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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Σελίδα 35
των John Playfair - 1837 - 318 σελίδες
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...is equal to the triangle BCD ; (l. 4) 44 THE SCHOOL EUCLID. PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. i. 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be...

Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...2ioo r on Al a Y % a h + ± ft" _± ± ± 1 ± t -I f 1 [ / <' -T ' it 9 \ l)s 8 a Cl .PROP. 37. — THEOR. Triangles upon the same base and between the same parallels are equal to one another. consequently, half the product of the base ana altitude gives the area of a triangle. PROP. 38. —...

Responsions

University of Oxford - 1863
...equal to three given straight lines, any two of these being greater than the third. 5. Parallelograms upon the same base, and between the same parallels, are equal to one another. 6. To a given straight line apply a parallelogram which shall be equal to a given triangle, and have...

Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...parallelogram EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same...parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be...

Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864
...is fractional or negative, and find the coefficient of x* in the expansion of (1 +#•+ £2)~5. 9. Triangles upon the same base and between the same parallels are equal to one another. ABC is an isoceles triangle, vertex A ; D and E are the points of bisection of AB and AC respectively,...

The Owl, a Wednesday journal of politics and society

...z. III. Find the limits of a hyperbola when it is produced by an Irish member. IV. Similar figures upon the same base, and between the same parallels, are equal to one another. Apply this theorem to show the base similarity of certain persons who cut similar figures in Parliament....

The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...divides the parallelogram A CDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one anuther. ( Let the parallelograms AB CD, -E-BCFbeuponthe same base 2? C, . and between the same parallels...

First Practical Lines of Geometrical Drawing ...

J F H. De Rheims - 1865
...upon the same base and between the same parallels are equal to one another. Prop. 37. — Theorem. Triangles upon the same base and between the same parallels are equal to one another. Prop. 47. — Theorem. In any right angled trinngle, the square which is described upon the side subtending...

Key to the Irish commissioners' Treatise on mensuration

William Kennedy Maxwell - 1871 - 119 σελίδες
...ft. 13. Here, as 4-1 : 65 : : 5 : 79-26, the height of the pole. Ans. 14. Now, triangles that stand upon the same base, and between the same parallels are equal to each other ; therefore, this question will, as shown in the figure, admit of two answers. Here, the...

Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 σελίδες
...CJEFGH, i. 35. v they are on the same base EH and between the same IIs ; QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. Let A s ABC, DBC be on same base BC and between same IIs AD, BC. Then must &ABC= A DBC. From B draw BE...




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