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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 Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - Mathematics - 1851 - 144 pages
...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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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...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 - 152 pages
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the parallelogram DBCF, because the diameter DC bisects it : PROPOSITION 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 synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...ABC is equal to the triangle DBC. Wherefore, triangles, &c. QED PROP. XXXVIII. — THEOREM. 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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...parallelogram eb С f Therefore parallelograms upon the same base, &c. QED PROPOSITION XXXVI. — THEOREM. Parallelograms upon equal bases, and between the same parallels, are equal to one anotJier. a de ЬЕТ abСd, efgh, be parallelograms upon equal bases bС, fg, and between the same...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 520 pages
...parallelograms as the unit is contained in AB, and BEFC into as many as the unit is contained in BE. Then since parallelograms upon equal bases and between the same parallels are equal to one another (41 Cor. 1), the smaller parallelograms which make up ABCD, and BEFC, are all equal. Therefore the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...upon the same base and on the same side of it, are between the same parallels. PROP. XXXVL THEOREM. Parallelograms upon equal bases and between the same parallels, are equal to one another. Let AC, EG be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...lines, make the alternate angles equal to each other, these two straight lines shall be parallel. 4. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. If a straight line be divided into any two parts, the rectangle contained by the whole and one of...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...parallelogram DBCF (Prop. 37) ; wherefore the triangle ABC is equal to the triangle DEC. XL. Triangles upon equal bases and between the same parallels are equal to one another. Let the triangles ABC, DEF (Fig. 32) be upon equal bases BC, EF, and between the same parallels BF, A D....
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