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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 ... - Strona 35
autor: John Playfair - 1855 - Liczba stron: 318
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...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
...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
...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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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....
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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...
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Papers Read at the Royal Institute of British Architects

1865
...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply...
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Loftus's inland revenue officer's manual

William Harris Johnston - 1865
...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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First Practical Lines of Geometrical Drawing ...

J F H. De Rheims - 1865
...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
...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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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...BC divides the parallelogram ACI>B into two equal parts. QED 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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