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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 26
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...equal^ZT " ABCD, EBCF, Ax. 7. .'. the /\K are equal to one another. Prop3 PROP. XXXV. THEOR. 36. 1 Eu. Parallelograms upon equal bases, and between the same...parallels, are equal to one another. Let ABCD, EFGH, be ZT" upon = bases BC, FG, and between the same ||s, AH, BG ; then r—r ABCD = Z=7 m EFGH. DE Ax '...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...triangle ABC is equal to the triangle DBC. Wherefore, Triangles %c. QED PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : the triangle...
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The principles and practice of arithmetic and mensuration: with the use of ...

James Wharton - 1847 - 222 pages
...parallelogram be 9 and 6, the area = 9 . 6 = 54. By Euclid, Book I., Props. 35 and 36., it is seen that parallelograms upon equal bases and between the same parallels are equal to one another, which is, that the areas of all parallelograms are equal to that of a rectangular parallelogram with...
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The First Book of Euclid's Elements, Simplified, Explained, and Illustrated ...

Euclides - 1847 - 128 pages
...and .'. i; with BC. (Prop. XXXIV.) Wherefore = D &c.— QED PROP. XXXVI. THEOR. GEN. ENUN. — Parallelograms upon equal bases, and between the same parallels, are equal to one another. ABCD, EFGH PART. ENUN. — Let upon equal bases BC, FG, and between the same || s AH, BG; then the...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848 - 388 pages
...and a segment of a circle, a sc alene triangle a rhomboid, and a trapezium. Section 2. 1. Prove that parallelograms upon equal bases and between the same parallels are equal to one another. 2. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...same base anti between the same parallels, are equal to one another. PROP. XXXVIII. THEOREM. Triangles upon equal bases and between the same parallels, are equal to one another. PROP. XXXIX. THEOREM. Equal triangles upon the same base and upon the same side of it, are between...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. QED PROP. XXXVni. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases BC, EF, and between the same parallels BF, AD : The triangle...
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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volume 2

Great Britain. Committee on Education - 1850 - 914 pages
...square, a circle, • multiple, similar rectilineal figures, and duplicate ratio. 2. Prove Euc. I. 36. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle...
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A Collection of Problems and Examples, Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...HENSLEY, MA, Trinity College. JOHN SYKES, MA, Pembroke College. TUESDAY. Dec. 31. 9. ..12. 1. TRIANGLES upon equal bases and between the same parallels are equal to one another. Let ABC, ABD be two equal triangles upon the same base AB and on opposite sides of it ; join CD meeting...
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Papers for the schoolmaster, Volume 3

1867 - 336 pages
...Determine the locus of the vertices of all equal triangles ou the same base and on the same lide of it. 3. Parallelograms upon equal bases, and between the same parallels, are equal to one another. Trisect a parallelogram by lines drawn from a givtu point in one of its sides. SECTION IV. 1. Eqnal...
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