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" Prove that parallelograms on the same base and between the same parallels are equal in area. "
Science Examination Papers - Page 243
by Great Britain. Education Department. Department of Science and Art - 1899
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The Popular Educator, Volumes 1-2; Volume 12

Geography - 1867 - 964 pages
...г, as we will proceed to show. The reader will remember that in Problem XXIV (page 308) it was shown that triangles on the same base and between the same parallels are equal to one another, and that triangles on equal bases and between the same parallels are also equal to...
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A Treatise of Practical Surveying: Which is Demonstrated from Its First ...

Robert Gibson - Surveying - 1806 - 452 pages
...of the bases the perpendicular was taken : since it has been shewn (in cor. to theo. 13, sect. 1.) that triangles on the same base, and between the same parallels are equal : but if you would draw a map from the bases and perpendiculars, it is evident that you must know at...
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A Treatise of Practical Surveying, ...

Robert Gibson - 1808 - 440 pages
...part of the base the perpendicular was taken : since it has been shewn (in cor. to theo. 13. seel. 1.) that triangles on the .same base, and between the same parallels are equal : but if you would draw a map from the bases and perpendiculars, it is evident that you must know at...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1814 - 564 pages
...which experience is equally incompetent to disprove or to confirm ? In like manner, when it is said, that " triangles on the same base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1821 - 604 pages
...part of the base the perpendicular was taken : since it has been shown (in cor. to theo. 13. geom.) that triangles on the same base, and between the same parallels, are equal ; but if you would draw a map from the bases and perpendiculars, it is evident that you must know at...
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Elements of the Philosophy of the Human Mind, Volume 2

Dugald Stewart - Psychology - 1821 - 350 pages
...doctrine, I shall only appeal to the thirty-seventh proposition of the first book, .' in which it is proved that triangles on the same base, and between the same parallels, are equal ; a theorem which appears, from a very simple construction, to be only a few steps removed from the...
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The Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829 - 442 pages
...which experience is equally incompetent to disprove or to confirm 1 In like manner, when it is said, that " triangles on the same base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...
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The Works of Dugald Stewart: Elements of the philosophy of the human mind

Dugald Stewart - 1829 - 418 pages
...which experience is equally incompetent to disprove or to confirm 1 In like manner, when it is said, that " triangles on the same base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if it should be supposed,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...triangle is half of a parallelogram on the same base and between the same parallels (41. 1.), and all triangles on the same base and between the same parallels are equal (37.1.); consequently ka b will denote the number of square feet in any plane triangle. Hence the surface...
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The Theory and Practice of Surveying: Containing All the Instructions ...

Robert Gibson - Surveying - 1832 - 290 pages
...part of the base the perpendicular was taken ; since it has been shown (in cor. to theo. 1 3 geom.) that triangles on the same base and between the same parallels are equal : but if you would draw a map from ' the bases and perpendiculars, it is evident that you must know...
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