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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
The school Euclid: comprising the first four books, by A.K. Isbister - Side 43
av Euclides - 1862
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The principles and practice of arithmetic and mensuration: with the use of ...

James Wharton - 1847
...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 definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...XXXVII. THEOREM. Triangles upon the same base anti between the same parallels, are equal to one another. PROP. XXXVIII. THEOREM. Triangles upon equal bases...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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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...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 first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 sider
...therefore the 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...
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Minutes of the Committee of Council on Education, with Appendices, Volum 2

Great Britain. Committee on Education - 1850
...• 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 - 1851 - 173 sider
...LEWIS 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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THE PRINCIPLES OF THE SOLUTION OF SENATE-HOUSE 'RIDERS'

FRANCIS J. JAMESON - 1851
...between the same parallels,* are equal to one another. Hence AECD - ABCE - ABEA = AAED. 1851. (A]. Triangles upon equal bases and between the same parallels are equal to one another, (i. 38.) (E). Let ABC, ABD be two equal triangles upon the same base AB, and on opposite sides of it...
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Papers for the schoolmaster, Volum 3

1867
...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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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Ralph Smyth, Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...proved that ABCD being a parallelogram, AB = CD and AD =BC. THEO. XII. All parallelograms on the same or equal bases and between the same parallels are equal to one another, that is if BD — GH, and the lines BH and AF are parallel, then the paralellogram ABD C = BDFE = EFGH....
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...triangle ABC is equal to the triangle DEC. Wherefore triangles, &c. QED OF EUCLID. 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 EC, EF, and between the same parallels BF, AD: The triangle...
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