
 | T S. Taylor - 1880 - 152 pages
...enunciations of Euc. I. 31, I. 37, and Axiom r. 3 General Enunciation. Equal triangles on the same 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... | |
 | Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...Wherefore, Triangles on equal bases, 'Ssc. QED PROP. XXXIX. THEOREM. Equal triangles on the same base, and on the same side of it are between the same parallels. Let ABC and DBC be equal triangles, on the same base BC and on the same (viz. the upper) side of it.... | |
 | James Russell Soley - Naval education - 1880 - 346 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... | |
 | Education, Higher - 1883 - 536 pages
...rectilineal figure said to be inscribed in another rectilineal figure ? 9. Equal triangles on the same base, and on the same side of it are between the same parallels. 10. Describe a square that shall be equal to a given rectilineal figure. 12. One circle cannot touch... | |
 | John Gibson - 1881 - 64 pages
...Triangles on the same base and between the same parallels are equal. 4. Equal triangles on the same base and on the same side of it are between the same parallels. 5. Prove that the diagonals of a parallelogram bisect each other. 6. Bisect a given triangle by a straight... | |
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DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. 
