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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Inventional Geometry: A Series of Problems, Intended to Familiarize the ... - Página 43
por William George Spencer - 1877 - 97 páginas
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 páginas
...Wherefore parallelograms, &c. QED 31. 1. 4 Def. 34. ] t 35. 1. 34. 1. TAx: PROPOSITION XXXVII. THEOR. — Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC : the triangle...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...parallelogram EFGH. (ax. 1.) Therefore parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC. Then the...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 páginas
...parallelogram AC is equal (I. ax. 1) to EG. Wherefore parallelograms, &c. PROP. XXXVII. TnEOR.t — Triangles upon the same base, and between the same parallels, are equal to one another. * lt will appear, from this proposition, that the perimeters of two equal parallelograms on the same...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 páginas
...and joined towards the same parts by the straight lines BE, CH : But __ H B F G PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels, AD, BC : The triangle...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...also the parallelogram ABCD is equal to EFGH. 'Wherefore, Parallelograms %c. QED PROP. XXXVII. THEOR. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC : the triangle...
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A course of practical geometry for mechanics

W. PEASE - 1846
...form the isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...•=• parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 3s. lEu. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXIV. FADE F \ . If the sides AD, DF, of the 1=1™ ABCD, DBCF, opp. to BC the base, be terminated...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - 1846
...two = parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 35. lEu. Parallelograms upon the same base, and be-tween the same parallels, are equal to one another. FA DEFAEDF \ . If the sides AD, DF, of the / — 7"" ABCD, DBCF, opp. to RC the base, be terminated...
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The London University Calendar

London univ - 1846
...exterior angles of any rectilineal figure are together equal to four right angles. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Show that the complements of the parallelograms which are about the diameter of any .parallelogram...
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The First Book of Euclid's Elements, Simplified, Explained, and Illustrated ...

Euclides - 1847
...KLNC (Ax.2) = Dm BMNC. Wherefore the sum of the areas &c. — QED PEOP. XXXVII. THEOR. GEN. ENUN. — Triangles upon the same base, and between the same parallels, are equal to one another. PART. ENUN. — Let the A ABC, DBC be upon the same base BC, and between the same || s AD, BC ; then...
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