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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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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 Seiten
...less than — — . MATHEMATICS. REV. CANON HEAVISIDE, MA Voluntary Paper, No. II. 1. Parallelograms upon the same base and between the same parallels are equal to one another. 2. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 Seiten
...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...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 Seiten
...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. —...
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Responsions

University of Oxford - 1863 - 328 Seiten
...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...
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 Seiten
...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...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 Seiten
...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,...
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The Owl, a Wednesday journal of politics and society, Ausgabe 1001;Ausgabe 2288

1864 - 368 Seiten
...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....
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 Seiten
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 Seiten
...parallelogram. EFGH. (ax. 1.) Therefore, parallelograms upon equal, &e. QE u. PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same...parallels, are equal to one another. Let the triangles ABC, DBC\lQ upon the same base BC, and between the same parallels AD, BC. Then the triangle ABC shall be...
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Key to the Irish commissioners' Treatise on mensuration

William Kennedy Maxwell - 1871 - 148 Seiten
...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...
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