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Books Books 31 - 40 of 59 on Solid parallelepipeds contained by parallelograms equiangular to one another, each....  
" Solid parallelepipeds contained by parallelograms equiangular to one another, each to each, that is, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The "
The Thirteen Books of Euclid's Elements - Page 347
by Euclid, Johan Ludvig Heiberg - 1908
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1876
...triplicate ratio of that which it has to the second. PROPOSITION D. THEOREM.—If solid parallelepipeds are contained by parallelograms equiangular to one another,...of which the solid angles are equal, each to each, they have to one another the ratio which is the same with the ratio compouaded of the ratios of their...
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SYLLABUS OF PLANE GEOMETRY

1876
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio...
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First B.A. examination: University of London. A hand-book to the study of ...

J. G - 1878
...including sides of the first to the including sides of the second. " 23." Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. We may observe that Prop. 7, which in ordinary editions of Euclid is...
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Elementary Geometry, Books 1-5

James Maurice Wilson - Geometry - 1878 - 261 pages
...antecedents to the rectangle contained by the consequents. THEOREM 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. Let ABC, DEF be two triangles, having the altitudes AG, DHrespectively;...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid ..., Books 1-6

Mathematical association - 1883
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio...
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The elements of plane geometry

Mathematical association - 1886
...and DC, the triangle ADE will be equal to the triangle BDC. THEOR. 15. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. Let ABC, HKL be two triangles, AD, HM their altitudes: then shall the...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching, Euclid - Euclid's Elements - 1888
...and DC, the triangle ADE will be equal to the triangle BDC. THEOR. 15. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. Let ABC, HKL be two triangles, AD, HM their altitudes : then shall the...
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A Key to the Exercises and Examples Contained in a Text-book of Euclid's ...

Henry Sinclair Hall, Frederick Haller Stevens - Geometry - 1892 - 211 pages
...ratio compounded of BC to FG and BM to FQ, for these par ms . are equiangular. .'. par ms . BD, FH have to one another the ratio compounded of the ratios of their bases and of their altitudes. But A ABC = half par" 1 . BD and AEFG = half par™. FH- Hence the same...
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THE WORKS OF ARCHIMEDES

T. L. HEATH - 1897
...cylinder passes through P. Proposition IO. It was proved by the earlier geometers that any two cones have to one another the ratio compounded of the ratios of their bases and of their heights*. The same method of proof will show that any segments of cones have to...
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The Works of Archimedes

Archimedes - Geometry - 1897 - 326 pages
...of their bases and of their heights*. The same method of proof will show that any segments of cones have to one another the ratio compounded of the ratios of their bases and of their heights. The proposition that any 'frustum' of a cylinder is triple of the conical...
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