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" The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. "
The Elements of Plane Geometry - Side 179
av Charles Austin Hobbs - 1899 - 240 sider
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Euclid, Rev. John Allen - 1822 - 494 sider
...and of CB to BL oy HE. Cor. 1.—By a similar reasoning it may be proved, that triangles, which have an angle of one, equal to an angle of the other, are to each other, in a ratio, compounded of the ratios, of the sides including the equal angles, Cor. 2.—A right line...
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The New Practical Builder and Workman's Companion, Containing a Full Display ...

Peter Nicholson - 1823 - 596 sider
...the two lines AD, DB, therefore AB2 = AC2 THEOREM 63. 161. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal Suppose* the two triangles joined, so as to have a common angle,...
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - 1848 - 324 sider
...(147) with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) angle of the other, are to each other as the products of the sides about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - 1856 - 216 sider
...two lines AD, DB, therefore AB'=AC*+BC9. THEOREM 54,. 125. Two triangles, which have an angle of the one equal to an angle of the other, are to each other as the rectangle of the sides about the equal angles. Suppose the two triangles joined, so as to have a common...
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Modern Methods in Elementary Geometry

E. M. Reynolds - 1868 - 112 sider
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC : A'BC'...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870
...have equal bases and equal altitudes are equal. G. Prove that two triangles which have an angle of the one equal to an angle of the other are to each other as the rectangles of the including sides. ENGLISH. I. Correct, criticize, and recast the following sentences:...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 sider
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22.) 220. Prove, geometrically, that the square described upon the sum of...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 sider
...THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. Let ABCD, AB'C'D', be the given tetraedrons, placed with...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 sider
...GEOMETRY.— BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22. ) 220. Prove, geometrically, that the square described upon the sum...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1872 - 368 sider
...PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. Let AB CD, AB'C'D', be the given tetraedrons, placed with...
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