Elements of Geometry and Trigonometry: With Applications in Mensuration |
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Page 83
... equivalent to . t THEOREM 1 . Parallelograms which have equal bases and equal altitudes , are equivalent . Place the base of one parallel- ogram on that of the other , so that AB shall be the common base of the two parallelograms ABCD ...
... equivalent to . t THEOREM 1 . Parallelograms which have equal bases and equal altitudes , are equivalent . Place the base of one parallel- ogram on that of the other , so that AB shall be the common base of the two parallelograms ABCD ...
Page 84
... equivalent . X THEOREM II . Triangles which have equal bases and equal altitudes , are equivalent . Place the base of one triangle F on that of the other , so that ABC and ABD shall be two trian- E gles , having a common base AB , and ...
... equivalent . X THEOREM II . Triangles which have equal bases and equal altitudes , are equivalent . Place the base of one triangle F on that of the other , so that ABC and ABD shall be two trian- E gles , having a common base AB , and ...
Page 85
... equivalent ( Th . i ) . But the triangle ABC is half the parallelogram BE ( Bk . I. Th . xxiii ) ; and ABD is half the equal parallelogram BF : hence , the triangle ABC is equivalent to the triangle ABD . THEOREM III . If a triangle and ...
... equivalent ( Th . i ) . But the triangle ABC is half the parallelogram BE ( Bk . I. Th . xxiii ) ; and ABD is half the equal parallelogram BF : hence , the triangle ABC is equivalent to the triangle ABD . THEOREM III . If a triangle and ...
Page 86
... equivalent . Let BD and FH be two rectangles , having the sides AB , BC , equal to the two sides EF , FG , each to each : then will the rectangle ABCD , described on the lines AB , BC , be equivalent to the rectangle EFGH , described on ...
... equivalent . Let BD and FH be two rectangles , having the sides AB , BC , equal to the two sides EF , FG , each to each : then will the rectangle ABCD , described on the lines AB , BC , be equivalent to the rectangle EFGH , described on ...
Page 87
... equivalent to each other since they have equal bases and equal altitudes ( Th . iv ) . But the rectangle AEFD will contain four of these partial rectangles , while the rectangle EBCF will contain three ; hence , the rectangle AEFD will ...
... equivalent to each other since they have equal bases and equal altitudes ( Th . iv ) . But the rectangle AEFD will contain four of these partial rectangles , while the rectangle EBCF will contain three ; hence , the rectangle AEFD will ...
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Common terms and phrases
adjacent angles allel altitude angles equal base multiplied bisect called centre chains chord circle whose diameter circular sector circumference column comp cone consequently convex surface Cosine Cotang cylinder decimal diagonal dicular distance divided draw drawn equal altitudes equal Bk equal to half equivalent figure find the area frustum greater half the arc half the product hence horizontal hypothenuse inches included angle inscribed intersection Let ABCD logarithm lower base measured by half Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane prism PROBLEM pyramid quadrilateral radii radius rectangle regular polygon Required the area rhombus right angled triangle right angles Bk segment side AC similar similar triangles Sine slant height sphere straight line subtract suppose Tang tangent THEOREM three sides triangle ABC upper base yards
Popular passages
Page 24 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 209 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 55 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line; it is required to divide it into two equal parts.
Page 11 - A circle (Fig. 38) is a figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within, called the center.
Page 60 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 25 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 130 - ... or cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a...
Page 124 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 133 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.