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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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C'... "
A Supplement to the Elements of Euclid - Σελίδα 558
των Daniel Cresswell - 1825 - 582 σελίδες
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

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...which any other chord has to the aggregate of the two chords that are next to it. PROP. VI. (XVII.) If two trapeziums have an angle of the one equal to...shall be equal to the remaining angles of the other. PROP. VIII. (xvin.) To divide a given finite straight line into two parts, such, that another given...

Elements of Geometry

Adrien Marie Legendre - 1819 - 208 σελίδες
...general properties of triangles involve those of all figures, THEOREM. 208. Two triangles, whkh Iiave an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Fig. 122. Demonstration. Let the angle A =...

The new practical builder, and workman's companion, Τόμος 2

Peter Nicholson - 1823
...equal to the sum of 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,...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 σελίδες
...the general properties of triangles involve those of all figures. THEOREM. 208. Two triangles, which have an angle of the one equal to an angle of the other and the sides about these angles proportional, are similar. Demonstration. Let the angle A = D (Jig. 122),...

Elements of Geometry

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...: FH : : CD : HI ; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, have an angle of the one equal to an angle of the other and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre - 1825 - 224 σελίδες
...AC : FH : : CD : HI; but we have seen that the angle ACD = FHI; consequently the triangles ACD, FHI, have an angle of the one equal to an angle of the other and the sides about the equal angles proportional ; they are therefore similar (208). We might proceed...

Elements of Geometry

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...the sides FG, GH, so that AB:FG::BC: GH. It follows from this, that the triangles ABC, FGH, having an angle of the one equal to an angle of the other and the sides about the equal angles proportional, are similar (208), consequently the angle BCA = GHF....

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...equal." Here we have a criterion whereby to judge of the equality of two triangular surfaces, which have an angle of the one equal to an angle of the other. For example : ABCD is a road cutting off a triangular field AOB. It is desirable that the line of road...

Dialogues on the First Principles of the Newtonian System, Τόμος 4

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...F, are equal; and so, if 'the angles at F had been supposed equal, the triangles would have had each angle of the one equal to an angle of the other, and the side CF lying between correspondent angles in each; whence also DF is equal to FE. Is this sufficiently...

Elements of Geometry: With Practical Applications, for the Use of Schools

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...vertices by the space of a quadrant, the sides will become parallel each to each. 3. — When they have an angle of the one equal to an angle of the other, and the sides including these angles proportional. Thus if the angle A = A (fig. 45), and if AB : AD :...




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