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" Parallelograms upon the same base and between the same parallels, are equal to one another. "
Geometry Without Axioms; Or the First Book of Euclid's Elements. With ... - Page 111
by Thomas Perronet Thompson - 1833 - 150 pages
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863 - 74 pages
...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 - Education, Higher - 1863 - 316 pages
...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 pages
...parallelogram ABCD is equal to the parallelogram EFGH. (ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon 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 pages
...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, Issue 1001; Issue 2288

1864 - 370 pages
...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 pages
...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 pages
...ABCD is equal to the parallelogram. EFGH. (ax. 1.) Therefore, parallelograms upon equal, &e. QE u. PROPOSITION XXXVII. THEOREM. Triangles upon 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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First Practical Lines of Geometrical Drawing ...

J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...Parallelograms 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...
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Elements of plane geometry, book i, containing nearly the same propositions ...

Euclides - 1865 - 80 pages
...the same thing are equal to one another; therefore the parallelograms ABCD and EBCF are equal. Cor. Triangles upon the same base and between the same parallels are equal to one another; for the triangle ABC is (40) half the parallelogram ABCD, and the triangle FCB is half the parallelogram...
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Loftus's Inland Revenue Officers' Manual ...

William Harris Johnston - 1865 - 478 pages
...respects oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms upon the same base and between the same parallels are equal to one another." Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique parallelogram...
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