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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...diameter BC divides the parallelogram ACDB into two equal parts. QED PROP. XXXV. THEOREM. Parallelograms upon the same base and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF, be upon the same base BC, and between the same parallels AF, BC; the parallelogram...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 Seiten
...divides the parallelogram a С db into two equal parts. QED PROPOSITION XXXV. — THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. LET the parallelograms abСd, ebСf (see the second figure) be upon the same base b С, andbetween the same...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...BC divides the parallellogram ACDB into two equal parts. QED PROPOSITION XXXV. THEOR. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, KBCF be upon the same base BC, and between the same parallels AF; BC : the parallelogram...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 Seiten
...FG is equal to that ratio (170), and join DH. Then DHG is the triangle required. For BDC, BDF, being triangles upon the same base and between the same parallels, are equal to one another (41). Also A.ADE — &ADG; .'.adding to these equals the AABD, it is evident that ADGF = the polygon...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 Seiten
...same EBCH : Therefore also the parallelogram ABCQ i* *qual to EFGH. PROP. XXXVII. THEOR. Trim gles upon the same base, and between the same parallels,...between the same parallels, AD, BC : The triangle ABC is equal to the trian- E A. PF gle DBC. " ' ~ " ~ ~ Produce AD both ways to the points E, F, and through...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...only which are at the vertices of any two of its opposite angles. PROP. XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms AС, B Г be upon the same base B С, and and between the same parallels AF, BС. The...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...times as great ? The line joining the bisections of two sides of a triangle is parallel to the base. 3. Triangles upon the same base, and between the same parallels are equal to one another. The lines joining the bisections of the sides of any quadrilateral figure, together constitute a parallelogram....
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1855
...equal, each to each, namely, those to which the equal sides are opposite, 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. In any triangle, if the square of one of the sides is equal to the squares of the two other sides,...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...BCD; therefore, the diameter BC divides the parallelogram into two equal parts. XXXVII. Parallelograms upon the same base and between the same parallels are equal to one another. Let the parallelograms ABCD, EBCF (Fig. 29) be upon the same base BC, and between the same parallels AF, BC...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D and E respectively...
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