Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 34
... ABCD , suppose AB equal and parallel to DC , then will the figure be a parallelogram . For , drawing BD , the two triangles ABD , CDB , have the common side BD , and AB of the first equal to CD of the second ; also , the included angles ...
... ABCD , suppose AB equal and parallel to DC , then will the figure be a parallelogram . For , drawing BD , the two triangles ABD , CDB , have the common side BD , and AB of the first equal to CD of the second ; also , the included angles ...
Page 36
... ABCD . Through F draw GH parallel to AD , and meeting DC produced . In the two triangles , FBH and FCG , we have the side FB = FC , the angle FBH equal to its alternate angle FCG , and the angle BFH equal its oppo- site angle CFG ...
... ABCD . Through F draw GH parallel to AD , and meeting DC produced . In the two triangles , FBH and FCG , we have the side FB = FC , the angle FBH equal to its alternate angle FCG , and the angle BFH equal its oppo- site angle CFG ...
Page 45
... ABCD . From the centre E draw EF and EG perpendicular to the chords AB and CD . Also through H , the middle point of the arc AC , draw the diameter HK . If we B D K revolve the portion of the figure on the left of SECOND BOOK . 45.
... ABCD . From the centre E draw EF and EG perpendicular to the chords AB and CD . Also through H , the middle point of the arc AC , draw the diameter HK . If we B D K revolve the portion of the figure on the left of SECOND BOOK . 45.
Page 71
... ABCD be the square , and AC its diagonal . Cutting off AF from the diagonal equal to AB , a side of the square , we have the remainder CF , which must be compared with CB . If we join FB , and draw FG perpendicu- lar to AC , the ...
... ABCD be the square , and AC its diagonal . Cutting off AF from the diagonal equal to AB , a side of the square , we have the remainder CF , which must be compared with CB . If we join FB , and draw FG perpendicu- lar to AC , the ...
Page 88
... ABCD be the A L B EL first parallelogram , and ABEF or ABE'F ' the second . Since these parallelograms have the same altitude , their superior bases will be situated in the same indefinite line LL ' , parallel to the lower base . If now ...
... ABCD be the A L B EL first parallelogram , and ABEF or ABE'F ' the second . Since these parallelograms have the same altitude , their superior bases will be situated in the same indefinite line LL ' , parallel to the lower base . If now ...
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume