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" PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... "
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... - Page 36
by Euclid, James Thomson - 1837 - 390 pages
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...— ax — bx (a — b)(x — a) (b — a)(x—b] Solve the equation x + y = 9^ a? + 2y* = 66 J 7. Parallelograms upon the same base and between the same parallels are equal to one another. 8. The angles in the same segment of a circle are equal to one another. 9. Inscribe an equilateral...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...the triangle ABC 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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Responsions

University of Oxford - Education, Higher - 1863
...length from a given point without it. 5. Describe a square equal to a given rectilineal figure. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Divide a straight line into two parts, so that the rectangle contained by the whole and one part...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...tiJ the next two divisions coincide, it will have moved 2-100th of an inch, &e. PEOP. 35.— THEOK. Parallelograms upon the same base and between the same parallels are equal, or rather equivalent to one another. DEK:-P. 84, Ax. 6, Ax. 1, Ax. 3, P. 29, P. 2*. ADE CASE L Sup....
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...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...
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The Owl, a Wednesday journal of politics and society, Issue 1001; Issue 2288

1864
...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
...the diameter BC 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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First book of mathematics

Hugo Reid - Mathematics - 1872 - 124 pages
...produced. 142. If ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base and between the same parallels are equal to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels...
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The Philosophy of Science: A Contribution Thereto, on Cause and Effect

Thomas Squire Barrett - Causation - 1872 - 213 pages
...former kind ' are truths which cannot but be ' true ; as that 1 9 and 1 1 are 30 ; — NOTE XIX. that parallelograms upon the same base and between the same parallels are equal ; — that all the angles in the same segment of a circle are equal. The latter are truths which it...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872
...a parallelogram is divided into two equal parts by either of its diagonals. (Prop. XXXIV.) 2. That parallelograms upon the same base and between the same parallels are equal. (Prop. XXXV.) 3. That the halves of equals are equal. (Ax. VIII.) Let ABC and ABD be two As upon the...
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