## Elements of Geometry and Trigonometry |

### From inside the book

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**equivalent**. The term equal , when applied to figures , designates those which are equal in every respect , and which being applied to each other will coincide in all their parts ( Ax . 13. ) : the term equi- valent implies an equality ... Page 70

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**equivalent**to the parallelogram ABCD ( Prop . I. Cor . ) . Cor . 2. All triangles , which have equal bases and altitudes , are**equivalent**, being halves of**equivalent**parallelograms . PROPOSITION III . THEOREM . Two rectangles having ... Page 74

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**equivalent**FD to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , AB BE A is equal to the area of the ... Page 75

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**equivalent**to the parallelogram ADKL , and is measured by EFX AL . But we have AL = DK ; and since the triangles IBL and KCI are equal , the side BL = CK : hence , AB + CD = AL + DK = 2AL ; hence AL is the half sum of the bases AB , CD ... Page 76

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**equivalent**to the sum of the squares described on the parts , together with twice the rectangle contained by the parts . • Let AC be the line , and B the point of division ; then , is AC2 or ( AB + BC ) 2 = AB2 + BC2 + 2AB × BC ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex