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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. "
The First Six Books of the Elements of Euclid, with a Commentary and ... - Σελίδα 22
των Euclid, Dionysius Lardner - 1828 - 324 σελίδες
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 σελίδες
...triangle BDE is equal 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.—...

Pure mathematics, Τόμος 1

Edward Atkins - 1874 - 426 σελίδες
...the triangle DEF. Therefore, triangles, <fec. QED Proposition 89. — 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...

Pure mathematics, Τόμος 1

Edward Atkins - 1874 - 428 σελίδες
...the triangle DEF. Therefore, triangles, &c. QED Proposition 39.— Theorem. Equal triangles upon tlie 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...

Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 σελίδες
...triangle BDE is equal 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...

Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 σελίδες
...to the triangle 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...

Examination Christmas,1875

Education Department,London - 1876 - 1010 σελίδες
...point P within the triangle, such that the triangles РЛВ, PBC, PCA may be equal. 2. Equal triangles on the same base and on the same side of it are beUveen the same parallels. 3. The square on the sum of two lines is equal to the square on their difference...

Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 σελίδες
...of it. If CD meets AB in E, then CE, ED are also equal. PROPOSITION XXXIX. THEOREM. Equal triangles on 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...

The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 282 σελίδες
...which the 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...

Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 σελίδες
...right-angled triangle, is equidistant from the two sides containing the right angle. 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The angular points of one triangle lie on the sides of another ; if the latter triangle be thus divided...

First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 σελίδες
...Repeat. — The 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...




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