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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 synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...because the diameter DC bisects it. But the halves of equal things are equal (Ax. 7.) ; therefore 5. The triangle ABC is equal to the triangle DBC. Wherefore,...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...the half of 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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...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 - 1854 - 192 sider
...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
...that, if a figure had a thousand sides, he could reduce it, by degrees, to an equivalent triangle. PROP. XXXVIII. THEOREM. Triangles upon equal bases,...between the same parallels, are equal to one another. Let the triangles ABС, DEF, he upon equal bases B С, EF, and between the same parallels BF, 'A D....
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...of the 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,...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...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 Calendar of King's College, London

1857
...on the same base AB, but on opposite sides of it; join CD, cutting AB in E: then shall CE = ED. 10. Triangles upon equal bases, and between the same parallels, are equal to one another. 11. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...2. 1 Pst. 2. 2 P. 31. 3 Def. A. 1 C.3&H. 2 3 P. 35. P. 34. 4 5 Ax. 7. Recap. CTE PROP. 38.— THEOR. Triangles upon equal bases and between the same parallels, are equal to one another. CONSTRUCTION. — Pst. 2. A st. line may be produced indefinitely. P. 31. To draw a line through a...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volum 1

Euclides - 1868
...equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon equal bases and between the same parallels are equal to one anoti Coy. Pst. 2. P. 31. Def. A. DEM. P. 36. 34. Ax. 7. EXP. 1 Hyp. 1. ,, 2. 2 Concl. CON. 1 Pst....
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