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" ... that triangles on the same base and between the same parallels are equal... "
A Treatise of Practical Surveying: Which is Demonstrated from Its First ... - Strona 207
autor: Robert Gibson - 1806 - Liczba stron: 452
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A Manual of Carpentry and Joinery

J. W. Riley - 1905 - Liczba stron: 500
...height area = base xr — c S— . 2i The shape of the triangle does not affect the result, as all triangles on the same base and between the same parallels are equal in area. The area of a triangle can also be determined by the following formula : \^s(s - a)(s - b)(x...
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - 1910 - Liczba stron: 302
...23 sq. cm. nearly; 3. 13-7 sq. cm. nearly; 4. 28'8 sq. cm.; 5. 36 ac. ; 6. 73 ac. nearly. THEOREM 5 Triangles on the same base and between the same parallels are equal in area. X BT Hypothesis.- — ABC, DEC are As on the same base BC and between the same ||s AD, BC....
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Modern Guns and Gunnery, 1910: A Practical Manual for Officers of the Horse ...

Henry Arthur Bethell - 1910 - Liczba stron: 443
...Fig. 144, or by reducing it to one triangle, as in Fig. 145, working on the principle that any two triangles on the same base and between the same parallels are equal. GUNNERY CALCULATIONS. KIG. 144. Circle. F'g- 145Let r be the radius ; then Circumference = 2*r Area,...
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Practical Geometry and Graphics for Advanced Students

Joseph Harrison, George Albert Baxandall - 1913 - Liczba stron: 677
...DK. Then DKG is a triangle having an area equal to the polygon. This solution is based on the theorem that triangles on the same base and between the same parallels are equal in area. 31. PROBLEM. — To construct a square equal in area to a given rectangle. Determine a mean...
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1920 - Liczba stron: 477
...line parallel to AD, meeting CD produced, at G. Join A G. The method depends upon Euclids' theorem that triangles on the same base and between the same parallels are equal to one another. By using a parallel ruler and a pricker the drawing in of all the constructional lines,...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - Liczba stron: 236
...geometry exhibited in the form of propositions are universal ie they have universal subjects. Ex. All triangles on the same base and between the same parallels are equal. All right angled triangles have this property that the square of the hypothenuse is equal to the squares...
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Riders in Geometry

Thomas Hadyn Ward Hill
...parallelograms on the same base and between the same parallels are equal in area. From this we have that triangles on the same base and between the same parallels are equal in area, and the converse; and also expressions for the areas of parallelograms, triangles, quadrilaterals...
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The Sanitary Record, Tom 19

1897
...; the method is mathematically accurate, and is based upon a familiar proposition of Euclid, viz., that triangles on the same base, and between the same parallels, are equal (vide Euc. I. 37). Suppose it is required to reduce the figure ABCDEF — which is supposed to be plotted...
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A Shorter Geometry

...opposite sides of a straight line AB; join DQ, CP: prove that CDQP is a parallelogram. 4. (a) Prove that triangles on the same base and between the same parallels are equal in area. (6) FGH is a triangle, K is the mid.point of GH, and P is any point on FK ; prove that the...
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Examination,Midsummer,1879

Education Department - 1879
...bisects it. If the diagonal also bisects the angles, show that the parallelogram is a rhombus. 2. Show that triangles on the same, base and between the same parallels are equal to each other. Hence show that a trapezium is equal in area to a triangle whose vertical height is...
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